An output feedback sliding mode control strategy for MIMO systems of arbitrary relative degree

This paper develops an output feedback sliding mode controller for multi‐input multi‐output (MIMO) systems of any relative degree. A minimal set of outputs and output derivatives are identified to determine an augmented system which is relative degree 1, and a robust sliding mode differentiator is presented as the means to construct the extended output signal. It is shown that the transmission zeroes of the original plant appear directly in the reduced order sliding mode dynamics relating to the augmented system. A super twisting control algorithm is shown to provide robust control performance. Simulation results for a rationalized helicopter model taken from the literature are used to demonstrate the attraction of the approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Discrete time output feedback sliding mode tracking control for systems with uncertainties

This paper describes a method for designing discrete time static output feedback sliding mode tracking controllers for uncertain systems that are not necessarily minimum phase or of relative degree one. In this work, a procedure for realizing discrete time controllers via a particular set of extended outputs is presented for systems with uncertainties. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to synthesize a control law that minimizes the effect of the disturbance on the sliding mode dynamics and the augmented outputs is given. The proposed control law is then applied to a benchmark aircraft problem taken from the literature that represents the lateral dynamics of a F‐14 aircraft under powered approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback

In this paper, a class of nonlinear interconnected systems with nonlinear nominal subsystems is considered. Matched and mismatched uncertainties are both dealt with. Based on sliding mode techniques, a decentralised robust control scheme, using only output information, is presented to stabilise the system locally, but under certain circumstances, global results can be obtained. The approach allows a more general structure for the interconnections and uncertainty bounds than other literature in this area. The conservatism in the results is reduced by fully using system output information and the uncertainty bounds. A numerical example is used to demonstrate the efficacy of the method.     

Robust output feedback sampling control based on second-order sliding mode

This paper proposes a new second-order sliding mode output feedback controller. This is developed in the case of finite sampling frequency and uses only output information in order to ensure desired trajectory tracking with high accuracy in a finite time in spite of uncertainties and perturbations. This new strategy is evaluated in simulations on an academic example.     

Discrete time neuro sliding mode control with a task-specific output error

The problem of obtaining the error at the output of a neuro sliding mode controller is analyzed in this paper. The controller operates in discrete time and the method presented describes an error measure that can be used if the task to be achieved is to drive the system under control to a predefined sliding regime. Once the task-specific output error is calculated, the neurocontroller parameters can be tuned so that the task is achieved. The paper postulates the strategy for discrete time representation of uncertain nonlinear systems belonging to a particular class. The performance of the proposed technique has been clarified on a third order nonlinear system, and the parameters of the controller are adjusted by using the error backpropagation algorithm. It is observed that the prescribed behavior can be achieved with a simple network configuration.     

Output feedback nonlinear control for a linear motor in suspension mode

This work extends an existing model of a permanent magnet linear synchronous motor and proposes a nonlinear controller for it. The motor is assumed to operate without mechanical bearings, so that the airgap length varies and requires regulation; accordingly, the extended model captures both longitudinal and normal dynamics. The output feedback control law mainly relies on the recently proposed power integrator method but also uses the standard techniques of exact feedback linearization and Lyapunov redesign. Uniformly bounded stability of the closed-loop system is achieved in spite of cogging forces and end-effects.     

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.     

不确定离散时间系统的复合非线性反馈积分滑模控制

针对不确定离散时间系统,提出一种基于离散复合非线性反馈的积分滑模(DCNF-ISM)控制策略,并将该算法应用于扰动下的磁盘跟踪问题.该算法由离散复合非线性反馈(DCNF)控制律与积分滑模(ISM)控制律两部分组成,其中DCNF控制律用于保证系统具有较好瞬态性能,基于改进的离散趋近律设计的ISM控制律用于保证系统鲁棒性.基于Lyapunov稳定性理论对本文提出的控制策略的稳定性进行了推导证明,证明了离散时间系统的一致最终有界性.仿真结果表明,本文提出的控制策略能保证系统在扰动下仍然能够精确跟踪给定的参考信号,与传统的DCNF控制相比,该算法能够保证系统具有响应速度快超调量小、鲁棒性强等优点.     

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.     

Output feedback sliding mode control for a linear multi-compartment lung mechanics system

In this paper, we develop a sliding mode control architecture to control lung volume and minute ventilation in the presence of modelling system uncertainties. Since the applied input pressure to the lungs is, in general, nonnegative and cannot be arbitrarily large, as not to damage the lungs, a sliding mode control with bounded nonnegative control inputs is proposed. The controller only uses output information (i.e., the total volume of the lungs) and automatically adjusts the applied input pressure so that the system is able to track a given reference signal in the presence of parameter uncertainty (i.e., modelling uncertainty of the lung resistances and lung compliances) and system disturbances. Controllers for both matched and unmatched uncertainties are presented. Specifically, a Lyapunov-based approach is presented for the stability analysis of the system and the proposed control framework is applied to a two-compartment lung model to show the efficacy of the proposed control method.     

Decentralized sliding mode control for a class of nonlinear interconnected systems by static state feedback

In this paper, a class of interconnected systems is considered, where the nominal isolated systems are fully nonlinear. A robust decentralized sliding mode control based on static state feedback is developed. By local coordinate transformation and feedback linearization, the interconnected system is transformed to a new regular form. A composite sliding surface which is a function of the system state variables is proposed and the stability of the corresponding sliding mode dynamics is analyzed. A new reachability condition is proposed and a robust decentralized sliding mode control is then designed to drive the system states to the sliding surface in finite time and maintain a sliding motion thereafter. Both uncertainties and interconnections are allowed to be unmatched and are assumed to be bounded by nonlinear functions. The bounds on the uncertainties and interconnections have more general forms when compared with existing work. A MATLAB simulation example is used to demonstrate the effectiveness of the proposed method.     

Event-triggered sliding mode control for a class of nonlinear systems

ABSTRACT

Event-triggering strategy is one of the real-time control implementation techniques which aims at achieving minimum resource utilisation while ensuring the satisfactory performance of the closed-loop system. In this paper, we address the problem of robust stabilisation for a class of nonlinear systems subject to external disturbances using sliding mode control (SMC) by event-triggering scheme. An event-triggering scheme is developed for SMC to ensure the sliding trajectory remains confined in the vicinity of sliding manifold. The event-triggered SMC brings the sliding mode in the system and thus the steady-state trajectories of the system also remain bounded within a predesigned region in the presence of disturbances. The design of event parameters is also given considering the practical constraints on control execution. We show that the next triggering instant is larger than its immediate past triggering instant by a given positive constant. The analysis is also presented with taking delay into account in the control updates. An upper bound for delay is calculated to ensure stability of the system. It is shown that with delay steady-state bound of the system is increased than that of the case without delay. However, the system trajectories remain bounded in the case of delay, so stability is ensured. The performance of this event-triggered SMC is demonstrated through a numerical simulation.     

On the sliding mode control of MIMO nonlinear systems: An input‐output approach

We address the sliding mode control design problem for output reference trajectory tracking problems in the special class of MIMO flat systems known as static feedback linearizable systems. We assume unavailable system state components but rely on available inputs and measurable flat outputs. Each controller will largely ignore state and control input couplings by adopting a standard sliding mode controller scheme derived from the SISO case and used this as decoupled input‐to‐flat‐output model. The standard controller arises from a vastly simplified pure integration, additively perturbed, system. The simplified pure integration system controlled trajectories are shown to be time‐scale homotopically equivalent to those of the nonlinear flat system. The basic sliding surface coordinate function design is approached from the perspective of structural integral reconstructors requiring only the inputs and the flat outputs of the system. Integral structural reconstructors were introduced by Fliess et al for the control of linear SISO and MIMO systems, giving rise to the generalized proportional integral control method. Simulations are presented for SISO and MIMO systems and experimental results are reported for a two‐degree‐of‐freedom fully actuated robotic manipulator.     

MIMO非线性不确定系统二阶滑模控制

提出了一种基于有限状态机切换策略的多输入多输出二阶滑模控制算法。算法保证了传统滑模控制对参数变化和扰动不灵敏的特点,削弱了滑模控制的“抖动”现象。在上界未知的测量噪声和参数变化的情况下,算法通过滑模量及其微分的符号构成控制律,实现了系统的镇定。仿真结果表明算法在噪声环境下能保证系统的稳定性,对参数不确定具有较强的鲁棒性。算法结构简单,便于实现。     

非线性不确定系统的直接自适应输出反馈模糊控制

针对一类单输入单输出非线性不确定系统，基于状态观测器并结合自适应模糊系统和滑模控制，提出一种稳定的直接自适应模糊输出反馈控制算法。该算法不需要系统状态可测的条件，并能保证闭环系统稳定。仿真结果表明了该方法的有效性。     

Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system

A novel fuzzy terminal sliding mode control （FTSMC） scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.     

Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system

A novel fuzzy terminal sliding mode control (FTSMC) scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.     

Robust nonlinear output feedback control for brake by wire control systems

This work proposes a nonlinear output feedback control law for active braking control systems. The control law guarantees bounded control action and can cope also with input constraints. Moreover, the closed-loop system properties are such that the control algorithm allows to detect—without the need of a friction estimator—if the closed-loop system is operating in the unstable region of the friction curve, thereby allowing to enhance both braking performance and safety. The design is performed via Lyapunov-based methods and its effectiveness is assessed via simulations on a multibody vehicle simulator.     

Time-varying sliding mode control for a class of uncertain MIMO nonlinear system subject to control input constraint

To solve the regulator problem of a class of uncertain MIMO nonlinear systems subject to control input constraint, three types of time-varying sliding mode control laws are proposed. The sliding surfaces pass the initial value of the system at the initial time, and are shifted/rotated towards the predetermined ones. The controller parameters are optimized by genetic algorithm (GA). Lyapunov method is adopted to prove the stability and robustness to the parameter uncertainties and external disturbance. By me...     

一类离散非线性时延系统的滑模变结构控制研究

针对时变时滞的离散非线性系统, 利用Takagi-Sugeno模糊模型对其进行线性逼近, 将系统在滑模面上渐近稳定的时滞相关稳定性条件转换为线性矩阵不等式(LMI)的求解问题。由于证明中引入了松弛矩阵变量, 因而所得结果具有较小的保守性。进而采用变速趋近率方法得到滑模变结构控制律。最后, 对具有时变时延的小车—拖车自动倒车系统, 运用T-S模糊模型建模, 实现了小车—拖车系统的自动倒车控制。仿真结果验证了控制器的有效性。