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Incorporation of fractional-order dynamics into an existing PI/PID DC motor control loop
Abstract
The problem of changing the dynamics of an existing DC motor control system without the need of making internal changes is considered in the paper. In particular, this paper presents a method for incorporating fractional-order dynamics in an existing DC motor control system with internal PI or PID controller, through the addition of an external controller into the system and by tapping its original input and output signals. Experimental results based on the control of a real test plant from MATLAB/Simulink environment are presented, indicating the validity of the proposed approach.
... To this day, many researchers have tried to introduce controllers that operate on the same principles as a classical PID controller. For example, in recent years, one can point to different types of PID-like controllers such as adaptive PID speed control design [10], fuzzy PID speed controller [11], fractional control enhanced PID control [12] and robust output feedback control [13]. Although these methods are developed to increase the performance of classical PID controllers, they simply use the PID control scheme as a framework and introduce quite a decent amount of complexity to the control system. ...
... (∞) → 0.(31)Eq.(12) and (31) reveal that and are bounded, thus, Eq. (31) can be used to prove the stability of the Control System. ...
Time Delay Control (TDC) is recognized as a simple yet effective alternative to model-based or intelligent-based control due to its simplicity and robustness. Proportional-Integral-Derivative (PID) control is one of the industry’s most used and straightforward control schemes. While this approach has proven to be effective, the tuning of its coefficients has remained a difficult task. Though showing similar performance, a definite connection between the two approaches has yet to be defined. In this paper, by taking advantage of padé approximation, a direct connection between the two control methods coefficients is obtained. As a result, a new approach for choosing the classical PID controller coefficients is introduced using TDC as the primary control scheme design framework, which has led to a decrease in the number of required control design coefficients of the PID control system. Further on, the uniformly ultimately bounded stability of the control system under bounded external disturbances is proven. Finally, via simulations on the SCARA robot, the obtained results and the validity of the proposed connection are explored.
... With changing speed characteristics and excellent efficiency, a fault-tolerant fuzzy controller can increase the beginning torque of an electric vehicle [15]. Fractional-order PID controllers, which introduce two more degrees of freedom, were created as a result of the non-integer order of the integrator and differentiator stages and the development of fractional calculus [16][17][18]. The noninteger order controller offers higher servo, regulatory, and resilience versus its integer-order equivalents. ...
... Fractional-order calculus has also developed into a promising topic because it can explain physical systems in more depth than the usually used integer order [17][18][19][20][21]. Since the fractional-order PID (FOPID) controller has one fractional-order derivative and one fractional-order integration, it is being studied for the control system. ...
... This results in better robustness, improved system performance, and design flexibility [3], [4]. The fractional-order controller provides attractive solutions in various control applications; it is well-suited for controlling dynamic systems [5] such as controlling the speed and position in motor drives [4], [6], satellite attitude system [7], robotic manipulators [8], twin-rotor aerodynamic system (TRAS) [9], and electrohydraulic servo system [10]. ...
... The experimental evaluation of the proposed controllers was performed by employing the Anadigm AN231E04 FPAA development board and the Anadigm Designer 2 VOLUME 4, 2016 5 This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and 0.2247 0.7186 5.74% ...
Complex-order controllers are a generalized version of conventional integer-order controllers and are known to offer greater flexibility, better robustness, and improved system performance. This paper discusses the design of complex-order PI/PID controllers to control the speed of an induction motor drive and an electric vehicle. The speed-tracking performance of the complex-order controllers is compared with fractional-order controllers and conventional integer-order controllers. Implementing complex-order controllers is challenging due to commercial complex-order fractance element unavailability. Hence, it is carried out by approximating the complex-order controller transfer function using an integer-order rational function with a curve-fitting approach, namely the Sanathanan Koener (SK) iterative method. This method is quite simple and can fit the required frequency range compared to the conventional Matsuda and Oustaloup approaches. The approximated controller transfer function can easily be realized by employing the AN231E04 Field Programmable Analog Array (FPAA). Simulation and experimental results highlight that the controller behaviour is in good agreement with the theoretical expectations.
... Therefore, it can be assumed that with some of the methods described in [18], the incorporation of PID controllers into the manufacturing process will be easier in the near future. An existing PID system for a DC motor was converted to a FOPID system by adding an additional loop [19], which was then tested. This allowed fractional dynamics to be introduced into the existing system without requiring any internal modifications to the original system. ...
... FOPID controllers have clear advantages over IOPID controllers, as shown in both simulations and experiments with real objects [15][16][17]; the comparison is strongly based on the global optimization setting for both types of controllers. An important benefit of FOPID controllers when applied to industrial problems is the potential reduction in control effort, which also leads to a reduction in energy waste [19]. ...
... The another contribution in this paper is involved in apply-211 ing the fractional TID and ID-T controllers. FO controllers 212 such as TID and ID-T have proliferated due to their flexi-213 bility in designing and stability, particularly with dynamical 214 systems [28]. They include extra tuning parameters compared 215 with conventional PID controller, which reduces processing 216 in optimum parameters demonstration [29]. ...
... 25: IF X PcC fitness is better than X PcC (t) fitness, 26: X PcC (t + 1) = X PcC . 27: END IF. 28: END FOR. 29: Evaluate X Pc2 , X Pc3 , X Pc4 , and X Pc5 from Eqs. 41 -44 30: FOR i := 2 to 5, 31: inspect and correct X Pci to be within a correct range. ...
This paper comprises two studies; the first one provides an advanced and low-cost implementation for a remote astronomical platform applicable for small and medium-sized telescopes. It has been carried out for the 14-inch observatory, which includes a Celestron German Equatorial (CGE) telescope at the Kottamia astronomical observatory (KAO) in Egypt. This integrated control system is based on embedded systems, internet of things (IoT) technology, row packets communication procedure, and the Transmission Control Protocol (TCP) based on the Internet Protocol (IP). Using this platform, remote astronomers could control the whole system, observe, receive images and view them efficiently and safely without any human physical intervention. The proposed design has been achieved without dependence on commercial control kits or software. Indeed, many previous studies have focused on this field; however, their area of interest was limited or non-affordable. The excellence in this practical research is revealed and compared with others in terms of cost, inclusiveness, and communication speed. The other contribution of this research is to enhance the performance of the telescope pointing and tracking to be adapted with remote action. It has been achieved based on the mathematical model of the telescope where two fractional controllers have been applied, tilt integral-derivative (TID) and integral derivative-tilted (ID-T) controllers. After that, they have been optimized using a recent optimization algorithm called peafowl optimization algorithm (POA) and compared with one of the well-known algorithms; particle swarm optimization (PSO). Simulation results under the MATLAB/SIMULINK environment reveal that modified ID-T-based POA has minimized the pointing error sharply. Moreover, compared with previous studies, it has significantly improved the telescope system characteristics represented in the times of overshoot, settling, and rising.
... Ziegler and Nichols gave the well-known Ziegler-Nichols tuning method in 1942-1943 [10,11]. Father Cohen and Coon gave the alternative for tuning in the 1950s which was accepted by certain types of plants [12]. ...
The paper presents a comprehensive analysis of three advanced control strategies:
Proportional-Integral-Derivative (PID) controllers, Fuzzy Logic Controllers (FLC), and
Sliding Mode Controllers (SMC) to achieve accurate speed control of a DC motor. The
proposed study is conducted both theoretically and practically, utilizing MATLAB and
AVR microcontrollers for real-time experiments. A modified SMC control law is
introduced to enhance system performance, reduce the inherent chattering effect, and
maintain robustness against parameter variations. The performance of each control
strategy is evaluated based on key specifications, including system stability, response time,
and adaptability to external disturbances. The findings highlight the strengths and
limitations of each control approach and provide valuable insights for selecting the most
suitable controller for specific applications. Additionally, the paper explores the
integration of artificial intelligence techniques to optimize controller performance in
dynamic and uncertain environments, contributing to the advancement of intelligent
control systems.
... Lack of robustness against uncertainties, poor disturbance rejection PID controller with an ACO [20] Improved speed and angular position control of motors Lack of robustness against uncertainties, poor disturbance rejection PID controller with a hybrid algorithm PSO-BF [21] Improved speed and angular position control of motors Poor disturbance rejection FOPID controllers [22][23][24][25][26][27][28][29][30] Improved speed and angular position control of motors, excellent performance against changes in engine-related parameters ...
Servo controllers are essential components in robotics, manufacturing, and various industrial applications. However, achieving fast and accurate reference tracking in servo systems remains challenging due to modelling uncertainties and external disturbances. In this paper, a hybrid control strategy is proposed that combines a Linear Quadratic Regulator (LQR) state‐feedback controller with deep learning to address these challenges. The LQR controller utilises system state measurements to optimise the control input, while the integration of a deep neural network enhances accuracy and dynamic response by adapting to changing system conditions. This approach provides robust control performance, effectively mitigating the impact of uncertainties and disturbances on servo system behaviour. The proposed method was validated using AC servo motors, among the most common servo systems, though the approach is adaptable to other servo‐like systems. Comparative evaluations are conducted against existing methods, including SIMC‐SMC, 2DOF‐IMC‐SMC, 2DOF‐IMC‐PID, and SIMC‐PD controllers, focusing on the angular position control of a servo motor. Simulation results demonstrate that the proposed controller outperforms these methods in terms of robustness, precision, and disturbance rejection. These findings highlight the potential of the proposed LQR‐deep learning framework to significantly improve servo system performance across a wide range of applications.
... By changing different K p and K d can get different function images. It is possible to obtain a much better result by studying each particular control problem in detail and applying it [6]. Compared with images 2-4, only K p is changed, and it is found that the response speed of the system and the change of the wave are both improved. ...
In this paper, the circuit optimization problem of precise control of DC motor through PID interface is studied. The main purpose of this research is to strategically coordinate resistance and capacitance elements in circuit design to explore and improve the speed of signal transmission and the accuracy of response. Additionally, by optimizing the interaction between these components, this paper attempts to achieve improved performance and efficiency in the motor control system, that is, changing different K_p and K_d to achieve the best fit parameters for the most system. The experimental approach employed in this study involves a collaboration between Tinkercad and Falstad software platforms to simulate and analyze the effects of various circuit configurations as well as coefficients. The effects of K_p and K_d on the system are obtained through systematic experiments and analysis. Meanwhile, it aim to verify the proposed optimization technique and evaluate its effectiveness in practical applications. The simulation results of Tinkercad and Falstad agree well with the expected theoretical results.
... This shows that the stability area has expanded and now offers additional outstanding design alternatives. Therefore, researchers are more interested in FOCs [24][25][26]. The FOCs provide various benefits, including the capacity to modify a closed-loop system's parameters, greater disturbance rejection, and resilience. ...
In this work, a new optimisation technique called Mountain Gazelle Optimizer (MGO) has been applied to optimise the parameters of the proposed Fractional-Order Integrated Proportional Derivative with Filter (FOIPDF) controller. For a realistic analysis of load frequency control, a Multi-Area Multi-Source (MAMS) system that includes thermal, hydro, and gas-based plants has been taken into consideration. This system includes uncertainties and different constraints, such as the Governor Dead Band and Generation Rate Constraints. In addition, renewable energy sources (RESs) such as solar and wind power plants have been analysed to evaluate the impact of their fluctuating power supply on the grid’s frequency deviation. By evaluating the convergence curve, peak overshoot, peak undershoot, settling time, rise time, and integral of time multiplied squared error (ITSE), the FOIPDF controller tuned MGO technique demonstrates superior performance to alternative optimisation methods (Archimedes Optimisation Algorithm (AOA), Whale Optimisation Algorithm (WOA), and Grey Wolf Optimisation (GWO)). As a result, by optimising the FOIPDF controller using MGO, the ITSE value, which is a performance indicator, is decreased by 83.04%, 96.63%, and 41.79% when compared to the optimisation of the FOIPDF controller using AOA, WOA, and GWO, respectively. Furthermore, when considering a specific example, the utilisation of MGO leads to a notable enhancement in the time required for settling frequency variations in area-1, area-2, and tie-line power, with improvements of 18.26%, 8.73%, and 47.56% accordingly, compared to the outcomes achieved by the implementation of GWO. The proposed FOIPDF exhibited superior performance in normalising frequency deviation and tie line power when compared to other controllers such as Fractional Order PID (FOPID), Tilt Integral Derivative (TID), and PID. The results of the simulation suggest that the MGO-based FOIPDF controller significantly improves the frequency and tie-line power deviation of the system in the presence of various load disturbances, incorporation of renewable energy sources (RESs) such as wind and solar, sensitivity and stability analysis. Moreover, the effectiveness of the MGO-tuned controllers is verified by conducting tests in hardware in loop (HIL) mode using OPAL-RT.
... Ziegler and Nichols gave the well-known Ziegler-Nichols tuning method in 1942-1943 [10,11]. Father Cohen and Coon gave the alternative for tuning in the 1950s which was accepted by certain types of plants [12]. ...
An overview of intelligent control techniques for the speed control of a direct current (DC)
motor has been described in this study. Using the MATLAB SIMULINK platform, the
individually excited DC motor speed control system implemented as a physical model. A
mathematical model for both the sliding mode control (SMC) method and PID control, a
traditional control methodology that ensures the speed controller has been developed. For
comparison's sake, fuzzy logic is constructed using the Mamdani Technique with two
inputs to obtain the necessary speed control. In addition, to select the optimal gain, the
output signal of The PID controller and SMC were contrasted with fuzzy logic in terms of
overshoot peak and stability time period. The outcomes prove the SMC's superiority over
the PI controller and fuzzy logic approach. Based on time domain characteristics, this
article presents a comparative study between Proportional-Integral-Derivative (PID), a
sliding mode control (SMC), and fuzzy logic controller (FLC) controllers. The study
concludes the less overshoot peak and fast response through fixed Properties for the DC
motor and its mechanical variations due to operating conditions. Based on transient
response study, the results show that SMC is superior to fuzzy logic and classical
controllers PID.
... The real-order derivative and integral particular enhance heredity and memory systems. Fractional order systems have successfully implemented some control mechanisms [22] [23]. [24] analyses the design of a FOPID for AVR application for power system. ...
... In recent years, the use of fractional calculus in control theory has led the development of more faster and powerful FOCs [8]- [10]. These controllers can offer many advantages such as greater flexibility and improved robustness compared to classical controllers [11]- [13]. ...
This paper presents a low-cost experimental platform for real time data acquisition, identification and fractional order control of some low dynamic systems using Arduino-Simulink interface. As a demonstrative example, a DC motor is considered and modeled as a first order plus time delay plant (FOPTD) using data acquisition-based Arduino setup. Then, simple analytical rules are used to design a robust fractional order controller (FOC) which required a high-performance computing. Several validation tests have been carried out using Arduino–Simulink interface. The comparison between the theoretical simulation and the experimental tests confirms that the proposed interface can be used to support research and teaching of feedback control systems using experimental tests and low-cost laboratory kit.
... [21]'de DC motorun kontrolü, bilinmeyen dinamiklerin kompanzasyonuna dayalı bir sinir ağı tabanlı çıkış geribeslemeli kontrolör ile gerçekleştirildi ve Lyapunov analiziyle zamanla değişen bilinmeyen dinamiklerle karşı karşıya kalınsa bile asimptotik kararlılığın sağlandığı gösterildi. [22]'de geri adımlamalı kontrolörün DC motorun hız denetimine uygulanmasına yönelik yapılan araştırmanın sonuçları verilmektedir. Bozucu etkiler yokken Lyapunov açısından asimptotik kararlılık başarılı olarak elde edilmektedir. ...
Bu çalışmada DC motorların hız kontrolü için Lyapunov tabanlı PI kontrolör önerilmektedir. Önerilen yöntemde, PI kontrolör ile elde edilen kontrol sinyalinin kararlı hal durumunda değişmediği varsayılarak, kontrol sinyalinin zamana göre türevi sıfıra eşitlenir ve Lyapunov fonksiyonu kullanılarak sistemin asimptotik kararlılığı garanti edilir. Önerilen kontrolör, parametreleri Ziegler Nichols yöntemi ile ayarlanan klasik PI kontrolör ile karşılaştırılmaktadır. DC motorun benzetimi MATLAB programı ile gerçekleştirilmiş olup, benzetim sonuçları önerilen Lyapunov tabanlı PI kontrolörün klasik PI kontrolöre göre hem değişken referans hız takibinde hem de değişken yük koşulları altında daha etkili olduğunu göstermektedir.
... Thus, it can replace a leadlag compensator with only three parameters to be tuned (Oustaloup et al., 2000). The FOPI controllers have been successfully applied for many practical applications including induction motor control, servo systems, hard disk drives and control of power electronic converters (Calderón et al., 2006;Luo et al., 2013;Tepljakov et al., 2016). The FOPI controllers have the ability to perform better as compared to the integer order PI controllers for the speed control of induction motors. ...
Because of their enhanced performance, the fractional order proportional-integral (FOPI) controllers are becoming an appealing choice for controlling induction motor speed. To implement FOPI controllers, several fractional order integral approximations are available in the literature. The approximation used, and the order of approximation affects the speed tracking, transient response, and induction motor power consumption. This further affects the energy consumption analysis if simulations are conducted based on such approximations. In this paper an electric vehicle (EV) traction system is simulated to investigate the effect of such approximations on the simulations of a battery powered, induction motor driven EV system. The system consists of an indirect field-oriented induction motor, a lithium-ion battery bank, and a three-phase inverter. This work presents a quantitative analysis of the performance of FOPI controllers using different approximations, and order of approximations is presented. The controllers are evaluated based on speed tracking, transient response, computational time, and power consumption. Both step functions and standard drive cycles are used as the speed reference signal to evaluate the effects of using different approximations and different orders of approximation, when different references are used. This work establishes a reference set of simulations that can be used to infer the amount of error in battery state of charge, and state of health analysis conducted on such an EV system, when dealing with FOPI controllers under different approximations and related settings.
... Especially for time delay, nonlinear, and non-minimum phase systems, the FOPD controller can perform better than classical PD. Indeed, the FOPD scheme was successfully applied to motors [21], robots [22], building structures [23], autonomous underwater vehicles [24], and converters [25], to mention a few. Nevertheless, for complex systems and high-control performance requirements, the capacity of the FOPD is still limited. ...
A new control strategy is proposed to suppress earthquake-induced vibrations on uncertain building structures. The control strategy embeds fuzzy logic in a fractional-order (FO) proportional derivative (FOPD) controller. A new improved FO particle swarm optimization (IFOPSO) algorithm is derived to adjust the initial parameters of the FOPD controller. An original fuzzy logic-FOPD (FFOPD) controller is then designed by combining the advantages of the fuzzy logic and FOPD control, to deal with large displacements on structures under earthquake excitation. Simulation experiments are carried out on uncertain building structures subjected to the effects of different kinds of seismic signals, illustrating the validity and feasibility of the proposed method.
... Notable examples include electric automobiles, rolling and robotic manipulators, and cutting and threading steel mills due to the need for accurate control features [5]. A technique to integrate the dynamics of fractional order into an available control system of a DC via an inner proportional integral (PI) or proportional integral derivative (PID) controller was developed in [6]. A novel adaptive speed path tracking control system for nonlinear SWDCMs subjected to changeable load torque and parametric uncertainty was proposed in [7]. ...
p>Many techniques have been developed for the speed manipulation of shunt-wound direct current motors (SWDCMs) established based on armature and field control. The current research proposes a controller based on the pole placement (PP) control technique and compares it with a proportional integral (PI) controller for trajectory speed control of SWDCM with uncertainty. The circuit of the DC/DC converters energizes the DC motor. The responses are analyzed according to the dynamic mathematical model of the implemented controllers and the model of the DC/DC converters. Comparison of the motor dynamical response of the conventional PI and proposed PP controllers indicates that the PP controller exhibits improved performance in terms of rise time and steady-state error</p
... The technology readiness level also suggests that such controllers can be deployed at the industrial level [37]. The performance of a tuned FOPID controller was assessed in [38]. Increased reliability can be achieved with further research in this domain, which will help the industrial sector to better adapt controllers, especially FOPID controllers. ...
Fractional-order proportional integral derivative (FOPID) controllers are becoming increasingly popular for various industrial applications due to the advantages they can offer. Among these applications, heating and temperature control systems are receiving significant attention, applying FOPID controllers to achieve better performance and robustness, more stability and flexibility, and faster response. Moreover, with several advantages of using FOPID controllers, the improvement in heating systems and temperature control systems is exceptional. Heating systems are characterized by external disturbance, model uncertainty, non-linearity, and control inaccuracy, which directly affect performance. Temperature control systems are used in industry, households, and many types of equipment. In this paper, fractional-order proportional integral derivative controllers are discussed in the context of controlling the temperature in ambulances, induction heating systems, control of bioreactors, and the improvement achieved by temperature control systems. Moreover, a comparison of conventional and FOPID controllers is also highlighted to show the improvement in production, quality, and accuracy that can be achieved by using such controllers. A composite analysis of the use of such controllers, especially for temperature control systems, is presented. In addition, some hidden and unhighlighted points concerning FOPID controllers are investigated thoroughly, including the most relevant publications.
... Fractional-order control systems represent a revolution for industry and became a standard in various industries. Implementation of fractional-order systems depends on the cost of the basic fractional elements [38]. FOPID controllers are more focused on twin rotor systems, wherein disturbance is rejected by the controller. ...
Fractional-order proportional integral derivative (FOPID) controllers are becoming increasingly popular for various industrial applications due to the advantages they can offer. Among these applications, heating and temperature control systems are receiving significant attention, applying FOPID controllers to achieve better performance and robustness, more stability and flexibility, and faster response. Moreover, with several advantages of using FOPID controllers, the improvement in heating systems and temperature control systems is exceptional. Heating systems are characterized by external disturbance, model uncertainty, non-linearity, and control inaccuracy, which directly affect performance. Temperature control systems are used in industry, households, and many types of equipment. In this paper, fractional-order proportional integral derivative controllers are discussed in the context of controlling the temperature in ambulances, induction heating systems, control of bioreactors, and the improvement achieved by temperature control systems. Moreover, a comparison of conventional and FOPID controllers is also highlighted to show the improvement in production, quality, and accuracy that can be achieved by using such controllers. A composite analysis of the use of such controllers, especially for temperature control systems, is presented. In addition, some hidden and unhighlighted points concerning FOPID controllers are investigated thoroughly, including the most relevant publications.
... The FOCs have several types of poles, such as the hyper-damped poles, that need to be fine-tuned. Accordingly, this leads to an expansion in the stable region, giving more flexibility in the controller design process [25]. Furthermore, there are several types of controllers belonging to the FOC family; the fractionalorder-proportional-integral-derivative (FOPID) is one member of this family that has been presented in [26,27]. ...
This study presents an innovative strategy for load frequency control (LFC) using a combination structure of tilt-derivative and tilt-integral gains to form a TD-TI controller. Furthermore, a new improved optimization technique, namely the quantum chaos game optimizer (QCGO) is applied to tune the gains of the proposed combination TD-TI controller in two-area interconnected hybrid power systems, while the effectiveness of the proposed QCGO is validated via a comparison of its performance with the traditional CGO and other optimizers when considering 23 bench functions. Correspondingly, the effectiveness of the proposed controller is validated by comparing its performance with other controllers, such as the proportional-integral-derivative (PID) controller based on different optimizers, the tilt-integral-derivative (TID) controller based on a CGO algorithm, and the TID controller based on a QCGO algorithm, where the effectiveness of the proposed TD-TI controller based on the QCGO algorithm is ensured using different load patterns (i.e., step load perturbation (SLP), series SLP, and random load variation (RLV)). Furthermore, the challenges of renewable energy penetration and communication time delay are considered to test the robustness of the proposed controller in achieving more system stability. In addition, the integration of electric vehicles as dispersed energy storage units in both areas has been considered to test their effectiveness in achieving power grid stability. The simulation results elucidate that the proposed TD-TI controller based on the QCGO controller can achieve more system stability under the different aforementioned challenges.
... The FOCs have several types of poles, such as the hyper-damped poles, that need to be fine-tuned. Accordingly, this leads to expansion in the stable region, giving more flexibility in the controller design process [20]. Furthermore, there are several types of controllers belonging to the FOCs' family, and the fractional-order PID (FOPID) is one of this family that has been presented in [21]. ...
This study proposes a new optimization technique, known as the eagle strategy arithmetic optimization algorithm (ESAOA), to address the limitations of the original algorithm called arithmetic optimization algorithm (AOA). ESAOA is suggested to enhance the implementation of the original AOA. It includes an eagle strategy to avoid premature convergence and increase the populations’ efficacy to reach the optimum solution. The improved algorithm is utilized to fine-tune the parameters of the fractional-order proportional-integral-derivative (FOPID) and the PID controllers for supporting the frequency stability of a hybrid two-area multi-sources power system. Here, each area composites a combination of conventional power plants (i.e., thermal-hydro-gas) and renewable energy sources (i.e., wind farm and solar farm). Furthermore, the superiority of the proposed algorithm has been validated based on 23 benchmark functions. Then, the superiority of the proposed FOPID-based ESAOA algorithm is verified through a comparison of its performance with other controller performances (i.e., PID-based AOA, PID-based ESAOA, and PID-based teaching learning-based optimization TLBO) under different operating conditions. Furthermore, the system nonlinearities, system uncertainties, high renewable power penetration, and control time delay has been considered to ensure the effectiveness of the proposed FOPID based on the ES-AOA algorithm. All simulation results elucidate that the domination in favor of the proposed FOPID-based ES-AOA algorithm in enhancing the frequency stability effectually will guarantee a reliable performance.
... In the process control arrangements, it became the standard controller employed at the elementary level and has regularly been further utilized in many other engineering areas [6]. It goes without saying that the PI/PID controller dominates the industrial control systems [7,8]. Nevertheless, to get a decent PID controller performance under various operational conditions, each of P, I and D parameters should be simultaneously tuned and firmly established first. ...
Automatic Voltage Regulator (AVR) is fabricated to sustain the voltage level of a synchronous generator spontaneously. Several control strategies have been introduced into the AVR system with the aim of gaining a better dynamic response. One of the most universally utilized controllers is the Proportional-Integral-Derivative (PID) controller. Despite the PID controller having a relatively high dynamic response, there are still further possibilities to improve in order to obtain more appropriate responses. This paper designed a sigmoid-based PID (SPID) controller for the AVR system in order to allow for an accelerated settling to rated voltage, as well as increasing the control accuracy. In addition, the parameters of the proposed SPID controller are obtained using an enhanced self-tuning heuristic optimization method called Nonlinear Sine Cosine Algorithm (NSCA), for achieving a better dynamic response, particularly with regards to the steady-state errors and overshoot of the system. A time-response specifications index is used to validate the proposed SPID controller. The obtained simulation results revealed that the proposed method was not only highly effective but also greatly improved the AVR system transient response in comparison to those with the modern heuristic optimization based PID controllers.
... The basic limitations of integer order PID is easily overcome by fractional order PID. Some of the glimpses of fractional PID are found in [2] magnetic bearing system, in [3] for the dc motor control, for structures in [4], and in [5] for air craft pitch control and in [6] for turbine regulation system. The more detailing about the fractional PID methods and tuning part can be found in [7]. ...
In this research paper the control algorithms like LQR and PID has been proposed for the integer and fractional order system. In this research paper the modeling of the selfbalance robot system has been carried out in integer domain and fractional domain. This research paper presents the simulation analysis of control algorithms for two wheel self-balancing robot using Linear Quadratic Regulator, Proportional-IntegralDerivative and Fractional order Proportional-Integral-Derivative control algorithm. These all control algorithm are applied on the integer order system and the fractional order system and comparative analysis has been done. The comparison between integer order PID against the fractional order PID is also been made for the self-balance robot. It has been demonstrated through simulation that fractional order controller gives better response as compared to integer order controller. Further it has been found out that fractional order controller gives better results when applied to fractional order system compared to its integer order counterpart.
... PID can be tuned using the Ziegler-Nichols (ZN) tuning method [19] which is the most popular method because of its ease of use among all of the PID tuning method [20]- [23]. PID can be used to stabilize DC motor [24]- [26] and servos [27]- [29]. ...
Tank is a war vehicle made of steel that can be operated on various fields. With various fields and a large amount of terrain that the tank had to pass, this made it necessary for the tank to be able to stabilize the cannon so that the cannon be able to fire right on the target. This study discusses the stability of the position of the cannon on the tank prototype using the PID control system. PID values are obtained by using the Ziegler-Nichols tuning formula and simulink. The system using Arduino MEGA 2560 as microcontroller, gyroscope & accelerometer for the feedback sensor and cannon that driven using three servos that representing the x-axis, y-axis and z-axis. The highest average error value is 4.67 degrees with an overall average value of 2.29 degrees and an accuracy percentage of 98% when the tank tilted randomly on the x-axis, y-axis and z-axis.
... This means that the stability region has been expanded, giving us more flexibility in designing controllers. Therefore, researchers have shown a great interest in FO controllers (FOCs) [18]. The FOCs have been applied to different electrical systems in [19][20][21]. ...
In this work, a modified structure of the tilted integral derivative (TID) controller, i.e. an integral derivative-tilted (ID-T) controller, is developed for the load frequency control issue of a multi-area interconnected multi-source power system. Moreover, a new optimization algorithm known as Archimedes optimization algorithm (AOA) is used to fine-tune the proposed ID-T controller parameters. The performance of the proposed ID-T controller based on AOA is evaluated through a two-area interconnected power system, each area containing various conventional generation units (i.e., thermal, gas, and hydraulic power plants) and renewables (wind and solar power). Furthermore, system nonlinearities (i.e., generation rate constraints, governor deadband, and communication time delays), system uncertainties, and load/renewables fluctuations are considered in designing the proposed controller. The effectiveness of the proposed ID-T controller based on AOA is verified by comparing its performance with other control techniques in the literature (i.e. integral controller, proportional integral derivative (PID) controller, fractional-order PID controller, TID controller, and I-TD controller). The AOA's optimization superiority has also been verified against a variety of other sophisticated optimization methods, including particle swarm optimization and whale optimization algorithm. The simulation results exhibit that the proposed ID-T controller based on the AOA presents a great improvement in the system frequency stability under several contingencies of different load perturbations, system uncertainties, physical constraints, communication time delays, high renewables penetration.
... [35] has used the FOMCON toolbox for control of an integrated cycle power plant through a particle swarm optimization (PSO)-based fuzzy FOPID. [36,37] are other works that have used the FOMCON toolbox. ...
In a thermal plant, the combustion system of the coal-fired boiler is a nonlinear time-varying system, which leads to undesired responses, if traditional proportional-integral-derivative controllers are utilized. Internal process delay is an important characteristic of the steam pressure in the boiler of coal-fired power plants, which affects the closed-loop dynamics. To compensate for this significant delay and reach the desired performance, a novel control strategy based on a combination of an optimal fractional-order proportional-integral-derivative (OFOPID) controller with a Smith predictor (SP) structure is suggested in this paper that achieves the desired control performance required for the optimal operation of the boiler. The simulation results of a coal-fired power plant boiler with the power of 300 MW show that the performance is improved considerably by having lower overshoot and lower rise and settling times, as well as a lower mean square error during the operation of the power plant Boiler.
... A fault-tolerant fuzzy controller can raise EV's initial torque with variable characteristics of speed and high efficiency [15]. The emergence of fractional calculus has led to the development of fractional order PID controller that offers two additional degrees of freedom, the non-integer order of the integrator and the differentiator stages [16]- [18]. The noninteger order controller provided better servo, regulatory performance, and robustness compared to its integer-order counterparts. ...
The phenomenal growth of the Electric Vehicle (EV) technology demands efficient and intelligent control strategies for the propulsion system. In this work, a novel fuzzy fractional order PID (FOPID) controller using Ant Colony Optimization (ACO) algorithm has been proposed to control EV speed effectively. The controller parameters and the fuzzy logic controller’s membership functions are tuned and updated in real-time using the multi-objective ACO technique. The proposed controller’s speed tracking performance is verified using the new European driving cycle (NEDC) test in the MATLAB-Simulink platform. The proposed controller outperforms the ACO-based fuzzy integer-order PID (IOPID), FOPID, and traditional IOPID controllers. The sensitivity analysis confirms the robustness of the proposed controller for varying parameters of the EV model. The stabilization of EV speed in the presence of external disturbance is also confirmed. In the proposed work, an attempt is made to analyze the system’s stability using Matignon’s theorem, considering the linearized EV model. The proposed controller gives optimum speed tracking performance compared to the Genetic Algorithm (GA) and the Particle Swarm Optimization (PSO) based fuzzy FOPID controllers. Additionally, the optimized fuzzy FOPID controller is realized using a second-generation current conveyor with extra inputs (EX-CCII) and fractional-order capacitors with electronic tunability. The controller circuit’s performance evaluation is carried out in the Cadence Analog Design Environment using GPDK 180 nm CMOS process.
This paper presents an optimal nonlinear fractional-order controller (ONFOC) designed to reduce the seismic responses of tall buildings equipped with a base-isolation (BI) system and friction-tuned mass dampers (FTMDs). The parameters for the BI and FTMD systems, as well as their combinations (BI-FTMD and active BI-FTMD or ABI-FTMD), were optimized separately using a multi-objective quantum-inspired seagull optimization algorithm (MOQSOA). The seismic performances of the BI, FTMD, BI-FTMD, and ABI-FTMD systems for a 15-storey building subjected to two far-field (Loma Prieta and Landers) and two near-fields (Tabas and Northridge) earthquakes were evaluated. The results indicated that structures with BI, FTMD, BI-FTMD, and ABI-FTMD systems outperformed the uncontrolled structure in reducing structural responses during the design earthquakes (Loma Prieta and Tabas). However, under validation earthquakes (Landers and Northridge), the peak acceleration of the building with the FTMD system was worse than that of the uncontrolled structure during the near-field Tabas earthquake. To address this issue, we proposed a combination of the active BI system and the FTMD system. Time history analysis results demonstrated that for the building equipped with the ABI-FTMD system, the peak displacement, peak acceleration, and peak inter-storey drift were reduced by approximately 60%, 64%, and 78%, respectively, as compared to the uncontrolled structure.
The rapid advancement of renewable energy sources (RESs) has led to a decrease in system inertia and an exacerbation of the instability issue. Hence, this study puts forward an approach to bolster the stability of the power grid amidst the presence of RESs and disturbances in load conditions. The strategy utilizes controlled energy storage systems, including plug-in electric vehicles and fuel cell systems, along with a secondary controller (SC). To improve the strategy's performance, novel controllers and an enhanced optimization technique are employed. The proposed controller combines proportional-integral-derivative (PID) and fractional order control methods, resulting in a new arrangement. The parameters of the controller are tuned using an improved optimization technique called an Enhanced Runge Kutta Optimizer. The effectiveness of the proposed algorithm is demonstrated through a performance comparison with conventional optimizers, using well-established mathematical equations. Additionally, the proposed controller's effectiveness is verified by comparing its performance with other controller arrangements, such as PID, combining TD-TI, and cascaded (1+PD)-PID controllers. The performance of the system is enhanced by 66% more with the proposed controller in SC compared to the (1+PD)-PID controller, which is regarded as the most optimal among the controllers examined in this study. Additionally, the system's performance is improved by 44% when the proposed strategy is implemented, as compared to the system's performance without the proposed strategy. Totally, the effectiveness of the proposed strategy is validated across various scenarios, including high penetration of RESs, significant load fluctuations, and system non-linearity.
This paper proposes a maiden intelligent controller design that consists of a fuzzy proportional-integral-derivative-double derivative (FPIDD) controller whose parameters are fine-tuned using the Gradient-Based Optimization algorithm (GBO). The proposed FPIDD 2 regulator is employed as a secondary regulator for stabilizing the combined voltage and frequency loops in a two-area interconnected power system. The proposed FPIDD 2 controller is tested in a two-area hybrid system, with each area comprising a mix of traditional (thermal, gas, and hydraulic power plants) and renewable generation units (wind and solar power). Additionally, the proposed controller takes into account system nonlinearities (such as generation rate limitations and governor deadband), system uncertainties, and load/renewables changes. The dynamic responses of the system demonstrate that FPIDD 2 has superior ability to attenuate the deviations in voltage and frequency in both areas of the system. In the investigated hybrid system, the suggested FPIDD 2 is compared to a GBO-tuned integral derivative tilted (ID-T) controller and FPID controller. As a fitness function for the GBO, the criteria of minimizing the integral time absolute error (ITAE) are applied. The results are presented in the form of MATLAB/SIMULINK time-domain simulations. The simulation outcomes prove that the presented controller has an outstanding performance compared with the other control strategies in the dynamic response of the system in terms of rising and settling times, maximum overshoot, undershoot values and ITAE. The ITAE value of the FPIDD 2 regulator tuned by the GBO technique was enhanced by 90.9% with the GBO-based ID-T and 55.4% with GBO-based FPID controllers. Ó 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
When it comes to fractional order systems, the Industry 4.0 sector is a unique application area. This is because high performance expectations, combined with uncertainty, make it difficult to design suitable control models or modules that can address a range of concerns. Industry 4.0 demands more efficient controllers with better connectivity and high dynamic performance. On the other hand, fractional-order controllers have very robust performance and, combined with certain properties, they could become the powerful controllers of the future. The purpose of this paper is to provide a comprehensive review of this field research. A bibliometric study of Industry 4.0 and fractional control research published in the Scopus database was conducted to identify the most significant publications in the field, as well as the countries that contribute most to these studies and the most frequently used key terms. The VOS Viewer software was used to map and display the bibliometric networks. The results show an upward trend in the number of publications in this discipline. And that India, Chile, Belgium, Ecuador and Romania are the top contributors to fractional control research in Industry 4.0. In addition, Shah and Warrier are the most cited authors, with two citations for each. In addition, the results indicate a variety of keyword levels, such as the first, which was related to Industry 4.0 in general, the second, which was relevant to controllers, and the third, which was related to embedded systems. These results can help academics better understand the issue of fractional control in Industry 4.0, as well as broaden the scope of study in related areas.
A lucid methodology for the design and implementation of integer order PID (IOPID), integer order PID with derivative filter (IOPID-F), fractional order PID (FOPID) and fractional order PID with fractional order filter (FOPID-F) controllers for precisely controlling the position of an unstable Magnetic Ball Levitation System (Maglev) is reported in this work. Controller parameter values are obtained by numerically solving a constrained optimization problem incorporating desired performance criteria formulated by judiciously choosing selective transient performance metrics. The recently introduced Atom Search Optimization algorithm, used in this work, is fast, efficient and provides intelligent solutions for such complicated engineering design problems. Physical constraints are imposed on the optimization process when defining the feasible search space for the optimum controller parameter values. Both simulation and experimentation are carried out to establish the efficacy of the proposed technique. It has been observed from both simulation and experimental results that the FOPID-F controller showcases comparatively better performance in terms of transient specifications, stability margins and input reference tracking capability. Robustness to parameter variations for the proposed controllers is established with extensive experimentation on the Maglev set up.
This chapter exploits the merits of fractional-order controllers for the Load Frequency Control (LFC) problem. In particular, the slight improvement in stability is remarkable when the fast-reacting system like interconnected power generation control. The idea of ever-improving fractional calculus is being incorporated into the control aspect of the whole power system. With the proven practical viability of proportional integral (PI) control, two simple yet effective structures are verified in the two area interconnected power system model. A fractional integrator achieves the extra degree of freedom to upsurge the flexibility in control. The controller parameters for all forms are optimized from the same metaheuristic algorithm in conjunction with the improved dual performance objective function. A numerical study with analyzed results can be seen for adequate robustness and disturbance rejections.KeywordsLoad frequency controlFractional-orderPIDFOPIDOptimizationInterconnected power system
This chapter designs a Robust Fractional Model Predictive Controller (R-FMPC) to control the DC motor’s speed. The proposed controller is developed in two stages. First, the DC motor’s fractional-order model is derived by adopting the fractional definitions such as Oustaloup and fractional Laplacian. The exponent value in the developed DC motors fractional model is chosen by comparing the performances with various orders/values. Then, the model predictive controller is designed by utilizing the developed DC motors’ fractional model. Further, by varying the system dynamics, the robustness of the developed fractional-order model is also verified. Finally, a simulation study is carried out for evaluating the performance of fractional model predictive controller (FMPC) and R-FMPC for the DC motor control system.
As large-scale scientific devices like particle accelerators and tokamaks become bigger and more complex, efficient measurements are needed for these devices. At present, when laser trackers are used to measure these devices, manually rotating reflectors is needed in many circumstances, but it's inefficient and it's inappropriate to be used in the areas where human can't approach. To solve the problem, we designed an active laser reflector, which can rotate to a target angle position controlled by a host computer software. We designed a fixture to embed and clamp a spherically mounted retro-reflector (SMR). And two custom-designed motors are used to drive the SMR to rotate horizontally and vertically respectively. The shaft of the motor has a flange to match another flange on the load, which can reduce the coaxiality error between them. The motor control system consists of two motor controllers and a host computer software, and they communicate through WIFI. We made a prototype of the active laser reflector based on the design scheme and measured the offset of the SMR center, which is around ±0.23 mm. The active laser reflector we designed can increase the measuring and monitoring efficiency for large-scale scientific devices.
West African okra [WAO] (Abelmoschus caillei (A. Chev.) Stevels.) is the amphidiploid hybrid product of A. esculentus and A. manihot found under cultivation and in the wild in humid and sub-humid parts of West, Central, and East Africa. It accounts for five to ten percent of okra cultivated globally and the yield depends on the landrace or cultivar as well as other specific agro-morpho-economic traits due to the enormous intra-specific variations inherent in the genetic resources. WAO is common in traditional agriculture systems and markets within its range and collection, cultivation, utilization, and conservation are linked to local knowledge systems and practices. The leaves, fruits, seeds, floral parts, and stems are considered invaluable because of the food and income security, medicinal and industrial potentials. Women and young girls are the major custodians of the genetic resources of WAO. However, the introduction of exotic and improved varieties is eroding landraces and cultivars, whose potentials have not been maximized. Therefore, there is a need to collect, document, and explore the potentials of WAO genetic resources. Information on the diversity and distribution can contribute to the rational use and conservation of WAO. Although it is a multipurpose crop, only food use is widely reported and the plant can benefit from research into the industrial potentials of the wood, mucilage, and other phytochemicals. Also, fibres from WAO are comparable and considered a substitute for cotton, jute, and other members of its family – Malvaceae. Threats from soilborne microorganisms and the reference of WAO as a minor crop is challenging the huge socio-economic potentials of the crop. Breeding resistant and improved varieties from landraces and cultivars will benefit WAO genetic resources.
This paper presents a new method for computationally effective implementation of a discrete-time fractional-order proportional–integral–derivative (FOPID) controller. The proposed method is based on a unique representation of the FOPID controller, where fractional properties are modeled by a specific finite impulse response (FIR) filter. The balanced truncation model order reduction method is applied in the proposed approach to obtain an effective, low-order model of the FOPID controller. The time-invariant FOPID controller implementation is presented first, and then the methodology is extended to the controller with time-varying gains. A comparative analysis shows that the proposed methodology leads to the effective modeling of discrete-time FOPID controllers. In addition to simulation runs, the effectiveness of the introduced methodology is confirmed in a real-life experiment involving the control of the DC motor servo system. The paper concludes with the implementation tools developed in the Matlab/Simulink environment.
In this study, the combination of magnetorheological dampers and tuned mass dampers (MR + TMD) as a hybrid control system is investigated on a 15-story shear building where MR damper is attached to the TMD to generate active control force of TMD. The seismic responses of the structure are reduced by employing MR + TMD on rooftop of the structure. The MR damper's control voltage is generated by combining IT2FLC and FOPID. The FOPID + IT2FLC, TMD, and control voltage parameters are optimized using the observer-teacher-learner-based optimization (OTLBO) algorithm to minimize the maximum displacement of the building rooftop under far-field and near-field earthquake excitations. To conduct additional research, the same method was used to mitigate structural responses for PID, FOPID, IT2FLC, and a combination of fuzzy logic type-1 (FLC) and FOPID (FOPID + FLC). All of these controllers' performances in mitigating seismic responses are compared to those of the uncontrolled system and to each other. The results indicate that FOPID + IT2FLC outperforms PID, FOPID, and FOPID + FLC controllers. Additionally, the building's rooftop displacement was reduced by an average of 35.06% using the FOPID + IT2FLC system for sixteen far-field and near-field earthquake records. Moreover, the hybrid MR + TMD system performs better than other conventional controllers.
In this chapter a survey of the fractional-order control techniques proposed by the author during the last decade are described. Since 1945 until 2020, a large number of fractional-order control techniques and their applications were proposed by many authors. However, except the abovementioned 75 years of using various fractional-order control techniques and fractional-order controllers and their utilization in control theory, the author proposed the following new types/strategies of fractional-order controllers:
•fractional-order nonlinear controllers,
•fractional-order adaptive controllers, and
•fractional-order extremal controller.
For these three control techniques, a description, tuning and implementation methods, and illustrative examples are described.
This chapter presents the state-of-the-art in the fields of the theory and applications of fractional-order systems. Since this book is edited under the auspices of the Committee on Automatic Control and Robotics of Polish Academy of Sciences, the main focus is on Polish contributions in this area. At the beginning, a brief history of fractional calculus is outlined and quantitative analysis of contributions to the field are given. The state-of-the-art is surveyed in the advances within four subareas related to fractional-order systems including foundations, implementations, applications and control systems.
Special characteristics of the DC motors such as high reliability, flexibility, low consumption and simplicity of control have expanded the use of these motors in different industrials for instance steel plants, electric trains and etc. However, in the majority of applications, this system still controlled via traditional Proportional Integral Derivative (PID) controllers and in some cases, these controllers have been adjusted with intelligent methods. But this paper, in order to DC motor speed control, suggests a novel method to create a fuzzy logic inference system that is completely optimized through Particle Swarm Optimization (PSO) algorithm. The proposed approach has applied to a DC motor model in the MATLAB/Simulink software simulation environment and compared with different methods based on PID controllers. Simulation results show the suggested approach improved the various time response terms such as rise time, delay time and settling time for DC motor speed control.
In this paper, we study the problem of fractional-order PID controller design for an unstable plant - a laboratory model of a magnetic levitation system. To this end, we apply model based control design. A model of the magnetic lévitation system is obtained by means of a closed-loop experiment. Several stable fractional-order controllers are identified and optimized by considering isolated stability regions. Finally, a nonintrusive controller retuning method is used to incorporate fractional-order dynamics into the existing control loop, thereby enhancing its performance. Experimental results confirm the effectiveness of the proposed approach. Control design methods offered in this paper are general enough to be applicable to a variety of control problems.
Fractional-order calculus presents a novel modeling approach for systems with extraordinary dynamical properties by introducing the notions of derivatives and integrals of noninteger order. In system theory this gives rise to extensions to linear, time invariant systems to enhance the description of complex phenomena involving memory or hereditary properties of systems. Standard industrial controllers, such as the PID controller and lead-lag compensator, have also been updated to benefit from the effects of noninteger integration and differentiation, and have advantages over classical controllers in case of both conventional and fractional-order process control. However, given the definitions of fractional operators, accurate digital implementation of fractional-order systems and controllers is difficult because it requires infinite memory. In this work we study the digital implementation of a fractional-order PID controller based on an infinite impulse response (IIR) filter structure obtained by applying the Oustaloup recursive filter generation technique. Software for generating digital fractional-order is developed and tested on an Atmel AVR microcontroller. The results are verified using a MATLAB/Simulink based real-time prototyping platform.
Fractional-order calculus offers flexible computational possibilities that can be applied to control design gaining improvement in control loop performance. In this paper, we study the practical aspects of tuning and implementing a fractional PD controller for a position servo system using FOMCON (“Fractional-order Modeling and Control”) toolbox for MATLAB. We provide an overview of the tools used to model, analyze, and design the control system. The procedure of tuning and implementation of a suitable digital fractional-order controller is described. The results of the real-time experiments confirm the effectiveness of used methods.
In this paper, we present the suite of tools of the FOMCON (“Fractional-order Modeling and Control”) toolbox for MATLAB that are used to carry out fractional-order PID controller design and hardware realization. An overview of the toolbox, its structure and particular modules, is presented with appropriate comments. We use a laboratory object designed to conduct temperature control experiments to illustrate the methods employed in FOMCON to derive suitable parameters for the controller and arrive at a digital implementation thereof on an 8-bit AVR microprocessor. The laboratory object is working under a real-time simulation platform with Simulink, Real-Time Windows Target toolbox and necessary drivers as its software backbone. Experimental results are provided which support the effectiveness of the proposed software solution.
In this paper, we present a flexible optimization tool suitable for fractional-order PID controller design with respect to given design specifications. Fractional-order controllers are based on the rapidly evolving scientific field called fractional-order calculus. Its concepts are applicable in solving many scientific and engineering problems, including robust control system design. The fractional PID is a natural evolution of the conventional PID controller and as such new tuning strategies are now possible due to enhanced accuracy of the fractional-order models. The presented tool, which is a part of FOMCON - a MATLAB fractional-order calculus oriented toolbox, - uses numerical optimization methods to carry out the tuning and obtain a controller for a chosen plant to be controlled, which can either be a fractional-order plant or an integer-order plant.
FOMCON is a new fractional-order modeling and control toolbox for MATLAB. It offers a set of tools for researchers in the field of fractional-order control. In this paper, we present an overview of the toolbox, motivation for its development and relation to other toolboxes devoted to fractional calculus. We discuss all of the major modules of the FOMCON toolbox as well as relevant mathematical concepts. Three modules are presented. The main module is used for fractional-order system analysis. The identification module allows identifying a fractional system from either time or frequency domain data. The control module focuses on fractional-order PID controller design, tuning and optimization, but also has basic support for design of fractional lead-lag compensators and TID controllers. Finally, a Simulink blockset is presented. It allows more sophisticated modeling tasks to be carried out.
In this paper, we investigate the practical problems of design and digital implementation of fractional-order PID controllers used for fluid level control in a system of coupled tanks. We present a method for obtaining the PIλDμ controller parameters and describe the steps necessary to obtain a digital implementation of the controller. A real laboratory plant is used for the experiments, and a hardware realization of the controller fit for use in embedded applications is proposed and studied. The majority of tasks is carried out by means of the FOMCON (“Fractional-order Modeling and Control”) toolbox running in the MATLAB computing environment.
Real objects in general are fractional-order (FO) systems, although in some types of systems the order is very close to integer order (IO). Since major advances have been made in the theory and practice of the identification of FO controlled objects and in the design of FO controllers, it is possible to consider also the real order of the dynamical systems and consider more quality criterion while designing the FO controllers with more degrees of freedom compared to their IO counterparts. In this paper, we present an application of the retuning method to design and apply new FO controller for the existing laboratory feedback control system with no modifications in the internal architecture of the oridinal feedback control system. Along with the mathematical description, presented are also simulation results.
Proportional-Integral-Derivative (PID) controllers have been the heart of control systems engineering practice for decades because of its simplicity and ability to satisfactory control different types of systems in different fields of science and engineering in general. It has receive widespread attention both in the academe and industry that made these controllers very mature and applicable in many applications. Although PID controllers (or even its family counterparts such as proportional-integral [PI] and proportional-derivative [PD] controllers) are able to satisfy many engineering applications, there are still many challenges that face control engineers and academicians in the design of such controllers especially when guaranteeing control system robustness. In this paper, we present a method in improving a given PID control system focusing on system robustness by incorporating fractional-order dynamics through a returning heuristic. The method includes the use of the existing reference and output signals as well as the parameters of the original PID controller to come up with a new controller satisfying a given set of performance characteristics. New fractional-order controllers are obtained from this heuristic such as PIλ and PIλDμ controllers, where λ,μ∈(0,2) are the order of the integrator and differentiator, respectively.
In recent years, it has been remarkable to see the increasing number of studies related to the theory and application of fractional-order controllers, especially PIλDμ controllers, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods to ensure robustness in new or classical control problems. In this paper, we investigate switching systems. A frequency-domain design method is developed for switching systems for both integer- or fractional-order controllers, taking into account specifications regarding performance and robustness and ensuring the quadratic stability of the controlled system. Some examples are given to show the applicability and effectiveness of the proposed tuning method.
In this paper, a fractional order PID controller is investigated for a position servomechanism control system considering actuator saturation and the shaft torsional flexibility. For actually implementation, we introduced a modified approximation method to realize the designed fractional order PID controller. Numerous simulation comparisons presented in this paper indicate that, the fractional order PID controller, if properly designed and implemented, will outperform the conventional integer order PID controller
Bulk reduction of reactor power within a small finite time interval
under abnormal conditions is referred to as step-back. In this paper, a
500MWe Canadian Deuterium Uranium (CANDU) type Pressurized Heavy Water
Reactor (PHWR) is modeled using few variants of Least Square Estimator
(LSE) from practical test data under a control rod drop scenario in
order to design a control system to achieve a dead-beat response during
a stepped reduction of its global power. A new fractional order (FO)
model reduction technique is attempted which increases the parametric
robustness of the control loop due to lesser modeling error and ensures
iso-damped closed loop response with a PI{\lambda}D{\mu} or FOPID
controller. Such a controller can, therefore, be used to achieve active
step-back under varying load conditions for which the system dynamics
change significantly. For closed loop active control of the reduced FO
reactor models, the PI{\lambda}D{\mu} controller is shown to perform
better than the classical integer order PID controllers and present
operating Reactor Regulating System (RRS) due to its robustness against
shift in system parameters.
This paper presents a solution to the problem of stabilizing a given fractional dynamic system using fractional-order PI^λ and PI^λD^μ controllers. It is based on plotting the global stability region in the (kp, ki)-plane for the PI^λ controller and in the (kp , ki , kd)-space for the PI^λD^μ controller. Analytical expressions are derived for the purpose of describing the stability domain boundaries which are described by real root boundary, infinite root boundary and complex root boundary. Thus, the complete set of stabilizing parameters of the fractional-order controller is obtained. The algorithm has a simple and reliable result which is illustrated by several examples, and hence is practically useful in the analysis and design of fractional-order control systems.
This technical note presents a solution to the problem of stabilizing a given fractional-order system with time delay using fractional-order PllambdaDmu controllers. It is based on determining a set of global stability regions in the (kp, Ki, Kd)-space corresponding to the fractional orders lambda and mu in the range of (0, 2) and then choosing the biggest global stability region in this set. This method can be also used to find the set of stabilizing controllers that guarantees prespecified gain and phase margin requirements. The algorithm is simple and has reliable result which is illustrated by an example, and, hence, is practically useful in the analysis and design of fractional-order control systems.
In the last decades, fractional differential equations have become more and more popular among scientists and daring engineers in order to model various stable physical phenomena with anomalous decay, say that are not of exponential type. Moreover in discrete-time series analysis, so-called fractional ARMA models have been proposed in the literature in order to model stochastic processes, the autocorrelation of which also exhibits an anomalous decay. Both types of models stem from a common property of complex variable functions: namely, multivalued functions and their behaviour in the neighborhood of the branching point, and asymptotic expansions performed along the cut between branching points. This more abstract point of view proves very much useful in order to extend these models by changing the location of the classical branching points (s = 0 for continuous-time systems, or z = 1 for discrete-time systems). Hence, stability properties of and modelling issues by generalized fractio...
In this paper, the three principal control effects found in present controllers are examined and practical names and units of measurement are proposed for each effect. Corresponding units are proposed for a classification of industrial processes in terms of the two principal characteristics affecting their controllability. Formulas are given which enable the controller settings to be determined from the experimental or calculated values of the lag and unit reaction rate of the process to be controlled. These units form the basis of a quick method for adjusting a controller on the job. The effect of varying each controller setting is shown in a series of chart records. It is believed that the conceptions of control presented in this paper will be of assistance in the adjustment of existing controller applications and in the design of new installations.
The vast majority of automatic controllers used to compensate industrial processes are PI or PID type. This book comprehensively compiles, using a unified notation, tuning rules for these controllers proposed from 1935 to 2008. The tuning rules are carefully categorized and application information about each rule is given. The book discusses controller architecture and process modeling issues, as well as the performance and robustness of loops compensated with PI or PID controllers. This unique publication brings together in an easy-to-use format material previously published in a large number of papers and books. This wholly revised third edition extends the presentation of PI and PID controller tuning rules, for single variable processes with time delays, to include additional rules compiled since the second edition was published in 2006.
Polarization Index (P.I.) is one of the measures used in evaluating the “goodness” of the insulation resistance of an electric machine. This particular parameter is defined by the IEEE Std 43 as the ratio of the insulation resistance of the motor measured after 10 minutes, i.e. I.R.10, with respect to the insulation resistance measured after 1 minute, i.e. I.R.1, after applying a step dc voltage. After a series of insulation tests done on various machines, it was observed that some of the dynamics of insulation resistances during the span of 10 minutes would actually follow the step response characteristics of the fractional-order transfer function P (s) = K/ (T sα + 1) for K, T > 0 and 0 < α < 1. This paper presents the results of an experiment done on a low-voltage synchronous permanent magnet motor as compared to its theoretical fractional-order model.
Note to Practitioners—Polarization Index (P.I.) is one of the measures used in evaluating the “goodness” of the insulation resistance of an electric machine. This particular parameter is defined by the IEEE Std 43 as the ratio of the insulation resistance of the motor measured after 10 minutes, i.e. I.R.10, with respect to the insulation resistance measured after 1 minute, i.e. I.R.1, after applying a constant voltage over the time duration. After
a series of insulation tests done on various machines, it was observed that some of the insulation resistance measurements during the 10-minute span would actually follow a pattern that would depict a mathematical model derived from fractional calculus—a mathematical concept where the order(s) of differentiation and/or
integration is/are not necessarily integers. This could be the reason why there are instances where the P.I. definition may vary and would not follow the usual P.I. = I.R.10/I.R.1 formula. While this paper presents the observation made on a low-power permanent magnet synchronous motor, it is also proposed that a re-investigation on the P.I. definition is done by the P43 Working Group of the IEEE Std 43 based on such findings.
Preface 1. Introduction to feedback control 2. Mathematical models of feedback control systems 3. Analysis of Linear control systems 4. Simulation analysis of nonlinear systems 5. Model based controller design 6. PID controller design 7. Robust control systems design 8. Fractional-order controller - an introduction Appendix. CtrlLAB: a feedback control system analysis and design tool Bibliography Index of MATLAB functions Index.
For the numerical approximation of fractional integrals with , g smooth, we study convolution quadratures. Here approximations to on the grid are obtained from a discrete convolution with the values of f on the same grid. With the appropriate definitions, it is shown that such a method is convergent of order p if and only if it is stable and consistent of order p. We introduce fractional linear multistep methods: The th power of a pth order linear multistep method gives a pth order convolution quadrature for the approximation of . The paper closes with numerical examples and applications to Abel integral equations, to diffusion problems and to the computation of special functions.
For all the stable first order plus time delay (FOPTD) systems, a fractional order proportional integral (FOPI) or a traditional integer order proportional integral derivative (IOPID) controller can be designed to fulfill a flat phase constraint and two design specifications simultaneously: gain crossover frequency and phase margin. In this paper, a guideline for choosing two feasible or achievable specifications, and a new FOPI/IOPID controller synthesis are proposed for all the stable FOPTD systems. Using this synthesis scheme, the complete feasible region of two specifications can be obtained and visualized in the plane. With this region as the prior knowledge, all combinations of two specifications can be verified before the controller design. Especially, it is interesting to compare the areas of these two feasible regions for the IOPID and FOPI controllers. This area comparison reveals, for the first time, the potential advantages of one controller over the other in terms of achievable performances. A simulation illustration is presented to show the effectiveness and the performance of the designed FOPI controller compared with the optimized integer order PI controller and the IOPID controller designed following the same synthesis for the FOPI in this paper.
In this paper, Fractional Order Proportional Integral Derivative Controller (FOPID) is designed for liquid level control of a spherical tank which is modeled as a First Order Plus Dead Time (FOPDT) system about an operating point. The response of designed FOPID controller is compared with the traditional integer order PID (IOPID) controller in simulation and with IOPI controller on experimental setup. The PIλDμ controller is designed using minimization of Integral Square Error (ISE) method. This method offers a practical and systematic way of the controllers design for the considered class of FOPDT plant. From the simulation and experimental results presented, the designed fractional order controller works efficiently with improved performance comparing with the integer order controller.
Perhaps the most often utilized means of closed-loop control of a servo system is proportional-derivative (PD) control. Linear analysis methods suggest the best tracking performance is achieved at maximum possible proportional and derivative gains. Maximum gains, however, drive the actuators into saturation, which renders the system nonlinear and the linear analysis invalid. This paper investigates the effect of actuator saturation on servo system tracking performance by formulating a frequency-based tracking performance measure roughly equivalent to the linear system −3 dB bandwidth. The proposed measure utilizes a series of band-limited pseudo-random tracking inputs to characterize the ‘bandwidth’ of the (nonlinear) saturating system. Numerical simulations based on this measure show that, for a servo system that exhibits actuator saturation, the best tracking performance is not achieved at maximum gain. Instead, performance improves up to a given gain, then begins to recede as the gain is increased further. The simulations also show that avoiding actuator saturation to ensure linear behavior significantly sacrifices tracking performance. The measure of tracking performance is compared with the −3 dB bandwidth utilized in linear analysis techniques, and the two are shown to be well correlated.
This paper deals with the design of fractional order PIλDμ controllers, in which the orders of the integral and derivative parts, λ and μ, respectively, are fractional. The purpose is to take advantage of the introduction of these two parameters and fulfill additional specifications of design, ensuring a robust performance of the controlled system with respect to gain variations and noise. A method for tuning the PIλDμ controller is proposed in this paper to fulfill five different design specifications. Experimental results show that the requirements are totally met for the platform to be controlled. Besides, this paper proposes an auto-tuning method for this kind of controller. Specifications of gain crossover frequency and phase margin are fulfilled, together with the iso-damping property of the time response of the system. Experimental results are given to illustrate the effectiveness of this method.
This paper deals with fractional-order reset control systems and their stability. The possibilities of use of a new fractional-order proportional-Clegg integrator (FPCI) in reset applications are investigated. The key feature of this controller is to tune its order α to achieve an optimized system performance, especially referred to avoid the Zeno solution. The stability of reset control systems is generalized for such fractional-order systems. Fractional- and integer-order reset controllers are designed and compared for the velocity control of a servomotor. Simulated and experimental results are given to show the benefits of using FPCI on the servomotor performance.
Here, we should mention the most important function used in fractional calculus — Euler’s Gamma function, which is defined as (2.1) This function is generalization of a factorial in the following form: (2.2)
First order plus time delay model is widely used to model systems with S-shaped reaction curve. Its generalized form is the use of a single fractional pole to replace the first order (single-time constant) model, which is believed to better characterize the reaction curve. Using time delayed system model with a fractional pole as the starting point, in this paper, designing fractional order controllers for this class of fractional order systems is investigated. The novelty of this paper is on designing the integer order PID and fractional order PI and [PI] controllers for these class of systems. The simulation and lab experimental results are both included to illustrate the effectiveness of the proposed tuning method. By comparing the results of PID controller, fractional order PI and [PI] controllers, the advantages of the fractional order controller are clearly demonstrated in the case of controlling the single fractional pole plants with constant time delay.
In this paper, systematic design schemes of fractional order proportional integral (FOPI) controller and fractional order [proportional integral] (FO[PI]) controller for the first order plus time delay (FOPTD) system are presented, respectively. For comparison between the fractional order and the integer order controllers, the integer order proportional integral derivative (IOPID) controller is also designed following the same proposed tuning specifications to achieve the robustness requirement. It is found that the three controllers designed by the proposed tuning methods not only make the system stable, but also improve the performance and robustness for the first order plus time delay (FOPTD) systems. Simulation results are presented to validate the proposed tuning schemes. Furthermore, from the simulation results, it can be seen that the FOPI controller outperforms the other two controllers.
This paper deals with some methods used in the fractional calculus
(theory of integration and differentiation of an arbitrary order) and
applications of the fractional calculus to modelling and control of
dynamical systems
In this paper, the three principal control effects found in present controllers are examined and practical names and units of measurement are proposed for each effect. Corresponding units are proposed for a classification of industrial processes in terms of the two principal characteristics affecting their controllability. Formulas are given which enable the controller settings to be determined from the experimental or calculated values of the lag and unit reaction rate of the process to be controlled. These units form the basis of a quick method for adjusting a controller on the job. The effect of varying each controller setting is shown in a series of chart records. It is believed that the conceptions of control presented in this paper will be of assistance in the adjustment of existing controller applications and in the design of new installations.
Standard control systems can be characterized by type in the s
-domain; typically these types are of integer order. Some of the
implications of noninteger order systems in the s -domain are
explored. To accomplish this, results from the area of fractional
calculus, which defines mathematics of noninteger order derivative and
integration, are utilized. Fractional calculus operators, Laplace
transformed differintegrals are shown to behave differently from their
standard integer-order counterparts
The state-of-the-art on generalized (or any order) derivatives in
physics and engineering sciences, is outlined for justifying the
interest of the noninteger differentiation. The problems subsequent to
its use in real-time operations are then set out so as to motivate the
idea of synthesizing it by a recursive distribution of zeros and poles.
An analysis of the existing work is also proposed to support this idea.
A comprehensive study is given of the synthesis of differentiators with
integer, noninteger, real or complex orders, and whose action is limited
to any given frequency bandwidth. First, a definition, in the
operational and frequency domains, of a frequency-band complex
noninteger order differentiator, is given in a mathematical space with
four dimensions which is a Banach algebra. Then, the determination of
its synthesized form, by a recursive distribution of complex zeros and
poles characterized by complex recursive factors, is presented. The
complex noninteger differentiation order is expressed as a function of
these recursive factors. The number of zeros and poles is calculated to
be as low as possible while still ensuring the stability of the
synthesized differentiator to be synthesized. A time validation is
presented. Finally, guidelines are proposed for the conception of the
synthesized differentiator
Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI λD μ-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The Laplace transform formula for a new function of the Mittag-Leffler-type made it possible to obtain explicit analytical expressions for the unit-step and unit-impulse response of a linear fractional-order system with fractional-order controller for both open- and closed-loops. An example demonstrating the use of the obtained formulas and the advantages of the proposed PI λD μ-controllers is given.
This contribution deals with the creation of numerical models for the simulation of the dynamic characteristics of fractional-order control systems and their comparison with analytical models. We give the results of the comparison of dynamic properties in fractional- and integer-order systems with a controller, designed for an integer-order system as the best approximation to given fractional-order system. Other open questions are pointed out, which should be answered in this area of research.
Advanced PID control, The Instrumentation, Systems
- K Åström
- T Hägglund
K. Åström, T. Hägglund, Advanced PID control, The Instrumentation, Systems,
and Automation Society (ISA), 2006.
Retuning of PI/PID controllers based on closed-loop model
- H M Son
H. M. Son, Retuning of PI/PID controllers based on closed-loop model, in:
The AUN/SEED-Net Fieldwise Seminar on Control Engineering, Montien Hotel, Bangkok Thailand, 2006.
[Last access time: 05.11
- Inteco Official Website Of
Official website of INTECO, LLC., [Last access time: 05.11.2014] (2013).
La D´ erivation non Enti` ere
- A Oustaloup
A. Oustaloup: La D´ erivation non Enti` ere. HERMES, Paris, 1995.
Feliu: On realization of fractional-order controllers. Conference Internationale Francophone d'Automatique
- B M Vinagre
- I Podlubny
- A Hernandez
B. M. Vinagre, I. Podlubny, A. Hernandez, V. Feliu: On realization of fractional-order controllers.
Conference Internationale Francophone d'Automatique, Lille, Jule 5-8, 2000. (to appear)
Fractional differential equations, Mathematics in science and engineering
- I Podlubny
I. Podlubny, Fractional differential equations, Mathematics in science and engineering, Academic Press, 1999.
- D Xue
- Y Q Chen
- D P Atherton
D. Xue, Y. Q. Chen, D. P. Atherton, Linear Feedback Control: Analysis and
Design with MATLAB (Advances in Design and Control), 1st Edition, Society
for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2008.