Adaptive sliding mode control for MIMO nonlinear systems based on fuzzy logic scheme

In this study an indirect adaptive sliding mode control (SMC) based on a fuzzy logic scheme is proposed to strengthen the tracking control performance of a general class of multi-input multi-output (MIMO) nonlinear uncertain systems. Combining reaching law approach and fuzzy universal approximation theorem, the proposed design procedure combines the advantages of fuzzy logic control, adaptive control and sliding mode control. The stability of the control systems is proved in the sense of the Lyapunov second stability theorem. Two simulation studies are presented to demonstrate the effectiveness of our new hybrid control algorithm.     

非匹配不确定非线性系统的自适应反演滑模控制

针对一类具有非匹配不确定性的最小相位仿射非线性系统,研究其在未知扰动作用下的调节问题。基于自适应反演设计方法和变结构控制设计了控制方案,实现不确定系统的鲁棒调节。与经典反演设计相比,本方案允许非参数化不确定性,增强了控制系统的鲁棒性。     

A New Robust Adaptive Control of Uncertain Nonlinear Systems and Pendulum Application

A new robust adaptive control of uncertain nonlinear systems is proposed in this paper. The proposed method combines sliding mode control with the immersion and invariance (I&I) adaptive scheme, and it has more available degrees of freedom than using the backstepping scheme. Via the proposed method, a class of nonlinear systems with mismatched parametric perturbations can be rendered asymptotically stable and the performance of the system can also be improved. Finally, the proposed method is applied to a simple pendulum with motor dynamics, and simulation results show the effectiveness and performance of the proposed method.     

基于观测器的滑模控制非线性中立型时滞系统

针对一类状态不可测的非线性不确定中立型时滞系统,基于滑模控制理论,采用线性矩阵不等式的处理方法,提出了滑动模态鲁棒渐近稳定时滞相关的充分条件,设计了一类滑模观测器,同时给出了该观测器存在的充分条件;然后应用滑模控制的趋近率方法和基于观测器所得到的系统估计状态,综合了一类滑模控制器,该控制器同时保证了估计状态下滑模面和估计误差状态下滑模面的渐近可达性;最后通过数值实例证明了该控制方案的可行性.     

SLIDING‐MODE LINEARIZATION TORQUE CONTROL OF AN INDUCTION MOTOR

This paper proposes a sliding‐mode linearization torque control (SMLTC) for an induction motor (IM). An ideal feedback linearization torque control method is firstly adopted in order to decouple the torque and flux amplitude of the IM. However, the system parameters are uncertainties, which will influence the control performance of the IM in practical applications. Hence, to increase the robustness of the IM drive for high‐ performance applications, this SMLTC aims to improve the immunity of those uncertainties. We modify the flux observer of Benchaib and Edwards [15] by means of the adaptive sliding‐mode method. This not only eliminates the estimation of the uncertainty bounds, but also improves the performance of sliding control. In addition, a practical application of the proposed SMLTC, with a model reference adaptive control (MRAC) scheme incorporated as the inner and outer loop controller used for position control, is also presented. Some experiments are presented to verify the control theory and demonstrate the robustness and effectiveness of the proposed SMLTC.     

Adaptive discrete-time sliding-mode control of nonlinear systems described by Wiener models

In this paper, we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters. The considered class of nonlinear systems is described by the block-oriented models, specifically, the Wiener models. These models consist of dynamic linear blocks in series with static nonlinear blocks. The proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete-time sliding-mode controller. The parameters adaptation are performed using a new recursive parametric estimation algorithm. This algorithm is developed using the adjustable model method and the least squares technique. A recursive least squares (RLS) algorithm is used to estimate the inverse nonlinear function. A time-varying gain is proposed, in the discrete-time sliding mode controller, to reduce the chattering problem. The stability of the closed-loop nonlinear system, with the proposed adaptive control scheme, has been proved. An application to a pH neutralisation process has been carried out and the simulation results clearly show the effectiveness of the proposed adaptive control scheme.     

非仿射系统的自学习滑模抗扰控制

针对一类单输入单输出(single-input single-output,SISO)非仿射非线性系统的控制问题,提出了一种自学习滑模抗扰控制方法.该方法用非线性光滑函数设计扩张状态观测器,实现SISO非仿射非线性系统内部不确定性和外部扰动的扩张状态估计,并将扩张状态观测器(extended state observer,ESO)与自学习滑模控制技术融为一体,实现SISO非仿射非线性系统的自学习滑模抗扰控制.该方法不依赖受控对象的数学模型,可以快速跟踪任意给定的参考信号.数值仿真试验表明了该方法响应速度快、控制精度高,具有很强的抗扰动能力,因而是一种鲁棒稳定性很强的控制方法,在SISO非仿射非线性系统控制领域具有重要作用.     

Adaptive sliding mode control of uncertain nonlinear systems with preassigned settling time and its applications

This paper investigates the adaptive tracking control of second‐order nonlinear systems with nonlinearly parameterized uncertainties and disturbances, as well as multiplicative uncertainty in the control coefficient matrix. A novel adaptive function augmented sliding mode control approach is proposed such that the tracking error converges to a neighborhood of zero with the preassigned size within the preassigned settling time. In the proposed control scheme, the control gains increase as the adaptive estimate values increase only when necessary, that is, when the current control gains are not big enough to suppress the uncertainties or disturbances; as a result, the conservativeness of control design caused by unnecessary high control gains can be effectively reduced. Moreover, the chattering phenomenon well known in the sliding mode control is eliminated by using the saturation function to replace the signum function, and the possible persistent increasing problem of the adaptive estimate values due to measurement disturbances or noises on the feedback is also well addressed by introducing “dead‐zone” nonlinearities in the adaptive laws. In addition, an improved method to construct the desired error trajectory is proposed, and this method could avoid the large undershoot‐like or overshoot‐like phenomena, which the traditional one may result in. The obtained results are finally applied to the motion control of the underwater vehicle and the rendezvous control of spacecraft, and the simulation results illustrate the effectiveness and the advantages of the proposed control approach.     

Fault tolerant sliding mode control for T-S fuzzy stochastic time-delay system via a novel sliding mode observer approach

In this paper, a fault estimation and fault-tolerant control problem for a class of T-S fuzzy stochastic time-delay systems with actuator and sensor faults is investigated. A novel sliding mode observer is proposed, which can simultaneously estimate the system states, actuator and sensor faults with good accuracy. Based on the state and actuator fault estimation, a new sliding mode control scheme is developed, which can effectively eliminate the influence of actuator fault. Sufficient conditions for the existence of the proposed observer and fault-tolerant sliding mode controller are provided in terms of linear matrix inequality, and moreover, the reachability of the sliding mode surface can be guaranteed under the proposed control scheme. The propose sliding mode observer and fault-tolerant sliding mode controller can overcome the restrictive assumption that the input matrix of all local modes is the same. Finally, a numerical example is provided to verify the effectiveness of the proposed sliding mode observer and fault-tolerant sliding mode control technique.     

Practical adaptive fractional‐order nonsingular terminal sliding mode control for a cable‐driven manipulator

For the high precise tracking control purpose of a cable‐driven manipulator under lumped uncertainties, a novel adaptive fractional‐order nonsingular terminal sliding mode control scheme based on time delay estimation (TDE) is proposed and investigated in this paper. The proposed control scheme mainly has three elements, ie, a TDE element applied to properly compensate the lumped unknown dynamics of the system resulting in a fascinating model‐free feature; a fractional‐order nonsingular terminal sliding mode (FONTSM) surface element used to ensure high precision in the steady phase; and a combined reaching law with adaptive technique adopted to obtain fast convergence and high precision and chatter reduction under complex lumped disturbance. Stability of the closed‐loop control system is analyzed with the Lyapunov stability theory. Comparative simulations and experiments were performed to demonstrate the effectiveness of our proposed control scheme using 2‐DOF (degree of freedom) of a cable‐driven manipulator named Polaris‐I. Corresponding results show that our proposed method can ensure faster convergence, higher precision, and better robustness against complex lumped disturbance than the existing TDE‐based FONTSM and continuous FONTSM control schemes.     

Sliding mode adaptive control for a class of nonlinear time‐varying systems

In this work, the problem of designing a control scheme capable of controlling dynamical systems with unknown time‐varying parameters and disturbances is proposed. In contrast with other works, based on two techniques, ie, adaptive backstepping and sliding modes, an improved method that guarantees the output asymptotic tracking of a smooth reference signal, the stability of the closed‐loop system, and the identification errors' boundedness is developed. By means of sliding mode observers, the adaptation errors' required information is extracted and injected to adaptive laws. The behavior of the proposed control scheme is analyzed by the Lyapunov method. The performance of the proposed system is verified with an academic example.     

高精度机械伺服系统的一种新型自适应滑模控制方法

针对高精度机械伺服系统,提出一种高性能的新型自适应滑模控制方法,使闭环系统渐近跟踪给定的参考模型.该方法对转动惯量的大范围变化及非线性摩擦等外干扰均具有很强的鲁棒性.该方法的主要思想是用滑模方法抑制系统中的外部力矩扰动,对系统参数进行自适应估计,用估计值来补偿转动惯量的变化.对于控制算法的全局稳定性,采用李雅普诺夫直接法给出了严格的证明.该算法简单,其实现不需要误差的高阶微分信号,适于实时控制.本文方法以某高精度飞行仿真转台为例,对提出方法进行了实验研究,结果表明了该方法具有良好的跟踪性能,暂态响应和鲁棒性.     

Passivity-based sliding mode control of uncertain singular time-delay systems

In this paper the problem of sliding mode control (SMC) with passivity of a class of uncertain nonlinear singular time-delay systems is studied. An integral-type switching surface function is designed by taking the singular matrix into account, thus the resulting sliding mode dynamics is a full-order uncertain singular time-delay system. By introducing some slack matrices, a delay-dependent sufficient condition is proposed in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive. The passification solvability condition is then established. Moreover, a SMC law and an adaptive SMC law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.     

Sliding mode observer–controller design for uncertain Markovian jump systems with time delays

This paper proposes a sliding mode observer–controller design method for uncertain Markovian jump systems with time delays and uncertain switching probabilities. Both the structures of a sliding mode observer and a sliding mode controller are given. By the mode‐dependent Lyapunov functional approach, a sufficient condition for the stochastic stability of the closed‐loop system is given, which can be converted into a convex optimization problem. The reachability of the sliding surfaces in both the estimation error space and the state estimate space can be ensured by the presented control scheme. Finally, the effectiveness of the proposed design method is demonstrated by a simulation example. Copyright © 2011 John Wiley & Sons, Ltd.     

An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems

In this paper, an optimal adaptive robust PID controller based on fuzzy rules and sliding modes is introduced to present a general scheme to control MIMO uncertain chaotic nonlinear systems. In this control scheme, the gains of the PID controller are updated by using an adaptive mechanism, fuzzy rules, the gradient search method, and the chain rule of differentiation in order to minimize the sliding surfaces of sliding mode control. More precisely, sliding mode control is used as a supervisory controller to provide sufficient control inputs and guarantee the stability of the control approach. To ascertain the parameters of the proposed controller and avoid trial and error, the multi-objective genetic algorithm is employed to augment the performance of proposed controller. The chaotic system of a Duffing-Holmes oscillator and an industrial robotic manipulator are the case studies to evaluate the performance of the proposed control approach. The obtained results of this study regarding both systems are compared with the outcomes of two notable studies in the literature. The results and analysis prove the efficiency of the proposed controller with regard to MIMO uncertain systems having challenging external disturbances in terms of stability, minimum tracking error and optimal control inputs.     

Adaptive type-2 fuzzy sliding mode controller for SISO nonlinear systems subject to actuator faults

In this paper, an adaptive type-2 fuzzy sliding mode control to tolerate actuator faults of unknown nonlinear systems with external disturbances is presented. Based on a redundant actuation structure, a novel type-2 adaptive fuzzy fault tolerant control scheme is proposed using sliding mode control. Two adaptive type-2 fuzzy logic systems are used to approximate the unknown functions, whose adaptation laws are deduced from the stability analysis. The proposed approach allows to ensure good tracking performance despite the presence of actuator failures and external disturbances, as illustrated through a simulation example.     

Robust decentralized actuator fault detection and estimation for large-scale systems using a sliding mode observer

In this paper, robust decentralized actuator fault detection and estimation is considered for a class of non-linear large-scale systems. A sliding mode observer is proposed together with an appropriate coordinate transformation to find the sliding mode dynamics. Then, based on the features of the observer, a decentralized fault estimation strategy is proposed using an equivalent output error injection, and a decentralized reconstruction scheme follows by further exploiting the structure of the uncertainty which is allowed to have non-linear bounds. The estimation and reconstruction signals only depend on the available measured information and thus the proposed strategy can work on-line. The theoretical results which have been obtained are applied to an automated highway system. Simulation shows the feasibility and effectiveness of the proposed scheme.     

Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.     

Sliding mode control of uncertain systems with distributed time-delay： parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.