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Abstract
The performance and robustness of well-known proportional-integral
formulas are discussed. Tuning formulas that optimize load disturbance
response have gain and phase margins that are smaller than those that
optimize for setpoint response. Tuning formulas that optimize setpoint
response mostly make use of the PI controller zero to cancel the process
pole. They typically have a gain margin of three and a phase margin of
60 degrees. The Ziegler-Nichols tuning formula gives phase margin that
varies greatly. Hence its performance varies greatly too. Approximate
analytical formulas to compute gain margin and phase margin are also
derived in this paper to facilitate online computation which could be
particularly useful for implementing adaptive control or auto-tuning
... The inverted non-linear characteristic linearizes the SISO-system and enables the application of the controller design methods known from linear control theory [54,55]. The controller synthesis has to find a compromise between controller performance and robustness [56]. ...
... The challenge of controller synthesis lies in the selection of the appropriate requirements for the application. The robust control of a first-order model by means of a PI controller is already the subject of research efforts [55,58,61] and is realised via high amplitude and phase reserves. For a first-order model, a proportional-integral controller results in an filtered integral behaviour in the open control loop and a second-order behaviour in the closed control loop [58]. ...
... The controller being optimized for disturbance response avoids cancelling of poles, that define the system behaviour of the plant. Cancelling the poles is problematic due to the large uncertainty and measurement noise and often occurs when controllers are optimized for setpoint response [55]. The robustness is considered sufficient because the closed-loop has a large phase margin and an infinite gain margin. ...
Arc based direct energy deposition combines the flexibility of additive manufacturing with high build rates and low investment costs. However, high geometric fidelity of manufactured components is not possible with state-of-the-art methods. Highly varying and geometry-dependent boundary conditions, e.g. heat dissipation and the interpass temperature, are quasi-random influences with a strong impact on the geometric fidelity and the manufactured microstructure. Without adjusting for these variations, process stability decreases, geometric deviations become more likely and defects accumulate from layer to layer. A high geometric fidelity of the manufactured components can therefore not be guaranteed with the state of the art. Due to the large number of influencing variables in the arc-based manufacturing process, this problem cannot be solved by the definition of simple setpoints. Closed-loop control, however, offers the opportunity to flexibly counteract any deviations that occur by adjusting the process parameters in real time. Since the manufactured part is created by solidification from the weld pool, a closed-loop control of the weld pool size is being developed. The developed controller uses the weld pool properties and the interpass temperature as feedback variables and takes into account the non-linear system behaviour as well as the process noise and the parameter uncertainties. The subordinate control of the welding power source is further used for improved process stability. To the best of our knowledge, this solution provides a level of robustness, steady-state accuracy and geometric fidelity that has not been achieved by previous approaches reported in the literature. To illustrate the performance of this closed-loop control for components with low heat dissipation, we demonstrate the fabrication of thin-walled components with high geometric accuracy for a fast 3D printing process and investigate the influence of the welding process variables on the microstructure, the evaluation of the geometric fidelity is based on EN ISO 1101.
... Here, kc and τi represent the tuning parameters of the compensator, which are the gain and the integral time (reset) of the compensator, respectively [10]. These parameters are determined using the off-line Ziegler-Nichols method [24] applied to processes represented by FOPTD models. This process follows a control diagram with a unitary feedback loop, as shown in Figure 5a. ...
... This process follows a control diagram with a unitary feedback loop, as shown in Figure 5a. According to [24] and considering (18), the specific formula for calculating the tuning parameters of the compensator is derived as follows ...
... This tuning process involves fine-tuning kc and τi by making incremental changes based on the system's response characteristics and desired performance criteria. Typically, manual iteration is used, where kc and τi are adjusted incrementally in accordance with observed system behavior and target objectives [12,24]. ...
This comprehensive research addresses a gap in the literature by providing an extensive examination of a single-component single-stage vaporizer process. The research involves sophisticated analyses such as dynamic modeling, comprehensive control system design and performance evaluation. The study systematically derives a linear state-space model from complex nonlinear dynamic models, laying the basis for the development of two highly effective control systems specifically designed for vaporizer level and temperature control. The simulations of these control structures demonstrate notable properties, including fast disturbance rejection, minimal overshoot, and virtually no steady-state error, emphasizing their robustness and precision. This research focuses on the stability and response of the system and provides insight into its transient behavior during disturbances and setpoint changes. The study's broad implications extend beyond the results and provide a path for future improvements. The results indicate ways to refine the start-up stage, minimize initial overshoot during system initialization, and further improve control strategies. This work has the potential to make a difference in advancing the field of vaporization processes, providing engineers and researchers with the tools and insights needed to improve system reliability and performance in industrial applications.
... A product of the results of the observability PHB test and the participation factor gives the degree of observability of each of the states of the system. Observability PBH of the K E{ input and the | E{ eigenvalue is given as: (23) where • "~ " X C " C K E{ S• Sand ~ is the | E{ eigenvalue. } ! ...
... A Bode plot of the control-to-output transfer function is given in Fig. 4. Based on the given transfer function a PID controller can be designed to meet a desired system response. From the obtained transfer function, the gains of the PID can be obtained using any of the well-known PID gain tuning algorithms such as the Ziegler-Nichols algorithm or any loop shaping method [23]. The phase margin test provides a powerful tool for analyzing the stability of the designed closed loop system from the Bode diagram of the loop gain of the system. ...
... Focusing on robustness analysis, gain and phase margins have always served as important indicators [18,19]. Robust PID controllers based on gain and phase margins measure were developed for stable processes in [18,19] and unstable processes in [20,21]. ...
... Focusing on robustness analysis, gain and phase margins have always served as important indicators [18,19]. Robust PID controllers based on gain and phase margins measure were developed for stable processes in [18,19] and unstable processes in [20,21]. However, as the development of FOPID controllers, the robust PID/PI/PD FO controllers have presented more satisfactory performance compared with conventional ones used on both FO plants and IO plants [11,[22][23][24][25][26]. ...
Most of the existing controller tuning methods are based on accurate system model and sensitive to some inevitable uncertainties and unmeasurable disturbance. Aiming at this problem, a thorough robustness analysis on a typical kind of fractional-order (FO) delay system has been made in this study. A kind of robust FO proportional and derivative controller is proposed based on phase and gain margins. The tuning methods are demonstrated under different circumstances, namely there is gain variation, time constant variation, order variation or even multiple parameters variations in system transfer function. Simulation results show that the closed-loop control system with the proposed controller can achieve both robustness and satisfactory dynamic performance, and outperform the conventional proportional-integral-derivative controller in all cases.
... Focusing on robustness analysis, gain and phase margins have always served as important indicators [18,19]. Robust PID controllers based on gain and phase margins measure were developed for stable processes in [18,19] and unstable processes in [20,21]. ...
... Focusing on robustness analysis, gain and phase margins have always served as important indicators [18,19]. Robust PID controllers based on gain and phase margins measure were developed for stable processes in [18,19] and unstable processes in [20,21]. However, as the development of FOPID controllers, the robust PID/PI/PD FO controllers have presented more satisfactory performance compared with conventional ones used on both FO plants and IO plants [11,[22][23][24][25][26]. ...
This study is concerned with observer design and observer-based output feedback control for a fractional reaction diffusion (FRD) system with a spatially-varying (non-constant) diffusion coefficient by the backstepping method. The considered FRD system is endowed with only boundary measurable and actuation available. The contribution of this study is divided into three parts: first is the backstepping-based observer design for the FRD system with non-constant diffusivity, second is the output feedback controller generated by the integration of a separately backstepping-based feedback controller and the proposed observer to stabilise the FRD system with non-constant diffusivity, and the last is the Mittag-Leffler stability analysis of the observer error and the closed-loop FRD systems. Specifically, anti-collocated location of actuator and sensor is considered in the stabilisation problem of this system with Robin boundary condition at x = 0 and the boundary feedback controller for Dirichlet actuation at x = 1. By designing an invertible coordinate transformation to convert the observer error system into a Mittag-Leffler stable target system, the observer gains are obtained. They are used to design the output feedback control law for stabilising the closed-loop system. Finally, a numerical example is shown to validate the effectiveness of the authors' proposed method.
... Hence, controller design for such process models is difficult and offers challenge in obtaining satisfactory closed-loop performance [3,6,21,32,33,35,37]. Proportional-Integral-Derivative (PID) controller or its subsets are widely used for process control because of their structural simplicity and past record of accomplishment [4,13,31]. Gain-Margin (GM) and Phase-Margin (PM) specification based PID controller design is one of the most commonly used technique [15,18,19,25]. A PID controller design methodology for general class of plants have been developed based on GM and PM specification in [30] with the gain crossover frequency chosen using additional Integral Timeweighted Absolute Error (ITAE) criterion. ...
... Substituting (1) and (4) in (16)- (19), one can obtain: ...
An integral-proportional derivative (I-PD) control strategy for integrating plus time-delay processes is proposed. The proposed scheme consists of an inner PD loop and an outer I-loop for taking care of the servo as well as the regulatory action. Explicit formulas for tuning of the proposed controller are derived in terms of gain margin, phase margin and critical gain. Moreover, pole-placement and frequency loop-shaping design methods are also explored for designing the I-PD controller. Simulation results show the superiority of the proposed I-PD controller over conventional P/PI/PID ones for integrating processes. The design is also validated through experiments on a temperature control process.
... To model the VSI, average theory is utilized [4], [5]. In order to design the controllers for the UPS inverter, phase margin method (frequency analysis) is used [6], [7]. ...
... This controller is based on a type-two compensator. The parameters used to calculate the transfer function are: cut-off frequency of 20Hz and phase margin of 30 [6], [22], [23]. ...
... This means that even within linear systems and without saturation of the control action it is analytically impossible to achieve an arbitrary performance indicator of the control system. Universal formulas for estimation of pa-rameters of a control system without modeling are mostly inaccurate [4], so it is possible to achieve a variety of performance indicators only using multi-criteria optimization. The first difficulty of this approach is the presence of unstable zones, due to which the algorithm can find some local minimum. ...
The goal of the work is the development of an algorithm and corresponding software, which allows the execution of multi-criteria optimization of a control system with PI controller and FOPDT plant. We use the following seven performance indicators to find the optimal tunings: gain margin, phase margin, cutoff frequency, critical frequency, relative delay margin, relative overshoot, maximum control action magnitude. Optimization criteria can include constraints on any number of indicators. The goal of the work has been achieved by solving the following tasks. The first task is to create formulas and procedures for accurate calculation of performance indicators of control systems. The second task is to develop a procedure for the fastest possible simulation of a control system with the orientation on using a model with internal delays structure and a special solver for it. The third task is to develop an algorithm for fast calculation of performance indicators in the range of all possible rational tuning of the controller for a given FOPDT plant model. The fourth task is to develop a software application with a graphical interface in MATLAB language, which allows convenient optimization for an arbitrary rational FOPDT model. The most significant result was that the pointed-out performance indicators can be accurately calculated for all possible rational tunings of a PI controller with an arbitrary FOPDT model in a second. The significance of the results was that it allows to reduce an optimization procedure to a table search and to achieve any multi-term performance criteria. The effectiveness of the procedure has been demonstrated on a set of different FOPDT models. It is shown that there is no dependence in accuracy of calculation from model or controller coefficients.
... Silva and Bhattacharyya discussed a stabilizing PI controller [31] and a stabilizing PID controller [32] which simultaneously satisfies desired A m and φ m and gives stabilizing sets for controller parameters. Ho et al. [33] compare different PI controllers for desired A m and φ m , whereas Hang et al. [35], Ho et al. [34] compares different PID controllers for desired A m and φ m . ...
This chapter considers the design of a fractional order (FO) internal model controller (IMC) for first order plus time delay (FOPTD) processes to satisfy a given set of desired stability margins in terms of gain margin and phase margin . The highlight of the design is the choice of a fractional order (FO) filter in the IMC structure which has two parameters ( and ) to tune as compared to only one tuning parameter () for traditionally used integer order (IO) filter. These parameters are evaluated for the controller so that and can be chosen independently. This is the first time when the IMC controller is designed without any approximation of the delay in the IMC which has always been approximated using Taylor’s series approximation or Pade approximation. Simulation studies are carried out for three different FOPTD processes and the proposed methodology is validated experimentally on a DC servo-motor system. The results are compared with different well-known IMC techniques and the performance of controllers is evaluated in terms of rise time (), settling time (), maximum overshoot () and integral square error (ISE).
... However, finding suitable methods for tuning these controllers automatically is still a subject of research. Tuning formulae exist for PI controllers for first-order systems [10][11][12], which may be suitable when the gain, time delay, and time constant of the system are known. However, this is seldom the case. ...
Control systems require maintenance in the form of tuning their parameters in order to maximize their performance in the face of process changes in minerals processing circuits. This work focuses on using deep reinforcement learning to train an agent to perform this maintenance continuously. A generic simulation of a first-order process with a time delay, controlled by a proportional-integral controller, was used as the training environment. Domain randomization in this environment was used to aid in generalizing the agent to unseen conditions on a physical circuit. Proximal policy optimization was used to train the agent, and hyper-parameter optimization was performed to select the optimal agent neural network size and training algorithm parameters. Two agents were tested, examining the impact of the observation space used by the agent and concluding that the best observation consists of the parameters of an auto-regressive with exogenous input model fitted to the measurements of the controlled variable. The best trained agent was deployed at an industrial comminution circuit where it was tested on two flow rate control loops. This agent improved the performance of one of these control loops but decreased the performance of the other control loop. While deep reinforcement learning does show promise in controller tuning, several challenges and directions for further study have been identified.
... In [W. K. Ho and Zhou (1955)], frequency domain specifications are used to tune the PID parameters. In [Prakash (2004)], ISE and interval arithmetic are used to find controller parameters for system with uncertainties. ...
In this paper, a near-optimal tuning method for PID controller which is based on minimizing the Integral Square Error (ISE) is presented. Parseval’s theorem is used to find the ISE as a function of controller parameters. Guaranteed optimization of the ISE is achieved using the Moore Skelboe Algorithm and interval analysis for the given range of the controller parameter. For stability assurance, Routh Hurwitz criterion is used. This method is effective for finding PID values for given initial range and applicable for all first and second order linear time-invariant (LTI) system and some of the higher-order LTI systems. Simulation results are presented using the MATLAB and INTLAB software. Experimental results are presented for pitch and yaw angle control of Twin Rotor Multiple Input Multiple Output (MIMO) system.
... At the same time, the system's rise time depends on the frequency at the gain crossover point [5], [6]. In general, a small stability margin results in a very oscillatory response, and a large stability margin corresponds to sluggish disturbance rejection [7]. The frequency ω where the open-loop's gain crosses the unit circle, also known as the gain-crossover frequency, is used as a design criterion in [5]. ...
This paper proposes an extension to the established loop-shaping method, where the loop-shaping method is modeled mathematically and solved as a mathematical optimization program. In this process, a novel cost function is proposed and employed as the objective of optimization in the controller tuning problem. This cost function evaluates different characteristics of the system in the frequency domain, such as the stability margins and the operability bandwidth. These characteristics reflect the quality of load disturbance rejection, set-point tracking, and operability bandwidth of the control system. Consequently, the proposed technique circumvents running a time-domain simulation completely. More importantly, the proposed technique can be used with any controller structure. The generic cost function can be customized to fit any control objective and application. This is conducted in the second half of this paper, with the aim of obtaining a system with near-optimum time-domain performance with respect to the integral of time times absolute error (ITAE) criterion. At the same time, the control system obtained with the customized cost function has better operability bandwidth than that of a system optimized in the time-domain for the ITAE criterion. The proposed optimization model is analyzed for two plant models: first order and second order plus dead-time (FOPDT), (SOPDT), respectively.
... At the same time, the system's rise time depends on the frequency at the gain crossover point [5], [6]. In general, a small stability margin results in a very oscillatory response, and a large stability margin corresponds to sluggish disturbance rejection [7]. The frequency ω where the openloop's gain crosses the unit circle, also known as the gaincrossover frequency, is used as a design criterion in [5]. ...
This paper proposes an extension to the established loop-shaping method, where the loopshaping method is modeled mathematically and solved as a mathematical optimization program. In this process, a novel cost function is proposed and employed as the objective of ptimization in the controller tuning problem. This cost function evaluates different characteristics of the system in the frequency domain, such as the stability margins and the operability bandwidth. These characteristics reflect the quality of load disturbance rejection, set-point tracking, and operability bandwidth of the control system. Consequently, the proposed technique circumvents running a time-domain simulation completely. More importantly, the proposed technique can be used with any controller structure. The generic cost function can be customized to fit any control objective and application. This is conducted in the second half of this paper, with the aim of obtaining a system with near-optimum time-domain performance with respect to the integral of time times absolute error (ITAE) criterion. At the same time, the control system obtained with the customized cost function has better operability bandwidth than that of a system optimized in the time-domain for the ITAE criterion. The proposed optimization model is analyzed for two plant models: first order and second order plus dead-time (FOPDT), (SOPDT), respectively.
... In this paper, the technique consists in constructing current error in a simulation for the objective function, instead of solving equations and designing a system model or transfer function through system identification (Eriksson, 2011) using MATLAB (Ho et al., 1995;Xu, 2013). This technique is fine, but it is difficult with lack of perfections and does not give precise and flawless results compared with the system. ...
This work aims to tune multiple controllers at the same time for a HVDC system by using a self-generated (SG) simulation-based optimization technique. Online optimization is a powerful tool to improve performance of the system. Proportion integral (PI) controllers of Multi-infeed HVDC systems are optimized by the evaluation of objective functions in time simulation design (TSD). Model based simulation setup is applied for rapid selection of optimal PI control parameters, designed in PSCAD software. A multiple objective function (OF), i.e. Integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE), integral time square error (ITSE), and integral square time error (ISTE), is assembled for testing the compatibility of OFs with nonlinear self-generated simplex algorithm (SS-SA). Improved control parameters are achieved after multiple iterations. All OFs generate optimum responses and their results are compared with each other by their minimized numerical values. Disturbance rejection criteria are also proposed to assess the designed controller performance along with robustness of system. Results are displayed in form of graphs and tables in this paper.
... The optimization process is conducted under two constraint conditions. First, the gain and phase margins are set to be larger than 3 and 60°, respectively, to guarantee the robustness of the system [24,25]. Second, the settling time (2% tolerance) is set to be less than 20 ms to guarantee the time domain performance. ...
When a fast-steering mirror (FSM) system is designed, satisfying the performance requirements before fabrication and assembly is vital. This study proposes a structural parameter design approach for an FSM system based on the quantitative analysis of the required closed-loop bandwidth. First, the open-loop transfer function of the FSM system is derived. In accordance with the transfer function, the notch filter and proportional-integral (PI) feedback controller are designed as a closed-loop controller. The gains of the PI controller are determined by maximizing the closed-loop bandwidth while ensuring the robustness of the system. Then, the two unknown variables of rotational radius and stiffness in the open-loop transfer function are optimized, considering the bandwidth as a constraint condition. Finally, the structural parameters of the stage are determined on the basis of the optimized results of rotational radius and stiffness. Simulations are conducted to verify the theoretical analysis. A prototype of the FSM system is fabricated, and corresponding experimental tests are conducted. Experimental results indicate that the bandwidth of the proposed FSM system is 117.6 Hz, which satisfies the minimum bandwidth requirement of 100 Hz.
... Over the years, a lot PID tuning procedures and simple rules have been developed (Ho et al., 1995(Ho et al., , 1996C.C.Hang et al., 2002;Liu et al., 2013;Padula and Visioli, 2011;Kurokawa et al., 2017). However, only very few tuning procedures are suitable for general linear process model, even non-minimum phase and/or with time delay. ...
The purpose of this paper is to introduce an advanced virtual tool for fractional PID (FPID) controller design. It implements generic Nyquist plot shaping and/or sensitivity functions shaping capabilities. In this context, one can define e.g. gain and phase margins, sensitivity functions limits or loop bandwidth. The procedure relies on generalized robustness regions method for fractional PID controllers. The technique is best applicable namely for any non-oscillatory or slightly oscillatory linear system even with dead time, both integer and fractional order. The robustness regions can be computed and painted for more system models hence the robust controller design can be done. Here the method is validated on three illustrative examples. The author believes, that the virtual lab will be worthwhile for both researchers and industrial practitioners and will help to boost the employment of fractional order PID controllers.
... For complex neural system where accurate model can hardly be achieved, plant exploration based method can be used. The initial estimation of the optimal operating points can be learnt from the Zeigler-Nichols tuning method [45]. And the final controller parameters can be determined by using an iterative procedure, based on the least root mean square error. ...
A brain-machine interface (BMI) creates an artificial pathway between the brain and the external world. The research and applications of BMI have received enormous attention among the scientific community as well as the public in the past decade. However, most research of BMI relies on experiments with tethered or sedated animals, using rack-mount equipment, which significantly restricts the experimental methods and paradigms. Moreover, most research to date has focused on neural signal recording or decoding in an open-loop method. Although the use of a closed-loop, wireless BMI is critical to the success of an extensive range of neuroscience research, it is an approach yet to be widely used, with the electronics design being one of the major bottlenecks. The key goal of this research is to address the design challenges of a closed-loop, bidirectional BMI by providing innovative solutions from the neuron-electronics interface up to the system level.^ Circuit design innovations have been proposed in the neural recording front-end, the neural feature extraction module, and the neural stimulator. Practical design issues of the bidirectional neural interface, the closed-loop controller and the overall system integration have been carefully studied and discussed. To the best of our knowledge, this work presents the first reported portable system to provide all required hardware for a closed-loop sensorimotor neural interface, the first wireless sensory encoding experiment conducted in freely swimming animals, and the first bidirectional study of the hippocampal field potentials in freely behaving animals from sedation to sleep.^ This thesis gives a comprehensive survey of bidirectional BMI designs, reviews the key design trade-offs in neural recorders and stimulators, and summarizes neural features and mechanisms for a successful closed-loop operation. The circuit and system design details are presented with bench testing and animal experimental results. The methods, circuit techniques, system topology, and experimental paradigms proposed in this work can be used in a wide range of relevant neurophysiology research and neuroprosthetic development, especially in experiments using freely behaving animals.
... Variety of frequency domain based techniques that use information about the desired phase and gain margins, and other system frequency response parameters were reported in a series of papers (Hagglund and Astrom, 1992;Tyreus and Luyben, 1992;Venkatashankar and Chidambaram, 1994;Wang et al., 1995;Ho et al., 1995aHo et al., ,b, 1996Luyben, 1996;Khan and Lehman, 1996;Poulin and Pomerleau, 1996Wang and Cluett, 1997;Loron, 1997;Shafiei and Shenton, 1997;Natarjan and Gilbert, 1997;Ho and Xu, 1998a,b;Fung et al., 1998;Luyben, 1998b). Assuming that the system transfer function is known, (Wang et al., 1999c) proposed a new technique for tuning PlO controllers using the root locus method. ...
Despite of a huge number of classic optimal control theory algorithms developed during the sixties, seventies, and eighties, and a large number of very sophisticated optimal control algorithms developed during the nineties, we are witnessing a real explosion of new theoretical results and new applications of PID controllers. This paper extracts the essence of the most recent developments and breakthroughs in design, tuning, implementations, and theoretic considerations of these controllers. It contains a complete survey of papers published between 1990 and 1999 in the leading control theory and applications journals in electrical, chemical, and mechanical engineering. The important papers published in other journals and classic papers published before 1990 are also included.
... For complex neural system where accurate model can hardly be achieved, plant exploration based method can be used. The initial estimation of the optimal operating points can be learnt from the Zeigler-Nichols tuning method [45]. And the final controller parameters can be determined by using an iterative procedure, based on the least root mean square error. ...
This paper presents a bidirectional brain machine interface (BMI) microsystem designed for closed-loop neuroscience research, especially experiments in freely behaving animals. The system-on-chip (SoC) consists of 16-channel neural recording front-ends, neural feature extraction units, 16-channel programmable neural stimulator back-ends, in-channel programmable closed-loop controllers, global analog-digital converters (ADC), and peripheral circuits. The proposed neural feature extraction units includes 1) an ultra low-power neural energy extraction unit enabling a 64-step natural logarithmic domain frequency tuning, and 2) a current-mode action potential (AP) detection unit with time-amplitude window discriminator. A programmable proportional-integral-derivative (PID) controller has been integrated in each channel enabling a various of closed-loop operations. The implemented ADCs include a 10-bit voltage-mode successive approximation register (SAR) ADC for the digitization of the neural feature outputs and/or local field potential (LFP) outputs, and an 8-bit current-mode SAR ADC for the digitization of the action potential outputs. The multi-mode stimulator can be programmed to perform monopolar or bipolar, symmetrical or asymmetrical charge balanced stimulation with a maximum current of 4 mA in an arbitrary channel configuration. The chip has been fabricated in 0.18 μ m CMOS technology, occupying a silicon area of 3.7 mm (2). The chip dissipates 56 μW/ch on average. General purpose low-power microcontroller with Bluetooth module are integrated in the system to provide wireless link and SoC configuration. Methods, circuit techniques and system topology proposed in this work can be used in a wide range of relevant neurophysiology research, especially closed-loop BMI experiments.
... A standard SISO control design is then performed on each diagonal entry, hoping that the off-diagonal dynamics remain well-behaved in closed-loop. To design the individual controllers, several standard automated tuning methods such as Ziegler-Nichols PID, internal model control (IMC), linear quadratic Gaussian (LQG) and optimization based approaches were tested and the best results were obtained for the IMC design method [56,57] with a time constant of τ = 1/3 s % 0.3333 s, resulting in well-damped responses settling in about t s = 4τ % 1.3333 s as seen in Fig 6. While the controllers seem to perform well on their individual nominal models, the real test is whether they will regulate the aircraft attitude successfully when used simultaneously under parameter uncertainties in nonlinear simulations. ...
Some level of uncertainty is unavoidable in acquiring the mass, geometry parameters and stability derivatives of an aerial vehicle. In certain instances tiny perturbations of these could potentially cause considerable variations in flight characteristics. This research considers the impact of varying these parameters altogether. This is a generalization of examining the effects of particular parameters on selected modes present in existing literature. Conventional autopilot designs commonly assume that each flight channel is independent and develop single-input single-output (SISO) controllers for every one, that are utilized in parallel for actual flight. It is demonstrated that an attitude controller built like this can function flawlessly on separate nominal cases, but can become unstable with a perturbation no more than 2%. Two robust multi-input multi-output (MIMO) design strategies, specifically loop-shaping and μ-synthesis are outlined as potential substitutes and are observed to handle large parametric changes of 30% while preserving decent performance. Duplicating the loop-shaping procedure for the outer loop, a complete flight control system is formed. It is confirmed through software-in-the-loop (SIL) verifications utilizing blade element theory (BET) that the autopilot is capable of navigation and landing exposed to high parametric variations and powerful winds.
... Space considerations dictate that only representative simulation results may be provided. In these results, approximate gain margin and phase margin are analytically calculated, using the method outlined by Ho, et al. (1995), for processes compensated using an appropriately tuned PI controller. The MATLAB package has been used in the simulations. ...
The ability of proportional integral (PI) and proportional integral derivative (PID) controllers to compensate many practical industrial processes has led to their wide acceptance in industrial applications. The requirement to choose either two or three controller parameters is perhaps most easily done using tuning rules. A summary of tuning rules for the PI control of single input, single output (SISO) processes with time delay is provided in this paper.
... Some work done to develop an expert system to allow greater automation of the procedure for recommending a tuning rule will be described; the experience of the author is that the expert system increases student motivation as well as providing a platform for further project work. The teaching approach is based on research work previously published by Ho et al. (1995), (1996) and O'Dwyer (1998), (2001. ...
This paper discusses an approach to the teaching of PID controller tuning methods to students in control engineering at Dublin Institute of Technology. The method involves analytically calculating the gain margin, phase margin and maximum sensitivity for PI and PID controlled systems whose process is modelled in first order lag plus time delay (FOLPD) form. Students can examine the performance of many tuning rules from graphical results, allowing insight to be developed as to the most rational choice of the tuning rule for the application. Some preliminary work done to develop an expert system to allow a greater automation of the procedure for recommending a tuning rule, for user defined requirements, is also described.
... There was a lot of PID tuning techniques developed since the popular Ziegler-Nichols method (Ziegler and Nichols (1942)) appeared. Some of them were evaluated in Ho et al. (1996). They are alltogether not very reliable (Schlegel (2002)) as they are only heuristic and based on one nominal process model. ...
The paper describes a new PID tuning approach suitable for both researcher and industrial practice. It justifies the authors' previous work where only intervals for particular controllers parameters were developed. Compared to other ones, the robustness regions method provides an admissible area of all controller parameters satisfying the required closed loop performance for exactly defined class of fractional processes. In contrast to common time domain tuning methods the process is characterized by three moments of its impulse response. The resulting areas serve as a common playground for future development of feature based tuning rules as shown in the illustrative example. The described procedure was partly implemented into the interactive Java applet freely accessible at www.pidlab.com.
... In classical control, over 90% of industrial controllers are of the PI type [11]. PI control method is frequently used in industrial applications because of its simplicity and satisfactory control performance. ...
This paper presents a design and implementation of Brushless DC (BLDC) motor speed control based on the TMS320F28335 DSP board interfacing to MATLAB/SIMULINK. To obtain the optimal tracking and regulating responses, the PI controller is conducted and designed by pole placement technique. With Back EMF detection, the proposed system is considered as a class of sensorless control. This scheme leads to the speed adjustment of the BLDC motor by PWM. This experiment aims to examine the effectiveness of BLDC motor by testing the BLDC motor of 100 watt. It was found that the speed response of BLDC motor can be regulated at the operating speed of 700 rpm and 1400 rpm at no load and full load conditions.
... As shown, in average the retuning improves the system performances significantly as stability margin increases more that twofold, %overshoot reduces more than six times and settling time reduces slightly. However, the iterative method that based on trial and error has several drawbacks, e.g., it takes considerable time to tune the parameters, it requires the system to be in the border of stability in order to tune the parameters, and it cannot be used to design compensator for systems that are not open-loop stable [7]. ...
Time delays, also known as transport lag, dead time or time lag, are components that hold signal flow off inside the systems. They arise in physical, chemical, biological and economic systems, as well as in the processes of measurement and computation. Time delays can be approximated using polynomial series to allow the systems be analyzed in the same manner as the non time-delay systems. In this paper, we study the influences of delay components to system’s stability, derive the Nyquist stability criterion for time-delay systems and use it to analyze stability of the systems, and utilize some polynomial series to approximate the delays and examine their performances. Moreover we study PID controller as delay compensation scheme using two tuning methods: the “iterative method” and Ziegler-Nichols method.
... The objective of the controller is to reach the target and be able to track a new set point values quickly. This control problem can be solved by a number of level control strategies ranging from conventional PID to Genetic algorithm based PID controllers [2], [3], [4].In level control applications the conventional Proportional-Integral-Derivative (PID) controller is generally used, but the tuning parameters of the controllers must be estimated by tuning technique either in frequency response or time response to attain the desired performances [5], [6].Many different tuning techniques have been proposed for attaining the desired control system response. These tuning techniques are developed based on one or more than one of the control objectives as selected criterion. ...
Automatic controllers are introduced for efficient control of the process industries. Proportional, Integral and derivative (PID) controllers are the most widely used controllers in the most process industries because of their robustness, easy implementation and simplicity. Various tuning methods like Ziegler-Nichols (Z-N) method, Cohen-Coon(CC) method, Minimum error integral criteria method and Genetic Algorithms (GAs) have been suggested for optimum setting of PID controller parameters. In this paper the performance of Genetic algorithm based PID controller is compared with conventional PID controller for various tuning techniques in the case of three tank level process control system. This comparative study is carried out for set point tracking of three tank level process using computer simulation.
... Often, the PID controller with manual or even default setting of parameters is used. There exist a lot of heuristic tuning methods Hägglund [1984, 1995]; Ho et al. [1995Ho et al. [ , 1996. Unfortunately, each of them fails for some kind of process (Schlegel et al. [2003]). ...
PID pulse autotuner based on moments of the impulse response was already proved suitable for industrial practice. The new concept proposed in this paper relieves several weaknesses of the first autotuner generation. The autotuning procedure works with so called model set, which contains all processes satisfying both a priori assumption about the transfer function form and experimentally obtained characteristic numbers. It is assumed that the process is represented by multiple fractional-order pole transfer function. Further, it is supposed that first three moments of the process impulse response are obtained experimentally. For particular frequency, the model set processes create so called value set in frequency domain. In authors' previous work the analytical relations for computing value set boundary were given. It was shown that band of value sets is bounded by two extremal processes which are significant for consequential controller design. These two processes can be computed directly from the impulse response moments. Here, it is shown that the resulting band of frequency responses is larger comparing to the case when only integer-order processes are a priori assumed. The results are given for different values of the minimum allowed pole order. Moreover, it is explained how to equip the autotuner by a new user parameter δ specifying its robust-ness/aggressiveness. The optimal PID controller parameters are computed as functions of normalized dead time and controller robustness δ for three modes of controller speed (SLOW / NORM / FAST).
Today, in automobile industries, cruise control is one of the most serious aspects that is necessary in a well‐planned controller which can suit the new improvements in innovation. One of the most favoured and significant models for control system engineering is the cruise control system (CCS). This speed control system proves to be a prominent laboratory prototype of an advanced control system. This CCS finds wide usage due to the ease in understanding and coverage of various predominant ancient and new design approaches. In this paper, the performance of different controllers, such as a proportional‐integral (PI) controller, proportional‐integral‐derivative (PID) controller, and fuzzy logic controller (FLC), is evaluated at different conditions of road to achieve the desired speed of the vehicle. The dynamic model of a vehicle or CCS considers the road grade and friction coefficient occurring between road and wheel. Modelling of the controller has been done with the help of MATLAB/Simulink software. At last, a comparison analysis of each controller with the different conditions will be done that is dependent on performance characteristics.
In many industrial processes, e.g. temperature and level control, chemical reactors can be classified as a variant of integrating plus time-delay system. Controlling these processes is a difficult task due to open-loop instability, which consists of time-delay and unbounded output for bounded input. 1DOF PID control always leads to a large overshoot in set-point tracking for IPTD processes. In a 2DOF PID structure, tuning the set-point weights and the controller parameters is important to achieve good tracking and disturbance rejection properties. But tuning the set-point weights and the parameters of the cascade-feedback controller together is a difficult task. Usually, predetermined values for set-points are chosen, and a controller design is followed. In the present work, an alternative simple approach to obtain controller parameters along with set-point weights is presented which are tuned to yield good tracking and load–disturbance rejection. Explicit controller parameters for different classes of integrating processes are obtained using gain-margin, phase-margin, and inverse plant model which can also be used for controller auto-tuning. To validate the effectiveness of the proposed controller, simulation comparisons with some recently developed methods are included. Moreover, the experimental validation of the proposed controller on a temperature control plant is also presented.
High frequency resonance (HFR) is a key issue of power electronics based systems. Two solutions can be applied for addressing HRFs, including 1)active damping method and 2)passive damping method. For modular multilevel converters (MMCs), most of existing harmonic resonance suppression methods are focused on active methods, including active filtering and virtual resistance. However, the active filtering may lead to negative damping in its attenuation band and the virtual resistance may become negative in high frequency range when influenced by control delay. In order to avoid the negative effects of control delay and increase the damping of MMCs in high frequency range, this paper reconsiders the arm inductor in MMCs and proposes a passive damper design method for MMCs. With the coordinated design between active controller and passive damper, the negative damping of MMCs in high frequency range can be effectively eliminated and the system stability can be improved. Also, the proposed passive damper has little impacts on the steady-state operation and increases few losses of the MMC. Effectiveness of the proposed passive damper is validated by electromagnetic transient (EMT) simulations in PSCAD/EMTDC.
This paper contributes to the design of a fractional order (FO) internal model controller (IMC) for a first order plus time delay (FOPTD) process model to satisfy a given set of desired robustness specifications in terms of gain margin (Am) and phase margin (Pm). The highlight of the design is the choice of a fractional order (FO) filter in the IMC structure which has two parameters (lambda and beta) to tune as compared to only one tuning parameter (lambda) for traditionally used integer order (IO) filter. These parameters are evaluated for the controller, so that Am and Pm can be chosen independently. A new methodology is proposed to find a complete solution for controller parameters, the methodology also gives the system gain cross-over frequency (wg) and phase cross-over frequency (wp). Moreover, the solution is found without any approximation of the delay term appearing in the controller.
Bidirectional neural interface with closed-loop operation is important for both fundamental neuroscience research and the development of next-generation neuroprosthetics. However, the circuit and system design of bidirectional closed-loop brain–machine interfaces have not been well explored. This chapter discusses two of the most important issues, stimulation artifacts and closed-loop controllers. Stimulation artifacts are known issues in simultaneous neural stimulation and recording, which corrupt the neural recording. Even though a lot of studies have proposed methods to cancel or attenuate the stimulation artifacts, a comprehensive study considering different electrode configurations and circuit topologies is missing. This chapter presents the analysis, methods, experimental results, and design suggestions to reduce the effects of artifacts. The importance of a closed-loop methodology cannot be overemphasized in neural engineering. However, the design of closed-loop neural interface electronics has been a missing link in BMI systems. This chapter summarizes the mechanisms of different closed-loop neural interface systems, and presents the design of a general–purpose analog PID controller. The PID controller is integrated in a bidirectional neural interface system-on-chip (SoC). Experimental results are presented.
This paper demonstrates a multi-input multi-output (MIMO) robust control approach where multiple scheduled designs are merged to produce a smooth control law. The design is verified using software-in-the-loop (SIL) testing based on blade element theory (BET) for highly realistic flight simulations. An inner-loop attitude controller balances performance and robustness, achieving a fast response time, low overshoot, good noise rejection and minimal lateral–longitudinal coupling. The controllers are formed at several predetermined grid points so the design covers a wide flight envelope. Blade element SIL testing shows that the flight control system preserves stable flight and follows the references well, even under tough weather conditions. The proposed strategy is also compared with a classical autopilot design procedure and is seen to be superior.
Future power generation systems are expected to be dominated by the penetration of renewable energy sources (RES) of which wind power is the most promising source. The penetration of wind power however, has got its associated problems due to the varying wind speeds. As a result the load frequency control (LFC) of the power system having wind power penetration becomes all the more difficult and complex. This paper considers the two-area power system integrated with doubly fed induction generator (DFIG) based wind power and attempts to study the impact of variations of wind power penetration levels on the LFC characteristics with varying step load disturbances. The parameters of interest are taken as frequency and tie-line power deviations. The proposed control scheme is a fuzzy based control technique. The conventional proportional integral (PI) controller is also implemented for comparison purpose. Simulation results are discussed whereby it is clear that the proposed control scheme is very effective and superior to the conventional PI controller.
Genetic Algorithm (GA) has been used in this chapter for a new approach of sub-optimal model reduction in the Nyquist plane and optimal time domain tuning of PID and fractional order (FO) PIλ
Dμ
controllers. Simulation studies show that the Nyquist based new model reduction technique outperforms the conventional H2 norm based reduced parameter modeling technique. With the tuned controller parameters and reduced order model parameter data-set, optimum tuning rules have been developed with a test-bench of higher order processes via Genetic Programming (GP). The GP performs a symbolic regression on the reduced process parameters to evolve a tuning rule which provides the best analytical expression to map the data. The tuning rules are developed for a minimum time domain integral performance index described by weighted sum of error index and controller effort. From the reported Pareto optimal front of GP based optimal rule extraction technique a trade-off can be made between the complexity of the tuning formulae and the control performance. The efficacy of the single-gene and multi-gene GP based tuning rules has been compared with original GA based control performance for the PID and PIλ
Dμ
controllers, handling four different class of representative higher order processes. These rules are very useful for process control engineers as they inherit the power of the GA based tuning methodology, but can be easily calculated without the requirement for running the computationally intensive GA every time. Three dimensional plots of the required variation in PID/FOPID controller parameters with reduced process parameters have been shown as a guideline for the operator. Parametric robustness of the reported GP based tuning rules has also been shown with credible simulation examples.
The internal model control (IMC)-based PID controller is widely used in industrial control problems. This scheme provides a good compromise among set-point tracking, disturbance attenuation, and robustness. Therefore, in this paper, we propose a simple technique to design IMC-PID controller. To illustrate the utility of the proposed technique, different types of linear and nonlinear second-order systems and approximated second-order models of higher-order systems are simulated. The proposed approach depicts quick response to set-point change, good disturbance attenuation, and optimal performances in most of the class of problems when compared to the conventional IMC-PID and other existing popular techniques. The beauty of this paper is that there is no need of highly complex mathematical approaches, and using only simple conventional IMC approach, the improved servo and regulatory results can be achieved.
This paper proposes a simple method for PI/PID controller setting for long dead-time parallel first-orderplus-dead-time model (FOPDT). Using a model approximation technique, the parallel first-order-plusdead-time model plant can be approximated to a FOPDT model. Based on the approximate FOPDT model, using a partial compensation obtains simple tuning rules for PI/PID controller. The unknown controller parameter is then designed on the basis of time-weighted absolute value of the error (ITAE) criterion. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.
The aim of this paper is to present a novel graphical method to design the digital PI controller for integrator plus dead time (IPDT) model which is suitable for many processes. To start with the process and controller transfer functions are transformed from s-domain to z-domain and then the open-loop transfer function is obtained in z-domain. Then the parameters to design the controller are determined. As we need to design the digital controller in frequency domain a bilinear transformation of z-domain to w-domain is used. Let us determine the stability region by combination the traditional D-partition technique and graphical technique in the controller parameters plane. Then sketch the loci of constant stability margins, such as the gain and phase margins, gain and phase crossover frequencies and Smith's vector margin in the parameter space. Also, it will be proven that by varying the coefficients of PI controller one can achieve the gain crossover frequency in the interval [0, ωA max] and the phase crossover frequency in the interval [0, ωB max), where ω A max and ω B max are determined by the parameters of process. By sketching the two loci of indices and obtaining their intersection point, one can approach to desired closed-loop systems specifications. Finally some examples are given to demonstrate the effectiveness of the proposed method.
A Novel approach of designing a feedback compensator for the Electric Vehicle Drive based on Indian Road conditions is dealt here. The performance analysis of PI controller as well as compensator design for the developed transfer function has been done.
This article mainly deals with the control and stability problems of networked Hammerstein with nonlinear input. A novel predictive controller design method is proposed to offset the effect of network delay and data dropout. The controller gain which depends on the time delay of the feedback channel is time-variant. Since we assume that the state is not measurable, the control signal is based on the state estimated by the observer. As for the nonlinear part of the input,We assume it satisfies a sector constraint and treat it as a input inaccuracy. Theoretical results are presented for the closed-loop stability by modeling the system as time-delay Hammerstein system with nonlinear inputs. A second-order Hammerstein system is implemented to show the enhanced performance of this control method.
This paper presents a new optimal PI/PID controller tuning algorithms for low-order plus time-delay processes via LQR approach. A new criterion for selection of the Q and R matrices is proposed which will lead to the desired natural frequency and damping ratio of the closed-loop system. The examples with various dynamics are included to demonstrate the effectiveness of the tuning algorithms and show significant improvement over the existing PID tuning methods. The robustness property of the tuning algorithms is also analyzed, and it is shown that the LQR system is robustly stable for the small modeling error.
This paper deals with intelligent tuning by hybrid system composed of genetic algorithm and clonal selection (CS). This paper uses gain margin (GM) and phase margin (PM) to define the tuning margin of control system for optimal tuning. Up to this time, many intelligent algorithms have been tried in order to improve the intelligent controller performance for industrial areas such as power plant, motor control, chemical control, and so on. However, in the actual plant, they are many limitations in tuning approaching because of computing speed. Therefore, it is difficult to apply for getting optimum value in tuning. In this paper, novel computing scheme has been done by hybrid CS algorithm and genetic algorithm, GM, and PM to obtain an advanced value and effective approach for optimal parameters.
Time delays are components that make time-lag in systems response. They arise in physical, chemical, biological and economic systems, as well as in the process of measurement and computation. In this study, we examine and compare error rates of seven polynomial series which approximate the delays. Moreover we study PID controller as delay compensation scheme, and measure its characteristics under compensated delay with using two tuning methods, “iterative method” and Ziegler-Nichols method.
Answering the greenhouse gases emission reduction and environmentally friendly energy production policies, Microgrids (MGs) represent a new thought pattern with respect to the electricity service. Since, heterogeneous power sources are leveraged to power a local load, fluctuating production from renewable sources (e.g. solar or wind), combined with variable profile of the consumption, can cause system instabilities. This paper focuses on the modelling and simulation of a flywheel energy storage system (FESS). Its contribution in smoothing the power production profile is analyzed, and simulations results are discussed.
This well-respected work discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude.
MATLAB statements and problems are thoroughly and carefully integrated throughout the book to offer readers a complete design picture. Many of the figures in the book were created by Matlab files, which are available to download at the link below for interested readers.
An analytical method is proposed to tune the PIIPID controller to pass through two design points on the Nyquist curve as specified by the gain and phase margins. They are the appropriate use of pole-zero cancellation and algebraic simplification of certain nonlinear functions. The required process parameters can be simply computed on the basis of the ultimate gain, ultimate period and static gain which may be supplied by the well-known relay-feedback or other auto-tuners. The excellent perfonnance of the tuning formulae has been substantiated by extensive simulation
The IMC-PID tuning rules reduce the tuning process to the selection of one tuning parameter as opposed to three. In addition, the single parameter is directly related to the closed-loop speed of response and robustness. Process models can be developed directly from open-loop tests or combinations of tests and first-principle equations. Disturbance rejection can be significantly improved for long time-constant-to-deadtime processes by assuming they are deadtime-plus-integrator forms. Finally, the rules are being successfully applied to industrial processes. The first example given illustrated how the application of the rules quickly led to high-quality tuning parameters for a troublesome level control loop. The second illustrated how the rules were applied to obtain very responsive tuning for control of composition for a high-purity distillation column.
Analytical formulae for designing PID controllers to give specified gain and phase margins have been proposed recently in the literature. This approach is attractive as the gain margin and phase margin serve as important measures of not only performance but also robustness. Another popular approach with similar emphasis is the internal model control method. In this paper, a comparison study of these two approaches for designing a PI and a PID controller is made. The comparison shows the differences and the similarities of the two approaches. Recommendations on when and which method to apply are also given.
The dynamic behavior of a multiple-capacity passive system is compared to that of a single-capacity system of appropriate “time constant with a finite time delay.” Such a comparison indicates that the latter system reproduces the dynamic behavior of the multiple-capacity system with sufficient accuracy for most engineering purposes. This fact makes it possible to characterize such systems by a single parameter, the ratio of the time constant (L) of the single-capacity system to the delay (D). Values of the control constants for various degrees of stability are plotted against this ratio (L/D) for proportional, proportional-plus-integral, proportional-plus-integral-plus-derivative type regulators. An electronic analog computer was used in obtaining the data.
Model uncertainty is one of the major problems facing control system designers in practice. In this paper a general approach is outlined for the assessment of the effects of model uncertainty on control system performance. Also discussed are methods for the design of controllers which meet given performance specifications despite model uncertainty. The power of the new techniques as well as the failure of the traditional ones is illustrated on two examples widely studied in the process control literature: The design of Smith predictor controllers and the design of 2-point composition controllers for high purity distillation columns.
The traditional methods for the actuator and sensor selection based on LQG theory have found only limited use in process control. The main reason is that LQG theory offers a handy design tool but the numerical value of the quadratic performance index lacks practical significance. A new approach to control structure synthesis using a frequency domain description of the system is suggested here. The screening of alternate control structures is carried out in two stages. At the first stage the fundamental limitations to control quality, which are shown to be RHP transmission zeroes and time delays, are identified and preliminary control structure selection is made. In the second stage the performance of the remaining systems is compared when they are robust with respect to a prespecified model-plant mismatch. The intuitive appeal of this screening procedure should make it attractive for industrial applications. Some features of this new method are illustrated on a heat exchanger network and a distillation column.
Simple formulae are derived to tune/design the PI and PID controllers to meet user-specified gain margin and phase margin. These formulae are particularly useful in the context of adaptive control and auto-tuning, where the controller parameters have to be calculated on-line. The results in this paper can be used to predict the achievable rise time of the closed-loop system, which is useful for self-diagnosis—a desirable feature of ‘intelligent’ controllers. New insights into the internal model control design for the PID controller are also given.
Adaptive techniques such as gain scheduling, automatic tuning and continuous adaptation have been used in industrial single-loop controllers for about ten years. This paper gives a survey of the different adaptive techniques, the underlying process models and control designs. An overview of industrial products is also presented, which includes a fairly detailed investigation of four different adaptive single-loop controllers.
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.
This paper is concerned with a theoretical study of the control of a single-capacity process with dead-period lag. Characteristic equations corresponding to the application of proportional, proportional-plus-derivative, proportional-plus-reset, and proportional-plus-reset-plus-derivative responses are used to graph the controller parameters necessary to obtain a desired degree of stability. The degree of stability is taken to be associated with the amplitude ratio of the lowest-frequency harmonic mode. Effects of the various controller parameters are shown and a method is suggested to determine the adjustable parameters for a desired degree of stability.
The paper first briefly reviews the analytical procedures for obtaining optimum PID controller settings for minimisation of time weighted integral performance criteria. The approach is then used to obtain formulae for setting the controller parameters for a first-order plus dead time plant model which is a common approximation used in the process industries. These results are further extended to obtain two procedures, which can be used with the relay autotuning approach, to find the required controller parameters for optimisation of the integral of time error squared criterion. Good results have been obtained when these criteria are used with other plant models.
The accuracy of the Ziegler-Nichols tuning formula is reviewed in
the context of PID and PI autotuning. For PID autotuning, it is shown
that, for excessive overshoot in the set-point response, set-point
weighting can reduce the overshoot to specified values, and the original
Ziegler-Nichols tuning formula can be retained. It is also shown that
set-point weighting is superior to the conventional solution of reducing
large overshoot by gain detuning or set-point filtering. However, for
excessive set-point undershoot, the tuning formula will have to be
modified. For PI autotuning, it is shown that the Ziegler-Nichols tuning
formula is inadequate and has to be completely revised. The application
of set-point weighting and the modification of the tuning formula can be
based simply on the knowledge of the normalised gain or normalised
deadtime of the process. These heuristic refinements, when incorporated,
will give appreciable improvement in the performance of autotuners
It is well known that some time-token medium access protocols for
local area networks (LANs) like the IEEE 802.4 token bus and the FDDI
token ring can guarantee the medium access delay for time-constrained
packets. However, a problem which has been largely overlooked is how
these protocols can be made to provide a maximum throughput for
nontime-constrained packets while guaranteeing the delay bound of
time-constrained packets. The authors first show how the parameters of
the IEEE 802.4 token bus and the FDDI token ring can be set to solve the
above problem. Then, they design a new timer mechanism for the
timed-token protocols which provides the highest guaranteed throughput
of nontime-constrained packets among a set of medium access protocols
called the token passing protocol, to which most of the existing
non-contention LAN protocols belong. They present numerical examples to
compare different protocols, all of which have shown the superiority of
the proposed protocol to the others
The CAMAC instrumentation system developed by the ESONE Committee of European laboratories has been endorsed by the U. S. AEC NIM Committee as a dataway system complementary to the NIM (Nuclear Instrument Module) system. CAMAC is described in a general way in this introductory paper which is followed by papers that discuss the system in greater detail. This paper is an updated version of the introductory paper that appeared in the April 1971 IEEE Transactions on Nuclear Science. Copyright © 1973 by The Institute of Electrical and Electronics Engineers, Inc.
In this paper the stability problem of a first-order system with time- or state-variable time delay is investigated and the proposition that the time-varying system is not always stable (unstable) even if the frozen-time system is stable (unstable) is verified for a variable time delay system by several examples.
Heterogeneous traffic types compete for access to a shared
resource (satellite channel, bus, etc.). If a packet is not immediately
given access to the resource, it waits in a buffer, which is assumed to
be infinite. The traffic types are partitioned into two groups:
interactive and noninteractive, and the average delay of each of the
interactive types is required below given thresholds. The problem of
finding an optimal scheduling policy that minimizes a linear combination
of the average delays for the noninteractive types while meeting the
design constraints is considered. Simple necessary and sufficient
conditions are derived for the existence of a policy that satisfies the
constraints. An algorithm is given that decomposes the traffic types
into an ordered arrangement of groups, and the existence of a policy
that gives strict priority accordingly is established. Under weak
conditions on the costs and rates, it is shown that all optimal policies
must have this structural property. Sensitivity and aggregation analyses
are given. An optimal policy is constructed and is shown to have many
appealing properties
Automatic tuning of optimum PID controllersTuning of PID controllers based on gain and phase margins specifications On the automatic control of generalized passive systems Automatic tun-ing and adaptation for PID controllers-A survey A comparison of two design methods for PID controllers
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Feedback Control of Dynamic Systems Optimum settings for automatic controllers Refinements of the Ziegler-Nichols tuning formula Theoretical consideration of retarded control
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- G A Cohen
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Gain and phase margins formula [lo] REFERENCES G. F. Franklin, J. D. Powell, and A. E. Naeini, Feedback Control of Dynamic Systems. New York Addison-Wesley, 1986. J. G. Ziegler and N. B. Nichols, " Optimum settings for automatic controllers, " Trans. ASME, vol. 64, pp. 759-768, 1942. C. C. Hang, K. J. Astrom, and W. K. Ho, " Refinements of the Ziegler-Nichols tuning formula, " IEE Proc. D, Contr. Theory Appl., vol. 138, no. 2, pp. 111-118, 1991. G. H. Cohen and G. A. Coon, " Theoretical consideration of retarded control, " Trans. ASME, vol. 75, pp. 827-834, 1953. M. Morari and E. Zafiriou, Robust Process Control. Englewood Cliffs, NJ: Prentice-Hall, 1989. I.-L. Chien and P. S. Fruehauf, " Consider IMC tuning to improve controller performance, " Chemical Eng. Progress, vol. 86, no. 10, pp. 33-41, 1990. C. A. Smith and A. B. Corripio, Principles and Practice of Automatic Process Control.