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Adaptive Control Based on RBF Neural Network Approximation in a Quadrotor
Abstract
This paper proposes an adaptive control for a quadrotor drone with uncertain dynamics and subject to unknown disturbances. Radial Base Function Neural Network (RBFNN) is used to approximate the unknowns in the system. The output layer of the RBFNN is used as a compensator that estimates and eventually eliminates the physical uncertainties along with an adaptive controller designed to give robustness to the system. Hence, faster error convergence can be achieved. The closed loop system was analyzed by a Lyapunov function and the proposed controller performance is tested by Matlab /Simulink. The results prove the efficiency of the proposed system.
... However, the location of COM should be consistent with the center of the geometry. Although [17] compensated for the model uncertainty through a radial base function neural network, the variation in COM location was not reflected in the orientational dynamic model. Unlike multiple studies [9] - [14] and [16] - [17], the estimation of the variation of COM, MOI, and mass through the adaptation law was presented in [18]. ...
... Although [17] compensated for the model uncertainty through a radial base function neural network, the variation in COM location was not reflected in the orientational dynamic model. Unlike multiple studies [9] - [14] and [16] - [17], the estimation of the variation of COM, MOI, and mass through the adaptation law was presented in [18]. The shortcoming of reference [18] is that the sharp increase or decrease in COM variation estimation occurs owing to motor saturation, and the convergence rate of MOI parameter estimation is too slow to be reflected in the control scheme. ...
This study focuses on the system identification of a quadrotor under an unknown payload with a time-optimal trajectory. A model-based control scheme should be utilized for a quadrotor, which does not necessarily guarantee robustness to model uncertainty. Thus, accurate system identification is required during flight. However, inertia parameter identification for the control scheme is vulnerable to sensor noise without a trajectory that produces rich data. We utilized Kalman filter (KF), which estimates the angular velocity, to reduce noise. In the process model of KF, the variance attributed to model uncertainty is derived, and the derived variance plays a pivotal role in adjusting Kalman gain. Recursive least squares (RLS) was utilized to identify the inertia parameter. However, all inertia parameters cannot always be observed with a time-optimal trajectory. Thus, this study proposes a criterion that distinguishes between observable and unobservable parameters and the correction law depending on the criteria. The correction law prevents RLS from correcting the unobservable parameters. We call this method the observability-aware RLS with KF. This study compared RLS, RLS with a low-pass filter (LPF), and observability-aware RLS with KF. While RLS with LPF shows a sharp increase or decrease in MOI, COM offset, and sensor location, ours does not. RLS without any filtering has an inaccurate estimation of MOI and the height of the sensor location. However, our approach is sufficiently accurate to be applied to model-based control.
In this paper, a fractional nonlinear control strategy based on the nested saturations technique and the Caputo-Fabrizio derivative for a quadrotor aircraft, to maintain desired position and orientation in stationary flight and trajectory tracking tasks, is proposed and developed. In addition, the dynamic model is obtained by using the Euler–Lagrange formulation, and then it is generalized to an arbitrary order through the Caputo-Fabrizio derivative. The traditional nonlinear control based on the nested saturation technique is also developed and implemented on the quadrotor for comparison purposes between both control schemes. Numerical simulations demonstrated the superiority of the proposed control strategy for stabilizing the quadrotor at hover and reaching the desired position and orientation, over its integer-order counterpart. In addition, three additional desired trajectories are considered, keeping the same gains and orders, to demonstrate the robustness of the proposed control scheme under different operating conditions. In this sense, our controller presents significant performance improvements, which were validated through system simulations. Our proposed control system and its traditional counterpart were tuned experimentally using the response of the system to a desired trajectory.
This paper investigates the adaptive finite-time tracking control problem for a class of switched nonlinear systems with unmodeled dynamics. In practical applications, switched systems usually possess unfavourable factors, such as unmeasured states and unmodeled dynamics both of which are taken into account in this paper. A dynamic signal defined with a special property is introduced in this paper to improve control performance while garanteeing stability of the controlled system. By designing an observer, a finite-time adaptive output-feedback tracking controller is constructed via the backstepping technique. Then, the finite-time stability problem of the considered systems is studied. It is shown that all the signals in the closed-loop system are semi-globally uniformly finite-time bounded (SGFUB), and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. It is noted that, the design process is less complex than some existing results on tackling control problems of nonlinear systems with unmodeled dynamics. In the example, the simulation result testifies the effectiveness of the proposed method.
Unmanned autonomous aerial vehicles have become a real center of interest. In the last few years, their utilization has significantly increased. During the last decade many research papers have been published on the topic of modeling and control strategies of autonomous multirotors. Today, they are used for multiple tasks such as navigation and transportation. This paper presents the development of a dynamic modeling and control algorithm-backstepping controller of an autonomous hexa-rotor microcopter. The autonomous hexa-rotor microcopter is an under-actuated and dynamically unstable nonlinear system. The model that represents the dynamic behavior of the hexa-rotor microcopter is complex. Unmanned autonomous aerial vehicles applications are commonly associated with exploration, inspection or surveillance tasks.
High-order sliding mode (HOSM) control is known to provide for finite-time-exact output regulation of
uncertain systems with known relative degrees. Yet the corresponding universal HOSM controllers are
typically constructed by special recursive procedures and have complicated form. We propose two new
families of homogeneous HOSM controllers of a very simple form. Lyapunov functions are provided for a
significant part of the first-family controllers. The second family consists of quasi-continuous controllers,
which can be done arbitrarily smooth everywhere outside of the HOSM manifold. A regularization
procedure ensures high-accuracy output regulation by means of control with required smoothness level.
Output-feedback controllers are constructed. Controllers of the orders 3–5 are demonstrated.
In this paper, we present a model of a four rotor vertical take-off and landing (VTOL) unmanned air vehicle known as quadrotor aircraft. And we explained its control architecture including vision based control. Quadrotors have generated considerable interest in both the control community due to their complex dynamics and military because of their advantages over regular air vehicles. The proposed dynamical model which comprises gyroscopic effects and its control strategies can be source for future works.
This paper addresses the robust trajectory tracking problem for a redundantly actuated omnidirectional mobile manipulator in the presence of uncertainties and disturbances. The development of control algorithms is based on sliding mode control (SMC) technique. First, a dynamic model is derived based on the practical omnidirectional mobile manipulator system. Then, a SMC scheme, based on the fixed large upper boundedness of the system dynamics (FLUBSMC), is designed to ensure trajectory tracking of the closed-loop system. However, the FLUBSMC scheme has inherent deficiency, which needs computing the upper boundedness of the system dynamics, and may cause high noise amplification and high control cost, particularly for the complex dynamics of the omnidirectional mobile manipulator system. Therefore, a robust neural network (NN)-based sliding mode controller (NNSMC), which uses an NN to identify the unstructured system dynamics directly, is further proposed to overcome the disadvantages of FLUBSMC and reduce the online computing burden of conventional NN adaptive controllers. Using learning ability of NN, NNSMC can coordinately control the omnidirectional mobile platform and the mounted manipulator with different dynamics effectively. The stability of the closed-loop system, the convergence of the NN weight-updating process, and the boundedness of the NN weight estimation errors are all strictly guaranteed. Then, in order to accelerate the NN learning efficiency, a partitioned NN structure is applied. Finally, simulation examples are given to demonstrate the proposed NNSMC approach can guarantee the whole system's convergence to the desired manifold with prescribed performance.
In this paper, an adaptive multi-model sliding mode controller for robotic manipulators is presented. By using the multiple models technique, the nominal part of the control signal is constructed according to the most appropriate model at different environments. Adaptive single-input–single-output (SISO) fuzzy systems or radial basis function (RBF) neural networks, regarding their functional equivalence property, are used to approximate the discontinuous part of control signal; control gain, in a classical sliding mode controller. The key feature of this scheme is that prior knowledge of the system uncertainties is not required to guarantee the stability. Also the chattering phenomenon in sliding mode control and the steady-state tracking error are eliminated. Moreover, a theoretical proof of the stability and convergence of the proposed scheme using the Lyapunov method is presented.
The latest technological progress in sensors, actuators and energy storage devices enables the developments of miniature VTOL systems. In this paper we present the results of two nonlinear control techniques applied to an autonomous micro helicopter called Quadrotor. A backstepping and a sliding-mode techniques. We performed various simulations in open and closed loop and implemented several experiments on the test-bench to validate the control laws. Finally, we discuss the results of each approach. These developments are part of the OS4 project in our lab.
The research on autonomous miniature flying robots has intensified considerably thanks to the recent growth of civil and military interest in unmanned aerial vehicles (UAV). This paper summarizes the final results of the modeling and control parts of OS4 project, which focused on design and control of a quadrotor. It introduces a simulation model which takes into account the variation of the aerodynamical coefficients due to vehicle motion. The control parameters found with this model are successfully used on the helicopter without re-tuning. The last part of this paper describes the control approach (integral backstepping) and the scheme we propose for full control of quadrotors (attitude, altitude and position). Finally, the results of autonomous take-off, hover, landing and collision avoidance are presented.
In this work, a novel structure of a Quadrotor Unmanned Aerial Vehicle (UAV) is proposed to change the dynamics during flight. The proposed mechanism is presented which consists of extendable plates that move along the horizontal axes from the body frame respectively. Essentially, the main goal behind this novel architecture is to enhance performance and improve flight duration in reaching the desired position. The Euler dynamic model is derived to represent the multirotor equation of motion. Basic PID controllers were implemented to demonstrate the concept and to analyse the vehicle behaviour as the structure is altered during flight. A physical modelling software is also used to study the multi-body interactions of rigid bodies as well as the dynamic response. By comparing the performance between the proposed system and the traditional version, the paper reveals improved flight performance for attitude and position tracking. The mathematical representation of the dynamic system was also verified using Msc ADAMS as identical control inputs where simultaneously applied.
The objective of this work is to improve tracking control of uncertain robotic manipulator systems. Parameter variations, unmodeled dynamics and unknown perturbations affect the tracking performance of robots which add more challenges to a model-based nonlinear controller. The proposed approach in this paper utilizes a modified terminal super-twisting that has a dynamic model of the sliding function and a new stability conditions which ensures good tracking, prevents chattering and resolves the singularity in nonlinear terminal switching functions. The developed modified fast terminal super twisting controller ensures accurate joint position tracking while bypassing the singularity problem and removing the chattering phenomenon. Finally, it is shown through analytical analysis and numerical simulations that the proposed nonlinear control technique is robust, presents less chattering than the standard supertwisting algorithm in addition to faster convergence of the tracking error to zero.
Considering the bias of the dynamics which is a global trend of the dynamical equation because of the gravity or the constant payloads, two kinds of adaptive bias radial basis function neural network (RBFNN) control schemes, which are the local bias scheme and the global bias scheme, are proposed to remedy the negative influence of the bias of the dynamics. Such slight modifications lead to the following two attractive features: 1) both of two schemes can improve the approximation accuracy of the RBFNN for the dynamics with significant bias, and then enhance the control performance correspondingly; 2) when the inputs deviate from the approximation domain of the RBFNN because of the large payloads, the controller with the local bias or global bias degrades to the PID controller to push the states back. It improves the robustness of the adaptive RBFNN controller further. We also propose a simpler controller structure that reduces the dimension of the input vectors from 4n to 3n, where n is the degree of freedom of the manipulator. It exponentially decreases the computation cost of the RBFNNs. Uniform ultimate boundedness of the closed-loop system is proved by the Lyapunov stability theory. Finally, simulation results demonstrate the effectiveness of the proposed two schemes.
When the electromagnetic suspension (EMS) type maglev vehicle is traveling over a track, the airgap must be maintained between the electromagnet and the track to prevent contact with that track. Because of the open-loop instability of the EMS system, the current must be actively controlled to maintain the target airgap. However, the maglev system suffers from the strong nonlinearity, force saturation, track flexibility, and feedback signals with network time-delay, hence making the controller design even more difficult. In this paper, the minimum levitation unit of the maglev vehicle system has been established. An amplitude saturation controller (ASC), which can ensure the generation of only saturated unidirectional attractive force, is thus proposed. The stability and convergence of the closed-loop signals are proven based on the Lyapunov method. Subsequently, ASC is improved based on radial basis function (RBF) neural networks, and a neural network-based supervisor controller (NNBSC) is thus designed. The ASC plays the main role in the initial stage. As the neural network learns the control trend, it will gradually transition to the neural network controller. Simulation results are provided to illustrate the specific merit of the NNBSC. Hardware experimental results of a full-scale IoT EMS maglev train are included to validate the effectiveness and robustness of the presented control method as regards time-delay.
The paper studies the asynchronous observer-based sliding mode control (SMC) for Markov jump systems (MJSs) with actuator failures. Considering the phenomena of unmeasurable states and the case that the controller/observer to be devised have different modes from the original systems, a hidden Markov model (HMM) is used to construct an asynchronous observer and the corresponding sliding surface is designed. Then, the asynchronous SMC strategy is developed to guarantee the reachability of the predetermined sliding surface in a limited time. A sufficient condition is established for the mean-square stability of the overall closed-loop systems and the desired controller is designed. Moreover, when the conditional probabilities describing the mode asynchronism are only partially known for the HMM in the systems, the related results are also given. Finally, simulation results show the usefulness of the developed techniques.
The output constraints widely exist in the physical systems and severely affect the performance of the closed-loop system. This paper considers the second-order sliding mode controller design subject to an output constraint. By constructing a new barrier Lyapunov function and applying the technique of adding a power integrator, a novel second-order sliding mode control algorithm, which can be used to deal with the output constraint problem, has been developed. The proposed sliding mode algorithm enables the output variable not to violate the boundary of the constraint region. Meanwhile, it has been shown that under the output constraint the sliding variable can still be stabilized to zero in a finite time. Finally, an academic example is given to verify the feasibility of the proposed second-order sliding mode algorithm.
Bilateral teleoperation system has raised expansive concern as it's excellent behaviors in executing the tasks in the remote, unstructured and dangerous areas via the cooperative operation systems. In this paper, an RBF-neural-network-based adaptive robust control design is proposed for nonlinear bilateral teleoperation manipulators to cope with the main issues including the communication time delay, various nonlinearities and uncertainties. Specifically, the slave environmental dynamics is modeled by a general RBF neural network, and its parameters are estimated and then transmitted for the environmental torque reconstruction in the master side. Since the parameters of neural network (which are non-power signals) are transmitted instead of the traditional environmental torque in the communication channel, the previous existing passivity problem under time delay is avoided. In both of master and slave sides, the trajectory creators are applied to generate the desired trajectories, and the RBF-neural-network-based adaptive robust controllers are designed subsequently to handle the nonlinearities and uncertainties. Theoretically, the proposed control algorithm can guarantee the global stability of bilateral teleoperation manipulators under time delay, and the good transparency performance with both position tracking and force feedback is also achieved simultaneously. The real platform comparative experiments are carried out, and the results show the good position tracking to execute precise operation and the good force feedback to detect the sudden disturbance in the environment dynamics.
In this paper, a Three Loop Uncertainties Compensator (TLUC) and Exponential Reaching Law Sliding Mode Controller (ERSM) is proposed and successfully applied to an Unmanned Aerial Vehicles (UAV) quadrotor. The TLUC estimates unknown time-varying uncertainties and perturbations to reduce their effects and to preserve stability. The ERSM is integrated based on the Lyapunov stability theory to obtain fast responses with the lowest possible chattering. The novelty of this paper is that the TLUC can estimate and compensate for uncertainties and unknown time-varying disturbances in three loops. This provides tracking of residual uncertainty to provide a higher level of support to the controller. The performance is verified through analyses, simulations and experiments.
This paper proposes an improved non-singular terminal super twisting control for the problem of position and attitude
tracking of quadrotor systems suffering from uncertainties and disturbances. The super-twisting algorithm STA is a
second order sliding mode known to be a very effective control used to provide high precision and less chattering
for uncertain nonlinear electromechanical systems. The proposed method is based on a non-singular terminal sliding
surface with new exponent that solves the problem of singularity. The design procedure and the stability analysis of the
closed loop system using Lyapunov theory are detailed for the considered system. Finally, the proposed control scheme
is tested in simulations and by experiments on the parrot-rolling spider quadrotor. Moreover, a comparison is made with
the standard STA in the simulation part. The results obtained show adequate performance in trajectory tracking and
chattering reduction.
The second-order sliding mode (SOSM) controller design problem for a class of sliding mode dynamics subject to an upper-triangular structure has been discussed in this paper. The proposed SOSM controller design involves two steps. First, a Lyapunov-based SOSM controller is developed by using the adding a power integrator technique to locally finite-time stabilize the sliding variables. Second, by combining the local SOSM controller with a saturation function, a novel SOSM controller with a saturation level is constructed. The feature of the new SOSM controller lies in that the saturation level can be tuned not only to guarantee the global convergence but also to improve the dynamic performance. Lyapunov analysis has been utilized to test the finite-time stability of the closed-loop sliding mode dynamics. The proposed method is eventually demonstrated by simulation results.
In order to overcome the disadvantages of the traditional PD control in manipulator, a new point to point control of manipulator with interference and gravity uncertainty is proposed. On the Basis of PD control structure, the RBF neural network is introduced to realize the gravity compensation, and a robustness analysis is also given with respect to the approximation error of RBF neural network. The lyapunov method shows that the better performance can be obtained with the new scheme as compared to the present control methods. © 2018, International Association of Engineers. All rights reserved.
This paper investigates a novel integral sliding mode control (ISMC) strategy for the waypoint tracking control of a quadrotor in the presence of model uncertainties and external disturbances. The proposed controller has the inner-outer loop structure: The outer loop is to generate the reference signals of the roll and pitch angles, while the inner loop is designed by using the ISMC technique for the quadrotor to track the desired x, y positions, roll and pitch angles. The Lyapunov stability analysis is provided to show that the negative effects of the bounded model uncertainties and external disturbances can be significantly decreased. The designed controller is then applied to a heterogeneous multi-agent system (MAS) consisting of quadrotors and two-wheeled mobile robots (2WMRs) to solve the consensus problem. We present the control algorithms for the 2WMRs and quadrotors. Consensus of the heterogeneous MAS can be reached if the switching graphs always have a spanning tree. Finally, the experimental tests are conducted to verify the effectiveness of the proposed control methods.
In this paper, a novel nonlinear control strategy along with its simulation for a quadrotor helicopter is proposed. The normal 6-DOF dynamic model of the quadrotor based on the Newton-Euler formula as well as the model with external uncertain disturbances are established. Considering the underactuated and strongly coupled characteristics of quadrotor helicopter, we design a nonlinear control method by using integral backstepping combined with the sliding mode control (integral BS-SMC) to stabilize the quadrotor attitude and to accomplish the task of trajectory tracking. The designed controllers based on the hierarchical control scheme can be divided into rotational controller and translational controller and their stability are validated by the Lyapunov stability theorem. By means of the proposed controllers, the chattering phenomenon and discontinuousness of control inputs faced by traditional sliding mode control (SMC) can be avoided. The feasibility of the control approach presented in this paper is verified by the simulations under different scenarios. The results show that the nonlinear control method not only has a better tracking performance than others but also has a higher robustness when unknown disturbances occur.
This paper presents an adaptive trajectory tracking control strategy for quadrotor micro aerial vehicles (MAVs). The proposed approach, while maintaining the common assumption of an orientation dynamics faster than the translational one, removes the assumption of absence of external disturbances and of geometric center coincident with the Center of Mass (CoM). In particular, the trajectory tracking control law is made adaptive with respect to the presence of external forces and moments (e.g., due to wind) and to the uncertainty of parameters of the dynamic model, such as the position of the CoM. A stability analysis is presented to analytically support the proposed controller, while numerical simulations are provided in order to validate its performance.
In this paper, we address an adaptive control problem for a class of nonlinear strict-feedback systems with uncertain parameter. The full states of the systems are constrained in the bounded sets and the boundaries of sets are compelled in the asymmetric time-varying regions, i.e., the full state time-varying constraints are considered here. This is for the first time to control such a class of systems. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions (TABLFs) are employed in each step of the backsstepping design and we also establish a novel control TABLF scheme to ensure the asymptotic output tracking performance. The performances of the adaptive TABLF-based control are verified by a simulation example.
In this paper, a robust adaptive control scheme is proposed based on backstepping techniques for a class of nonlinear systems with unknown parameters. A modeling error may also exist in every state equation or channel and it is bounded by a known function which is allowed to depend on all system states. It is shown that the proposed adaptive control scheme can ensure all signals in the closed-loop system bounded, if the strength of system modeling errors is sufficiently weak. Transient performance is also established. Thus stabilizing systems in classical strict-feedback forms with sufficiently small non-triangular structural perturbations is successfully addressed. In the case that system parameters are known, a non-adaptive robust controller is designed to globally exponentially stabilize such a class of nonlinear systems. Finally simulation studies are used to verify the effectiveness of the proposed scheme.
Emerging applications of quadrotor vertical take-off and landing (VTOL) unmanned aerial vehicles (UAVs) in various fields have created a need for demanding controllers that are able to counter several challenges, inter alia, nonlinearity, underactuated dynamics, lack of modeling, and uncertainties in the working environment. This study compares and contrasts type-1 and type- 2 fuzzy neural networks (T2FNNs) for the trajectory tracking problem of quadrotor VTOL aircraft in terms of their tracking accuracy and control efforts. A realistic trajectory consisting of both straight lines and curvatures for a surveillance operation with minimum snap property, which is feasible regarding input constraints of the quadrotor is generated to evaluate the proposed controllers. In order to imitate the outdoor noisy and timevarying working conditions, realistic uncertainties, such as wind and gust disturbances, are fed to the real-time experiment in the laboratory environment. Furthermore, a cost function based on the integral of the square of the sliding surface, which gives the optimal parameter update rules, is used to train the consequent part parameters of the T2FNN. Thanks to the learning capability of the proposed controllers, experimental results show that the efficiency and efficacy of the learning algorithms that the proposed T2FNN-based controller with the optimal tuning algorithm is 50% superior to a conventional proportional-derivative (PD) controller in terms of control accuracy but requires more controls effort. T2FNN structures are also shown to possess better noise reduction property as compared to their type-1 counterparts in the presence of unmodeled noise and disturbances.
This study gives the mathematic model of a quadrotor unmanned aerial vehicle (UAV) and then proposes a robust nonlinear controller which combines the sliding-mode control technique and the backstepping control technique. To achieve Cartesian position trajectory tracking capability, the construction of the controller can be divided into two stages: a regular SMC controller for attitude subsystem (inner loop) is first developed to guarantee fast convergence rapidity of Euler angles and the backstepping technique is applied to the position loop until desired attitudes are obtained and then the ultimate control laws. The stability of the closed-loop system is guaranteed by stabilizing each of the subsystems step by step and the robustness of the controller against model uncertainty and external disturbances is investigated. In addition, an adaptive observer-based fault estimation scheme is also considered for taking off mode. Simulations are conducted to demonstrate the effectiveness of the designed robust nonlinear controller and the fault estimation scheme.
The design of an adaptive output feedback compensator is addressed to reject biased multi-sinusoidal disturbances of unknown amplitudes, phases and frequencies, acting on unknown stable single-input single-output linear systems of unknown order and relative degree. A single biased sinusoidal disturbance is first considered. It is shown that the knowledge of the sign of the real part (or the imaginary part) of its transfer function at zero and at the disturbance frequency is sufficient for the explicit design of an adaptive compensator which guarantees local exponential convergence to zero of the system output and of the frequency estimation error. This result is generalized to the case of biased multi-sinusoidal disturbances. As a special case, an adaptive notch filter which provides the unknown frequencies contained in the disturbance is obtained.
This article presents a new method of designing the adaptive backstepping controller for triangular fractional order systems with non-commensurate orders. The fractional order indirect Lyapunov method is available for the case, by introducing the appropriate transformations of frequency distributed model. Meanwhile, based on the semigroup property of fractional order derivative and the fractional order tracking differentiator, we extend the result to the case. The case of controlling fractional order systems with unknown control input coefficient is also investigated. Simulation examples are given to demonstrate the effectiveness of the proposed controllers.
Radial Basis Function (RBF) Neural Network Control for Mechanical Systems is motivated by the need for systematic design approaches to stable adaptive control system design using neural network approximation-based techniques. The main objectives of the book are to introduce the concrete design methods and MATLAB simulation of stable adaptive RBF neural control strategies. In this book, a broad range of implementable neural network control design methods for mechanical systems are presented, such as robot manipulators, inverted pendulums, single link flexible joint robots, motors, etc. Advanced neural network controller design methods and their stability analysis are explored. The book provides readers with the fundamentals of neural network control system design. This book is intended for the researchers in the fields of neural adaptive control, mechanical systems, Matlab simulation, engineering design, robotics and automation. © Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg 2013. All rights are reserved.
Advanced Sliding Mode Control for Mechanical Systems
___Design, Analysis and Matlab Simulation
In the formulation of any control problem there will typically be discrepancies between the actual plant and the mathematical model developed for controller design. This mismatch may be due to unmodelled dynamics, variation in system parameters or the approximation of complex plant behavior by a straightforward model .The engineer must ensure that the resulting controller has the ability to produce the required performance levels in practice despite such plant /model mismatches. This has led to an intense interest in the development of so-called robust control methods which seek to solve this problem. One particular approach to robust controller design is the so-called sliding mode control methodology.
One of the most intriguing aspects of sliding mode is the discontinuous nature of the control action whose primary function of each of the feedback channels is to switch between two distinctively different system structures (or components) such that a new type of system motion, called sliding mode, exists in a manifold. This peculiar system characteristic is claimed to result in superb system performance which includes insensitivity to parameter variations, and complete rejection of disturbances.
Sliding mode control is a particular type of variable structure control. In sliding mode control, the control system are designed to drive and then constrain the system state to lie within a neighborhood of the switching function .There are two main advantages to this approach. Firstly, the dynamic behaviour of the system may be tailored by the particular choice of switching function. Secondly, the closed-loop response becomes totally insensitive to a particular class of uncertainty. The latter invariance property clearly makes the methodology an appropriate candidate for robust control. In addition, the ability to specify performance directly makes sliding mode control attractive from the design perspective.
The sliding mode design approach consists of two components. The first involves the design of a switching function so that the sliding motion satisfies design specifications. The second is concerned with the selection of a control law which will make the switching function attractive to the system state. Note that this control law is not necessarily discontinuous.
The chattering phenomenon is generally perceived as motion which oscillates about the sliding manifold. There are two possible mechanisms which produce such a motion. First, in the absence of switching non-idealities such as delays, i.e., the switching device is switching ideally at an infinite frequency, the presence of parasitic dynamics in series with the plant causes a small amplitude high-frequency oscillation to appear in the neighborhood of the sliding manifold. These parasitic dynamics represent the fast actuator and sensor dynamics. Secondly, the switching non-idealities alone can cause such high-frequency oscillations.
It is our goal to accomplish these objectives:
• Provide reasonable methods of the chattering phenomenon alleviating;
• Offer a catalog of implementable robust sliding mode control design solutions for engineering applications;
• Provide advanced sliding mode controller design methods and their stability analysis;
• For each sliding mode control algorithm, we offer its simulation example and Matlab program.
This book provides the reader with a thorough grounding in the sliding mode controller design. From this basis, more advanced theoretical results are developed. Typical sliding mode controller design is emphasized using Matlab simulation. In this book, concrete case studies, which present the results of sliding mode controller implementations, are used to illustrate the successful practical application of the theory.
The book is structured as follows. Chapter 1 introduces the concept of sliding mode control and illustrates the attendant features of robustness and performance specification using a straightforward example and graphical exposition, several typical sliding mode controllers for continuous system are introduced, detailed stability analysis, simulation examples and Matlab programs are given. Chapter 2 introduces several normal sliding mode controllers design, including sliding mode control based on nominal model, global sliding mode control, sliding mode control based on linearization feedback technology and sliding mode control based on low pass filter. Chapter 3 introduces two kind of advanced sliding mode controllers design, including sliding mode control based on LMI technology and sliding mode control based on backstepping technology. Chapter 4 introduces discrete sliding mode controller design, including discrete sliding mode controller design analysis and a kind of discrete sliding mode controller design based on disturbance observer. Chapter 5 introduces a kind of dynamic sliding mode controller design. Chapter 6 introduces a kind of adaptive sliding mode controller design for mechanical systems. Chapter 7 introduces three kind of terminal sliding mode controllers design, including a typical terminal sliding mode controller design, a nonsingular terminal sliding mode controller design and a fast terminal sliding mode controller design. Chapter 8 introduces sliding mode control based on several observers, four kinds of observers are used, including high gain observer, extended state observer, integral-chain differentiator, disturbance observer and delayed output observer. Chapter 9 introduces four kind of fuzzy sliding mode controllers design, including fuzzy sliding mode control based on equivalent control, sliding mode control based on fuzzy switch-gain regulation, sliding mode control based on fuzzy system approximation and adaptive fuzzy control based on fuzzy compensation for manipulator. Chapter 10 introduces two kind of neural network sliding mode controllers design, including sliding mode controller design based on RBF neural network approximation and adaptive RBF network sliding mode control for manipulator. Chapter 11 introduces three kind of sliding mode controllers design for robot, including sliding mode controller design based on input-output stability, sliding mode controller design based on computed torque method and adaptive sliding mode controller design for manipulator. Chapter 12 introduces two kind of sliding mode controllers design for aircraft, which are sliding mode control for helicopter and sliding mode control for an uncertain VTOL aircraft.
Modern non-inertial robots are usually underactuated, such as fix or rotary wing Unmanned Aerial Vehicles (UAVs), underwater or nautical robots, to name a few. Those systems are subject to complex aerodynamic or hydrodynamic forces which make the dynamic model more difficult, and typically are subject to bounded smooth time-varying disturbances. In these systems, it is preferred a formal control approach whose closed-loop system can predict an acceptable performance since deviations may produce instability and may lead to catastrophic results. Backstepping provides an intuitive solution since it solves underactuation iteratively through slaving the actuated subsystem so as to provide a virtual controller in order to stabilize the underactuated subsystem. However it requires a full knowledge of the plant and derivatives of the state, which it is prone to instability for any uncertainty; and although robust sliding mode has been proposed, discontinuities may be harmful for air- or water-borne nonlinear plants. In this paper, a novel robust backstepping-based controller that induces integral sliding modes is proposed for the Newton–Euler underactuated dynamic model of a quadrotor subject to smooth bounded disturbances, including wind gust and sideslip aerodynamics, as well as dissipative drag in position and orientation dynamics. The chattering-free sliding mode compensates for persistent or intermittent, and possible unmatched state dependant disturbances with reduced information of the dynamic model. Representative simulations are presented and discussed.
In this paper, an adaptive compensation control scheme is developed via disturbance observer and quantum information technology for the four-rotor helicopter, which can handle the control problems of helicopter's attitude with the unknown actuator failures and external disturbance effectively. Both the digital simulations and the semi-physical simulations in a Quanser 3-DOF hover platform illustrate the effectiveness of the proposed compensation control scheme. © 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
This paper presents the development of a nonlinear quadrotor simulation framework together with a nonlinear controller. The quadrotor stabilization and navigation problems are tackled using a nested loops control architecture. A nonlinear Backstepping controller is implemented for the inner stabilization loop. It asymptotically tracks reference attitude, altitude and heading trajectories. The outer loop controller generates the reference trajectories for the inner loop controller to reach the desired waypoint. To ensure boundedness of the reference trajectories, a PD controller with a saturation function is used for the outer loop. Due to the complexity involved in controller development and testing, a simulation framework has been developed. It is based on the Gazebo 3D robotics simulator and the Open Dynamics Engine (ODE) library. The framework can effectively facilitate the development and validation of controllers. It has been released and is available at Gazebo quadrotor simulator (2012).
A new approach for induction motor drive control is presented in this paper. The new scheme is based on the direct application of an artificial neural network, trained with sliding mode control, into the feedback control system. Neural network learning is implemented with an on-line adaptation algorithm that inherits robustness and high speed of learning from Sliding Mode Control. The results showed that proportional and integral or proportional, integral and differential controllers used in classical motor drives can be replaced with a neural network with on-line learning. Copyright © 2003 John Wiley & Sons, Ltd.
This brief proposes an adaptive neural sliding mode control method for trajectory tracking of nonholonomic wheeled mobile robots with model uncertainties and external disturbances. The dynamic model with model uncertainties and the kinematic model represented by polar coordinates are considered to design a robust control system. Self recurrent wavelet neural networks (SRWNNs) are used for approximating arbitrary model uncertainties and external disturbances in dynamics of the mobile robot. From the Lyapunov stability theory, we derive online tuning algorithms for all weights of SRWNNs and prove that all signals of a closed-loop system are uniformly ultimately bounded. Finally, we perform computer simulations to demonstrate the robustness and performance of the proposed control system.
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006. Includes bibliographical references (p. 105-107). We present the vision-based estimation of the position and orientation of an object using a single camera relative to a novel target that incorporates the use of moire patterns. The objective is to acquire the six degree of freedom estimation that is essential for the operation of vehicles in close proximity to other craft and landing platforms. A target contains markers to determine relative orientation and locate two sets of orthogonal moire patterns at two different frequencies. A camera is mounted on a small vehicle with the target in the field of view. An algorithm processes the images extracting the attitude and position information of the camera relative to the target utilizing geometry and 4 single-point discrete Fourier transforms (DFTs) on the moire patterns. Manual and autonomous movement tests are conducted to determine the accuracy of the system relative to ground truth locations obtained through an external indoor positioning system. Position estimations with accompanying control techniques have been implemented including hovering, static platform landings, and dynamic platform landings to display the algorithm's ability to provide accurate information to precisely control the vehicle. The results confirm the moire target system's feasibility as a viable option for low-cost relative navigation for indoor and outdoor operations including landing on static and dynamic surfaces. by Glenn P. Tournier. S.M.
In this paper, a combined kinematic/torque output feedback control law is developed for leader-follower-based formation control using backstepping to accommodate the dynamics of the robots and the formation in contrast with kinematic-based formation controllers. A neural network (NN) is introduced to approximate the dynamics of the follower and its leader using online weight tuning. Furthermore, a novel NN observer is designed to estimate the linear and angular velocities of both the follower robot and its leader. It is shown, by using the Lyapunov theory, that the errors for the entire formation are uniformly ultimately bounded while relaxing the separation principle. In addition, the stability of the formation in the presence of obstacles, is examined using Lyapunov methods, and by treating other robots in the formation as obstacles, collisions within the formation are prevented. Numerical results are provided to verify the theoretical conjectures.
Tolérance aux défauts via la méthode backstepping des systèmes non linéaires: application système UAV de type quadrirotor
- khebbache
Tolérance aux défauts via la méthode backstepping des systèmes non linéaires: application système UAV de type quadrirotor
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H. Khebbache, "Tolérance aux défauts via la méthode
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Experimental investigation of rotational control of a constrained Authorized licensed use limited to: Qatar National Library. Downloaded on February 02,2021 at 14:12:12 UTC from IEEE Xplore. Restrictions apply. quadrotor using backstepping method
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Authorized licensed use limited to: Qatar National Library. Downloaded on February 02,2021 at 14:12:12 UTC from IEEE Xplore. Restrictions apply.
quadrotor using backstepping method," in International
Micro Air Vehicle Conference, 2016, pp. 17-21.
Modelling, identification and control of a quadrotor helicopter
- T Bresciani
T. Bresciani, "Modelling, identification and control of a
quadrotor helicopter," MSc Theses, 2008.
Modeling and Control of Inverted Flight of a Variable-Pitch Quadrotor
- N Gupta
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N. Gupta and M. Kothari, "Modeling and Control of
Inverted Flight of a Variable-Pitch Quadrotor," arXiv
preprint arXiv:1709.06407, 2017.
PARROT Minidrones Support from Simulink
Mathworks.
(2018).
PARROT
Minidrones
Support
from
Simulink
[website].
Available:
https://www.mathworks.com/hardware-support/parrotminidrones.html