动态滑模控制及其在移动机器人输出跟踪中的应用

针对轮式移动机器人的输出跟踪问题,提出一种动态滑模控制方法,首先给出机器人的动力学简化模型,然后将其分解成两个低阶子系统,并给出其输出跟踪的动态滑模控制器设计方法,仿真试验表明该方法能明显地削弱滑模控制系统的抖振。     

Adaptive dynamical variable structure feedback regulation for nonlinear uncertain systems

In this article an adaptive discontinuous dynamical feedback strategy is presented for asymptotic output stabilization problems defined on nonlinear controlled systems exhibiting linear parametric uncertainty. A dynamical feedback controller, ideally achieving output stabilization via exact linearization, is obtained by means of output differentiation and sliding mode control ideas. The adaptive version of the dynamical variable structure controller is then obtainable via standard, direct, overparametrized adaptive control techniques available for linearizable systems through static state feedback. An illustrative example from the chemical process control area, including simulations, is provided.     

二阶动态滑模控制在移动机械臂输出跟踪中的应用

针对移动机械臂的输出跟踪问题,结合高阶滑模控制和动态滑模控制的设计思想为其设计了一种二阶动态滑模控制器.首先给出了包括驱动电机动态特性的移动机械臂的简化动态模型,然后通过微分同胚和输入变换将其分解为四个低阶子系统,并给出了其输出跟踪的二阶动态滑模控制器的设计方法.仿真结果表明,所设计的二阶动态滑模控制器不仅能很好地跟踪给定轨迹,而且能有效地削弱滑模控制系统的抖振.     

Global stabilisation for a class of nonlinear time-delay systems based on dynamical output feedback sliding mode control

In this article, global stabilisation for a class of nonlinear time-varying delay systems with mismatched uncertainty is considered. The bound on the uncertainty is nonlinear and involves time-delay. For this system, a dynamical compensator is first designed. A delay free sliding surface in the augmented space formed by the system output and the compensator state variables is proposed. The stability of the sliding mode dynamics, which include the time-delay effects, are analysed using the Lyapunov–Razumikhin approach. Then, a delay dependent sliding mode control is proposed such that the system can be driven to the sliding surface in finite time and maintain a sliding motion on it thereafter. Finally, a simulation is presented to illustrate the effectiveness of the obtained results.     

带有非线性不确定奇异系统的积分滑模控制

针对一类含有非线性不确定的奇异系统, 提出了一种面向性能的鲁棒控制器. 控制器由3部分组成: 积分滑模控制、附加的非线性控制及复合非线性反馈控制. 积分滑模控制可将匹配不确定完全抵消并使系统轨迹进入理想滑模; 附加的非线性控制用来抑制理想滑动模态上非匹配不确定对系统稳定性和性能的影响; 复合非线性反馈控制则保证闭环系统输出按性能要求渐近地跟踪参考输入信号. 最后通过算例说明所提算法的有效性.     

ADAPTIVE SLIDING MODE BACKSTEPPING CONTROL OF NONLINEAR SYSTEMS WITH UNMATCHED UNCERTAINTY

This paper considers an adaptive backstepping algorithm for designing the control for a class of nonlinear continuous uncertain processes with disturbances that can be converted to a parametric semi‐strict feedback form. Sliding mode control using a combined adaptive backstepping sliding mode control (SMC) algorithm, is also studied. The algorithm follows a systematic procedure for the design of adaptive control laws for the output tracking of nonlinear systems with matched and unmatched uncertainty.     

Fractional order predictive sliding-mode control for a class of nonlinear input-delay systems: singular and non-singular approach

Nonlinear models of physical systems usually suffer from input delay and external disturbances. Moreover, when a delayed state is in the input signal gain, it can be non-singular or singular. So, designing a robust controller in a nonlinear system with input and state delay, suitable for non-singular and singular input signal gain, is imperative. The main contribution of our study is to design a new state feedback fractional order predictive sliding mode control (FOPSMC) procedure which not only guarantees the stability of a nonlinear system with known constant input and state delay but also controls the output signal to the desired value. Firstly, a predictor is designed for the system to achieve an input-delay-free one. Then, a state feedback FOPSMC is proposed based on a fractional order sliding signal for a nonlinear system with non-singular control gain. Also, a state feedback FOPSMC and a fractional order sliding mode observer (FOSMO) for the virtual disturbance are designed for singular control gain situation. It is proved analytically, through the Lyapunov stability criteria, that both control procedures can stabilise the system and can control the output signal to the desired value, effectively. Finally, the simulation results verify the effectiveness of the analytical achievements.     

Quantized output feedback stabilization of uncertain systems with input nonlinearities via sliding mode control

This paper is concerned with the quantized output feedback stabilization problem for a class of uncertain systems with nonsmooth nonlinearities in the actuator device via sliding mode control schemes. It is assumed that system signals are quantized before being transmitted through communication channels. First, a dynamical compensator is developed to estimate unmeasurable system state. Then a sliding surface, in the augmented space using the system output and the estimated state, is proposed, and an adaptive sliding mode control scheme with a static adjustment law of the quantization parameter is established. It is shown that the proposed quantized feedback control strategy is able to tackle parameter uncertainty, external disturbances, and nonsymmetric input nonlinearity simultaneously and guarantees the reachability of the sliding modes of the uncertain system. Finally, an example is given to verify the validity of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

Output Feedback Terminal Sliding Mode Control for a Class of Second Order Nonlinear Systems

In this study, a novel output feedback terminal sliding mode control (TSMC) approach is proposed for a class of second order nonlinear systems in light of the equivalent output injection sliding mode observer (SMO) method and TSMC principle. The SMO method is applied to reconstruct full states in finite time and the non‐singular TSMC algorithm is designed to stabilize system states to equilibrium points in finite time. The corresponding stability analysis is presented. An indispensable illustrative example is bench tested to validate the effectiveness of the proposed approach.     

Static output feedback sliding mode control for time‐varying delay systems with time‐delayed nonlinear disturbances

In this paper, a robust stabilization problem for a class of linear time‐varying delay systems with disturbances is studied using sliding mode techniques. Both matched and mismatched disturbances, involving time‐varying delay, are considered. The disturbances are nonlinear and have nonlinear bounds which are employed for the control design. A sliding surface is designed and the stability of the corresponding sliding motion is analysed based on the Razumikhin Theorem. Then a static output feedback sliding mode control with time delay is synthesized to drive the system to the sliding surface in finite time. Conservatism is reduced by using features of sliding mode control and systems structure. Simulation results show the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Discrete time output feedback sliding mode control for nonlinear MIMO system: a stepper motor case

This article, presents discrete sliding mode control algorithm using multirate output feedback for control of stepper motor. The algorithm developed by the authors uses past output samples and past control inputs. When all the states of the system are neither physical variable nor available for measurement, multirate output feedback can be used. The stepper motor is known to be a differentially flat system. The dynamics of the stepper motor are highly nonlinear, hence feedback linearization based on endogenous feedback has been used. The linear model is obtained and multirate output feedback-based discrete sliding mode control has been designed. The discrete sliding mode control with multirate output feedback has been applied for regulator as well as tracking case for the motor. The proposed algorithm uses only two outputs. It is essentially shown that first output needs to be sampled only once and second output must be sampled at least thrice in every τ sampling interval in order to achieve acceptable performance. The system parameter variation has been considered and the results obtained are found to be satisfactory. Thus, it has been shown that discrete sliding mode control algorithm using multirate output feed back can be extended to a class of nonlinear MIMO system.     

Fast terminal sliding‐mode finite‐time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems

This paper presents a fast terminal sliding‐mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time‐varying disturbances. Fast terminal sliding‐mode finite‐time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite‐time control effort, the fast terminal sliding‐mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high‐precision output tracking performance in uncertain nonlinear systems.     

严格反馈非线性系统的自适应神经网络输出反馈控制

基于非线性反馈函数,文章设计神经网络状态观测器,解决一类非线性系统的输出反馈控制问题.非线性反馈神经网络观测器在系统存在不确定性函数的情况下实时估计系统状态.利用所获得的状态信号,设计了自适应神经网络动态面控制器,同时保证了闭环系统的稳定性和所有信号的有界性.通过调节设计参数的取值能够达到期望的闭环跟踪性能.数值仿真表明,所设计的状态观测器不需要对原系统做状态变换,能够克服输出反馈滑模控制器带来的抖震问题.     

On the design of sliding mode output feedback controllers

The development of sliding mode controllers for uncertain linear systems using only a subset of the state information is considered. The case of static output feedback is first reviewed. The use of low order dynamical compensators (which do not possess observer interpretations) is explored. It will be shown that the constraint of global sliding surface reachability which is usually employed in the state feedback case is unnecessarily restrictive when developing controllers based on output measurements only. A case study involving steer-by-wire of a passenger vehicle is employed throughout the paper to illustrate the theoretical results.     

Output‐feedback tracking in causal nonminimum‐phase nonlinear systems using higher‐order sliding modes

Asymptotic output‐feedback tracking in a class of causal nonminimum phase uncertain nonlinear systems is addressed via sliding mode techniques. Sliding mode control is proposed for robust stabilization of the output tracking error in the presence of a bounded disturbance. The output reference profile and the unknown input/disturbance are supposed to be described by unknown linear exogenous systems of a given order. Local asymptotic stability of the output tracking error dynamics along with the boundedness of the internal states are proven. The unstable internal states are estimated asymptotically via the proposed multistage observer that is based on the method of extended system center. A higher‐order sliding mode observer/differentiator is used for the exact estimation of the input–output states in a finite time. The bounded disturbance is reconstructed asymptotically. A numerical example illustrates the efficiency of the proposed output‐feedback tracking approach developed for causal nonminimum phase nonlinear systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Global tracking sliding mode control for a class of nonlinear systems via variable gain observer

A novel output‐feedback sliding mode control strategy is proposed for a class of single‐input single‐output (SISO) uncertain time‐varying nonlinear systems for which a norm state estimator can be implemented. Such a class encompasses minimum‐phase systems with nonlinearities affinely norm bounded by unmeasured states with growth rate depending nonlinearly on the measured system output and on the internal states related with the zero‐dynamics. The sliding surface is generated by using the state of a high gain observer (HGO) whereas a peaking free control amplitude is obtained via a norm observer. In contrast to the existing semi‐global sliding mode control solutions available in the literature for the class of plants considered here, the proposed scheme is free of peaking and achieves global tracking with respect to a small residual set. The key idea is to design a time‐varying HGO gain implementable from measurable signals. Copyright © 2010 John Wiley & Sons, Ltd.     

一类非匹配不确定非线性系统的鲁棒跟踪控制制

针对一类半严格反馈型不确定非线性系统,提出一种鲁棒反演滑模变结构控制方法.采用反演控制方法设计了使前n-1阶子系统稳定的虚拟控制律,抑制非匹配不确定性的影响;在第n步设计了一种连续可导的滑模变结构控制律,消除控制抖振,实现了对存在未知不确定性及扰动系统的鲁棒输出跟踪.通过Lyapunov定理证明了闭环系统所有信号最终有界.仿真结果验证了该方法的有效性.     

RCMAC-based adaptive control for uncertain nonlinear systems.

An adaptive control system, using a recurrent cerebellar model articulation controller (RCMAC) and based on a sliding mode technique, is developed for uncertain nonlinear systems. The proposed dynamic structure of RCMAC has superior capability to the conventional static cerebellar model articulation controller in an efficient learning mechanism and dynamic response. Temporal relations are embedded in RCMAC by adding feedback connections in the association memory space so that the RCMAC provides a dynamical structure. The proposed control system consists of an adaptive RCMAC and a compensated controller. The adaptive RCMAC is used to mimic an ideal sliding mode controller, and the compensated controller is designed to compensate for the approximation error between the ideal sliding mode controller and the adaptive RCMAC. The online adaptive laws of the control system are derived based on the Lyapunov stability theorem, so that the stability of the system can be guaranteed. In addition, in order to relax the requirement of the approximation error bound, an estimation law is derived to estimate the error bound. Finally, the simulation and experimental studies demonstrate the effectiveness of the proposed control scheme for the nonlinear systems with unknown dynamic functions.     

Asymptotic Stabilisation of Multiple Input Nonlinear Systems via Sliding Modes

A dynamic feedback controller design method is proposed for multiple input systems. The method uses a novel choice of sliding surface to effect asymptotic linearisation of nonlinear differential input output systems and a class of state space systems. The stability of the overall system, that is a canonical state space form with a dynamic feedback, is analysed with a generalised Lyapunov approach plus an asymptotic analysis in a neighbourhood of the origin. The nonlinear system does not have to be expressed in regular form as is the case in many other sliding mode control approaches. A type of zero dynamics, which are the dynamics of the control, are involved. The resulting dynamic feedback is shown to provide chatter free control if the system is minimum phase with respect to the zero dynamics. The theoretical results are applied to Gas Jet systems with two controls.     

Dynamic output feedback integral sliding mode control design for uncertain systems

This paper addresses the problem of designing a dynamic output feedback sliding mode control algorithm for linear MIMO systems with mismatched parameter uncertainties along with disturbances and matched nonlinear perturbations. Once the system is in the sliding mode, the proposed output‐dependent integral sliding surface can robustly stabilize the closed‐loop system and obtain the desired system performance. Two types of mismatched disturbances are considered and their effects on the sliding mode are explored. By introducing an additional dynamics into the controller design, the developed control law can guarantee that the system globally reaches and is maintained on the sliding surface in finite time. Finally, the feasibility of the proposed method is illustrated by numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.