Sliding Mode Control Design Method Research Articles

Fast and High Accuracy CSM Control Under Manipulator Actuator Fault Conditions

The dynamic performance metrics of manipulators are decreased when actuator faults happen. To ensure the response speed and improve the tracking accuracy under actuator fault, the complementary sliding mode (CSM) controller is designed in this article. Different from the general sliding mode control (SMC), there are two sliding surfaces in the CSM controller design process, and the mathematical complexity of the controller is simplified through the relationship of the two complementary sliding surfaces, which helps to reduce the response time. Also, the structural parameter changes and disturbance existed in the real manipulator system are also considered in this paper by introducing uncertainty item during modeling, thus the robustness of the controller is improved. In the experimental part, the control effect of the CSM proposed is compared with that of the conventional sliding mode method. Normal conditions and actuator constant deviation fault of the manipulator are studied. The results show that the CSM has superiority in control accuracy and response speed. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In recent years, the control problem of manipulators under complex conditions has attracted particular attention. The key to the design of the controller lies in its stability while keeping the tracking performance. Many complex auxiliary methods are proposed to guarantee this, but a few can achieve acceptable performance. This article proposed the complementary sliding mode controller design method, in which two sliding surfaces are used to simplify the proof in the controller design. We choose the error variables to construct the sliding surface, so the CSM could handle several actuator faults very well, which enhances the adaptive ability of the algorithm.

Dissipativity-Based Event-Triggered Sliding Mode Control of Discrete-Time 2-D Systems

This paper focuses on dissipativity analysis and dissipativity-based sliding mode control (SMC) of discrete-time two-dimensional (2-D) systems described by Roesser model. First, dissipativity is introduced for 2-D systems. Aimed at the characteristics of Roesser model, the horizontal and vertical sliding surface functions are constructed for the addressed 2-D systems, respectively. Then sufficient conditions are proposed to guarantee the asymptotic stability and the pre-specified dissipativity for the resultant reduced-order 2-D sliding mode dynamics. Next, the SMC law is developed such that the system trajectories are driven into the quasi-sliding mode band in a finite region and maintained there all the time. In order to achieve a better resource utilisation, the event-triggered strategy is further incorporated in the design of SMC law. The event-triggered rule is also established to implement the event-triggered SMC scheme for 2-D systems. In the meantime, the corresponding quasi-sliding mode band is obtained. Finally, one verification example is given to show the effectiveness of the proposed SMC design method.

Consensus of Nonlinear Multiagent Systems With Uncertainties Using Reinforcement Learning Based Sliding Mode Control

This paper investigates distributed control protocols design for uncertain nonlinear multi-agent systems with the goal of achieving the optimal consensus. The critical challenges encountered when designing the optimal distributed control protocols are mainly caused by the internal coupling of agents, uncertainty and nonlinear dynamics. Communication delay among agents makes overcoming these challenges even more difficult. To this end, a novel sliding mode control design method is developed based on the sliding mode control principle and the reinforcement learning technique. The remarkable highlights of the developed method in this paper include the design of distributed sliding mode controllers and the integrated framework of sliding mode control and reinforcement learning, which bring the outcome of successfully learning the composite distributed control protocols for multi-agent systems. Thus, all agents can successfully eliminate the negative impacts brought by system uncertainties and communication delay among agents, and finally follow the leader with a nearly optimal approach. The reachability of sliding mode surfaces and the optimal consensus are rigorously proven and analyzed. Finally, simulation results illustrate the effectiveness of the developed method.

Sliding Mode Control of Networked Control Systems: An Auxiliary Matrices-Based Approach

A novel sliding mode control design method is developed to address the robust stabilization problem for uncertain time-varying networked control systems subject to state delay, which utilizes auxiliary matrices to avoid the difficulties of finding quadratic Lyapunov functions and solving the linear matrix inequalities. By embedding the original system into a higher dimensional system, simplified piecewise nonnegative functions can be used to analyze the system. Stability criteria are obtained which can be satisfied and verified easily. An optimization problem is defined based on these criteria, to obtain the sliding mode control parameters to ensure the exponential stability of the closed-loop system.

Event-triggered asynchronous sliding mode control of CSTR based on Markov model

In this paper, an asynchronous sliding mode control design method based on the event-triggered strategy is proposed for the continuous stirred tank reactor (CSTR) under external disturbance. Firstly, with the purpose of appropriately modeling the multi-mode switching phenomenon in the CSTR caused by the fluctuation of temperature and concentration, the Markov process is applied. Secondly, the asynchronous switching characteristics are introduced to describe mismatch between the controller and the system, which caused by some factors such as signal transmission delay and packet dropout. In order to effectively estimate the system states that cannot be measured in real time, an observer based on the event-triggered strategy is proposed, which also can reduce the computational cost. In addition, a sliding mode controller is designed to ensure the dynamic stability and the sliding dynamics is reachable in a finite time. Finally, the effectiveness of the proposed method is verified by simulation experiments.

Sliding mode controller design for frequency regulation in an interconnected power system

In this paper, a Sliding mode controller design method for frequency regulation in an interconnected power system is presented. A sliding surface having four parameters has been selected for the load frequency control (LFC) system model. In order to achieve an optimal result, the parameter of the controller is obtained by grey wolf optimization (GWO) and particle swarm optimization (PSO) techniques. The objective function for optimization has been considered as the integral of square of error of deviation in frequency and tie-line power exchange. The method has been validated through simulation of a single area as well as a multi-area power system. The performance of the Sliding mode controller has also been analyzed for parametric variation and random loading patterns. The performance of the proposed method is better than recently reported methods. The performance of the proposed Sliding mode controller via GWO has 88.91% improvement in peak value of frequency deviation over the method of Anwar and Pan in case study 1 and similar improvement has been observed over different case studies taken from the literature.

Observer-Based Adaptive Sliding Mode Control for T–S Fuzzy Singular Systems

This paper investigates the problem of adaptive ${H}_{\infty}$ sliding mode control (SMC) for a class of nonlinear systems via Takagi–Sugeno (T–S) fuzzy model approach. The input matrices and output matrices in all local linear systems are different. A novel observer is designed to estimate the unmeasured states. Based on such an observer, the control input is only appeared in the T–S fuzzy singular system and error system. A new integral sliding surface is put forward to match the characteristic of T–S fuzzy singular system with different input and output matrices. Based on the new integral sliding surface, a new adaptive SMC scheme is designed to guarantee the admissibility of the T–S fuzzy singular system with ${H}_{\infty}$ performance and the reachability of the T–S fuzzy integral sliding surface. A simulation result is presented to illustrate the effectiveness and feasibility of the developed observer-based SMC design method.

Two-dimensional event-triggered sliding mode control for Roesser model with time delays

This paper is concerned with the event-triggered sliding mode control (SMC) strategy for the discrete-time two-dimensional (2-D) systems represented by Roesser model with time delays. Firstly, the linear sliding surface functions combined with the event-triggered scheme are constructed for the 2-D Roesser model. Then sufficient conditions are established for the asymptotic stability of the reduced-order sliding mode dynamics and the existence of linear sliding surface functions in terms of linear matrix inequality. Subsequently, the event-triggered sliding mode control law is designed by the Lyapunov function approach to drive the state trajectories of the resultant closed-loop system into a bounded region and maintain there for subsequent time. Finally, a numerical example is given to illustrate the effectiveness of the proposed SMC design method.

Multi-packet transmission aero-engine DCS neural network sliding mode control based on multi-kernel LS-SVM packet dropout online compensation.

In view of the strong nonlinear characteristics of the multi-packet transmission Aero-engine DCS with induced delay and random packet dropout, a neural network PID approach law sliding-mode controller using sliding window strategy and multi-kernel LS-SVM packet dropout online compensation is proposed. Firstly, the time-delay term in the system model is transformed equivalently, to establish the discrete system model of multi-packet transmission without time-delay; furthermore, the construction of multi-kernel function is transformed into kernel function coefficient optimization, and the optimization problem can be solved by the chaos adaptive artificial fish swarm algorithm, then the online predictive compensation will be made for data packet dropout of multi-packet transmission through the sliding window multi-kernel LS-SVM. After that, a sliding-mode controller design method of proportional integral differential approach law based on neural network is proposed. And online adjustment of PID approach law parameters can be achieved by nonlinear mapping of neural network. Finally, Truetime is used to simulate the method. The results shows that when the packet dropout rate is 30% and 60%, the average error of packet dropout prediction of multi-kernel LS-SVM reduces 29.21% and 44.66% compared with that of combined kernel LS-SVM, and the chattering amplitude of the proposed neural network PID approach law sliding-mode controller is decreased compared with other five approach law methods respectively. This controller can ensure a fast response speed, which shows that this method can achieve a better tracking control of the aeroengine network control system.

Multiple step ahead prediction based high order discrete-time sliding mode control design with actuator and communication delays

Sliding mode control (SMC) is a well-known nonlinear control strategy which is robust against the model uncertainty; however it can produce control signals with high frequency response (chattering phenomena). To deal with chattering effect, high order SMC has been proposed in the literature, but it has weakness in dealing with measurement noise, and actuator and communication delays. This paper presents a predictive-based discrete higher order SMC design method for multi-input-multi-output linear systems in noisy environment with measurement and actuator delay. The proposed method utilizes distributed multiple step ahead prediction method which is optimal in terms of prediction error variance. The stability of the proposed controller in the sense of mean and mean square is proved. Besides, the lower and upper bound for the reaching time to the sliding surface of the proposed controller is analytically determined. The resulting technique is verified through simulation and experimental test performed on a four-tank process.

Robust stabilization of one-sided Lipschitz nonlinear systems via adaptive sliding mode control

In this paper, the problem of adaptive sliding mode control for varied one-sided Lipschitz nonlinear systems with uncertainties is investigated. In contrast to existing sliding mode control design methods, the considered models, in the current study, are affected by nonlinear control inputs, one-sided Lipschitz nonlinearities, unknown disturbances and parameter uncertainties. At first, to design the sliding surface, a specific switching function is defined. The corresponding nonlinear equivalent control is extracted and the resulting sliding mode dynamic is given. Novel synthesis conditions of asymptotic stability are derived in terms of linear matrix inequalities. Thereafter, to ensure the reachability of system states and the occurrence of the sliding mode, the sliding mode controller is designed. Any knowledge of the upper bound on the perturbation is not required and an adaptation law is proposed. At last, two illustrative examples are introduced.

Two-Dimensional Sliding Mode Control of Discrete-Time Fornasini–Marchesini Systems

This paper is concerned with the problem of discrete-time two-dimensional (2-D) sliding mode control (SMC) for Fornasini–Marchesini (FM) systems subject to exogenous nonlinear disturbances. With the introduction of the time instant and global state in the 2-D case, the discrete-time sliding surface function for 2-D systems is constructed. Then, based on the corresponding sliding mode dynamics, the solvability condition for the desired sliding surface function is derived. Subsequently, a sliding mode controller is designed to guarantee that the state trajectories can enter into a neighborhood of the specified sliding surface. Meanwhile, the stability of the 2-D sliding mode dynamics is also ensured. Finally, a simulation example is provided to illustrate the feasibility and the effectiveness of the presented new 2-D SMC design method. Different from existing results, the proposal focuses on the features of multi-dimension and the dynamics of 2-D systems, which is expected to develop a completely different SMC design approach for discrete-time 2-D systems.

Fuzzy sliding mode control of a wearable rehabilitation robot for wrist and finger

PurposeThe purpose of this paper is to introduce a new design for a finger and wrist rehabilitation robot. Furthermore, a fuzzy sliding mode controller has been designed to control the system.Design/methodology/approachFollowing an introduction regarding the hand rehabilitation, this paper discusses the conceptual and detailed design of a novel wrist and finger rehabilitation robot. The robot provides the possibility of rehabilitating each phalanx individually which is very important in the finger rehabilitation process. Moreover, due to the model uncertainties, disturbances and chattering in the system, a fuzzy sliding mode controller design method is proposed for the robot.FindingsWith the novel design for moving the DOFs of the system, the rehabilitation for the wrist and all phalanges of fingers is done with only two actuators which are combined in one device. These features make the system a good choice for home rehabilitation. To control the robot, a fuzzy sliding mode controller has been designed for the system. The fuzzy controller does not affect the coefficient of the sliding mode controller and uses the overall error of the system to make a control signal. Thus, the dependence of the controller to the model decreases and the system is more robust. The stability of the system is proved by the Lyapunov theorem.Originality/valueThe paper provides a novel design of a hand rehabilitation robot and a controller which is used to compensate the effects of the uncertain parameters and chattering phenomenon.

Sliding Mode Control for Nonlinear Stochastic Semi-Markov Switching Systems With Application to SRMM

In this paper, the sliding mode control (SMC) design for nonlinear stochastic semi-Markov switching systems (S-MSSs) is studied via the bound of time-varying transition rate matrix, in which semi-Markov switching parameters, stochastic disturbance, uncertainty, and nonlinearity are all considered in a unified framework. The system under consideration is more general, which covers the Markov switching system with sojourn-time-independent transition rate matrix as a special case. Many practical systems subject to unpredictable structural variations can be characterized by nonlinear stochastic S-MSSs with sojourn-time-dependent transition rate matrix. The specific information about the bound of time-varying transition rate matrix is known for the sliding mode controller design. First, by using the stochastic semi-Markov Lyapunov function, sojourn-time-dependent sufficient conditions are developed to guarantee the closed-loop sliding mode dynamics stochastically stable. Then, the SMC law is constructed to ensure the reachability of the sliding mode dynamics in a finite-time level. Finally, one joint of space robot manipulator model is described as nonlinear stochastic S-MSSs to illustrate the validity of the proposed SMC design method.

A new fuzzy sliding mode controller design for delta operator time-delay nonlinear systems

ABSTRACTThis paper investigates the sliding mode control (SMC) problem for a class of delta operator uncertain time-delay nonlinear systems through Takagi–Sugeno fuzzy models. Some new sufficient conditions for asymptotic stability analysis of the sliding motion are obtained in terms of linear matrix inequalities with some convexification techniques. Then two new dynamic SMC design methods are synthesised to force the resulting closed-loop system states onto the sliding surface in finite time. Two simulation examples are finally given to illustrate the effectiveness of the proposed approaches.

Nonsingular terminal sliding-mode control of nonlinear planar systems with global fixed-time stability guarantees

Abstract This paper proposes the use of a novel nonsingular Terminal Sliding surface for the finite-time robust stabilization of second order nonlinear plants with matched uncertainties. Mathematical characteristics of the proposed surface are such that a fixed bound naturally exists for the settling time of the state variable, once the surface has been reached. A simple redesign of the control input able to ensure the feature of fixed-time reaching of the sliding surface will be also presented, and fixed-time stability will be guaranteed by the proposed Terminal Sliding Mode Control design method. A careful simulation study has been performed using a benchmark system taken from the literature.

An adaptive sliding mode approach for Markovian jump systems with uncertain mode-dependent time-varying delays and partly unknown transition probabilities

This paper deals with the problems of stochastic stability and sliding mode control for a class of continuous-time Markovian jump systems with mode-dependent time-varying delays and partly unknown transition probabilities. The design method is general enough to cover a wide spectrum of systems from those with completely known transition probability rates to those with completely unknown transition probability rates. Based on some mode-dependent Lyapunov-Krasovski functionals and making use of the free-connection weighting matrices, new delay-dependent conditions guaranteeing the existence of linear switching surfaces and the stochastic stability of sliding mode dynamics are derived in terms of linear matrix inequalities (LMIs). Then, a sliding mode controller is designed such that the resulted closed-loop system's trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. This paper also proposes an adaptive sliding mode controller design method which applies to cases in which mode-dependent time-varying delays are unknown. All the conditions obtained in this paper are in terms of LMI feasibility problems. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Sliding mode control of continuous-time Markovian jump systems with digital data transmission

This paper investigates the design problem of sliding mode control for a class of continuous-time Markovian jump systems with digital communication constraints. Two types of classical quantization schemes, that is, dynamical uniform quantizer and static logarithmic quantizer, are employed to perform the design work, respectively. In this study, a novel quantized sliding mode control design method is developed to stabilize the closed-loop systems in the presence of both state and input quantization and unknown time-varying actuator faults. Under the proposed quantized control strategies, the quantization effects can be completely compensated via injecting quantizer parameters into the controller gains. Moreover, in both quantization cases, the proposed robust quantized sliding mode controllers can guarantee the state trajectories of the closed-loop systems to be mean-square stable, and ensure the reachability of the specified sliding surface with probability 1 at the same time. Finally, a numerical example with an F-404 aircraft engine system is provided to show the effectiveness of the proposed digital control design approach.

Sliding mode tracking control for miniature unmanned helicopters

A sliding mode control design for a miniature unmanned helicopter is presented. The control objective is to let the helicopter track some predefined velocity and yaw trajectories. A new sliding mode control design method is developed based on a linearized dynamic model. In order to facilitate the control design, the helicopter’s dynamic model is divided into two subsystems, such as the longitudinal-lateral and the heading-heave subsystem. The proposed controller employs sliding mode control technique to compensate for the immeasurable flapping angles’ dynamic effects and external disturbances. The global asymptotic stability (GAS) of the closed-loop system is proved by the Lyapunov based stability analysis. Numerical simulations demonstrate that the proposed controller can achieve superior tracking performance compared with the proportional-integral-derivative (PID) and linear-quadratic regulator (LQR) cascaded controller in the presence of wind gust disturbances.

Attitude Control of Chaotic Satellite with Unknown Input and uncertainties based on Sliding Control

attitude control of missiles, spacecraft and satellites is essential; in order to remain them fixed in space to perform their missions accurately. The attitude equation of a satellite is a six- dimensional nonlinear system which includes some types of nonlinear behavior such as periodic trajectory, chaotic dynamics. In this paper, a sliding mode control design method for stabilization of the attitude chaotic satellites with unknown inputs and uncertainties. Using Lyapunov theory, the stability control system is proven. Simulation results show that the proposed controller can be chaotic satellite attitude in the presence of unknown inputs and uncertainties will converge to the unstable equilibrium points. In this section, the satellite system and the chaotic dynamics are studied. In (16) the problem of satellite attitude control with redundant thrusters, and in (17) satellite attitude control with an uneven inertia distribution has been investigated. However, given that the satellite attitude motion under external disturbances becomes chaotic mode, the control satellite system will be very complex. So, be very careful satellite control system is designed. In (13) and (14) satellite attitude control of chaotic behavior has been investigated. The orientation of the satellite at a given point can be locally described in terms of three angles