Sliding mode observers for a class of linear parameter varying systems

In this paper, a new framework for the synthesis of a class of sliding mode observers for affine linear parameter varying (LPV) systems is proposed. The sliding mode observer is synthesized by selecting the design freedom via linear matrix inequalities ( LMIs ). Posing the problem from a small gain perspective allows existing numerical techniques from the literature to be used for the purpose of synthesizing the observer gains. In particular, the framework allows affine parameter‐dependent Lyapunov functions to be considered for analyzing the stability of the state estimation error dynamics, to help reduce design conservatism. Initially a variable structure observer formulation is proposed, but by imposing further constraints on the LMIs, a stable sliding mode is introduced, which can force and maintain the output estimation error to be zero in finite time. The efficacy of the scheme is demonstrated using an LPV model of the short period dynamics of an aircraft and demonstrates simultaneous asymptotic estimation of the states and disturbances.     

基于鲁棒滑模观测器的多电机卷绕系统故障检测和隔离

针对多电机卷绕系统故障检测和隔离问题,提出了基于滑模观测器的鲁棒故障检测和隔离策略.首先,考虑到多电机卷绕系统运行环境变化引起的摩擦系数、杨式模量、半径和转动惯量等参数的不确定性,通过引入非线性未知输入干扰对系统不确定参数进行描述,将多电机卷绕系统转化为包含执行器故障的一般不确定非线性系统;其次,构造鲁棒滑模观测器并用作故障检测观测器,通过滑模控制来抑制未知输入干扰,使观测器具有鲁棒性,在此基础上,结合多观测器故障隔离的思想,提出了可以同时对多个执行器故障进行检测和隔离的方法;然后,根据李雅普诺夫理论得到使观测器系统指数收敛的充分条件,同时给出了观测器增益的求解方法;最后,仿真结果验证了所提方法的鲁棒性和有效性.     

Sliding mode control-based linear functional observers for discrete-time stochastic systems

Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method.     

Disturbance decoupled fault reconstruction using sliding mode observers

This paper investigates and presents conditions that guarantee disturbance decoupled fault reconstruction using sliding mode observers, which are less stringent than those of previous work, and show that disturbance reconstruction is not necessary. An aircraft model validates the ideas proposed in this paper. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Reduced order observers for the sliding mode control of mechanical systems with elastic joints

In this article the control of mechanical systems with elastic joints is addressed. This kind of system is characterised by a high relative degree. The mechanical control input must be designed to be continuous. Different reduced order observers are introduced and conditions are found to guarantee the exponential convergence of the observation errors. The error stability is ensured provided a certain matrix inequality has a solution. The proposed second-order sliding mode point-to-point controller based on the observed state is proven to stabilise the mechanical system with elastic joints about the desired reference position.     

Fault detection and isolation for nonlinear systems via high‐order‐sliding‐mode multiple‐observer

In this paper, fault detection and isolation problems are studied for a certain class of nonlinear systems. Under some structural conditions, multiple high‐order sliding‐mode observers are proposed. The value of the equivalent output injection is used for detecting faults and the multiple‐model approach for isolating particular faults in the system. The proposed method provides fast detection and isolation of actuator and plant faults. Simulation results support the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Design of first- and second-order sliding mode observers for induction motors using a stator-flux model

We extend current research in the area of ‘sensorless’ control of induction motors by presenting two observers based on first- and second-order sliding mode control theories for the simultaneous estimation of flux and speed. We base the observers on the stator-flux model of the motor instead of the usual rotor-flux model mainly because of the uncertain rotor resistance that plays a significant role in the latter. By designing the observers as if they are sliding mode controllers, we lend the properties of parameter insensitive closed-loop dynamics and finite time convergence to the stator flux and speed estimation schemes. We also present simulation and experimental results to validate the operation of the observers.     

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.     

Nonlinear sliding mode high-gain observers for fault estimation

A robust high gain observer for state and unknown inputs/faults estimations for a special class of nonlinear systems is developed in this article. Ensuring the observability of the faults/unknown inputs with respect to the outputs, the faults can be estimated from the sliding surface. Under a Lipschitz condition for the nonlinear part, the high gain observers are designed under some regularity assumptions. In the sliding mode, the convergence of the estimation error dynamics is proven similar to the analysis of high-gain observers.     

A sliding mode observer for monitoring and fault estimation in a network of dynamical systems

In this paper, a novel fault estimation strategy is proposed for a network of dynamical systems at a supervisory monitoring level. The network nodes include linear and Lipschitz nonlinear dynamics and time‐varying coupling strength. The aim is to enhance the autonomy level of this class of systems by means of this inherently robust, nonlinear strategy based on sliding mode ideas. The faults are reconstructed from the equivalent output error injection signal which is used to maintain sliding. A key facet of the strategy is that the synthesis of the sliding mode observer for the network depends solely on the dynamics of an individual node of the network. The theoretical results developed in the paper are demonstrated with an example consisting of a network of pendulums. Copyright © 2013 John Wiley & Sons, Ltd.     

New results in robust actuator fault reconstruction for linear uncertain systems using sliding mode observers

This paper presents a robust actuator fault reconstruction scheme for linear uncertain systems using sliding mode observers. In existing work, fault reconstruction via sliding mode observers is limited to either linear certain systems subject to unknown inputs, relative degree one systems or a specific class of relative degree two systems. This paper presents a new method that is applicable to a wider class of systems with relative degree higher than one, and can also be used for systems with more unknown inputs than outputs. The method uses two sliding mode observers in cascade. Signals from the first observer are processed and used to drive the second observer. Overall, this results in actuator fault reconstruction being feasible for a wider class of systems than using existing methods. A simulation example verifies the claims made in this paper. Copyright © 2007 John Wiley & Sons, Ltd.     

Sliding mode observers for detection and reconstruction of sensor faults

This paper proposes two methods for detecting and reconstructing sensor faults using sliding mode observers. In both methods, fictitious systems are introduced in which the original sensor fault appears as an actuator fault. The original sensor faults are then reconstructed using a ‘secondary’ sliding mode observer. For both methods, there are certain conditions which must be satisfied for successful fault detection and reconstruction. The methods are demonstrated using a chemical process example.     

Terminal sliding mode observers for a class of nonlinear systems

This paper proposes a terminal sliding mode observer for a class of nonlinear systems to achieve finite time convergence for all error states. Compared to standard sliding mode observers which only enable finite time convergence of the output error, the observer in this paper makes use of fractional powers to reduce other non-output errors to zero in finite time. A 2-degree-of-freedom robotic manipulator is used to demonstrate the effectiveness of the proposed observer.     

State estimation and unknown input reconstruction via both reduced-order and high-order sliding mode observers

This paper considers the problems of the simultaneous estimation of the system states and the unknown inputs for linear systems when the so-called observer matching condition is not satisfied. An auxiliary output vector is introduced so that the observer matching condition is satisfied with respect to it. A high-order sliding mode observer is considered to get the exact estimates of both the auxiliary outputs and their derivatives in a finite time based on the system measured outputs. After this, a reduced-order observer is constructed by using the estimated auxiliary outputs as the new system outputs. The reduced-order observer is able to asymptotically estimate the system states without suffering the influence of the unknown inputs. A kind of unknown input reconstruction method based on both the state and the auxiliary output derivative estimates is developed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.     

Adaptive sliding mode control and observation

ABSTRACT

This editorial article gives a short introduction to Special Issue of International Journal of Control on Adaptive Sliding Mode Control and Observation.     

Sliding mode predictive control: A survey

This paper reviews the development and application of sliding mode predictive control (SMPC) in a tutorial manner. Two core design paradigms are revealed in the combination of sliding mode control (SMC) and model predictive control (MPC). In the first case, MPC is used in the reaching phase to ensure a sliding mode is attained. In the second case, MPC is used to solve the existence problem and define the required performance in the sliding mode. The two approaches are discussed in detail from the perspectives of both theory and application. Finally, some future challenges and opportunities in the area of SMPC are summarized.     

基于级联观测器的多输入多输出非线性系统的故障诊断

将块观测方法应用于非线性系统的故障检测和分离.首先给出了非线性系统的块观测形式,针对传感器故障和执行器故障对非线性系统进行分块,得到了带有故障系统的块观测器形式.利用滑模观测器实现系统状态观测,得到观测器误差;利用所设计的观测器对非线性系统进行故障的诊断和分离;采用等效输出注入概念重构了故障信号,使得多变量输入输出非线性系统的故障诊断问题得到了解耦;针对异步电动机系统实现了传感器故障的分离.仿真结果证明了算法的有效性.     

Sliding mode for detection and accommodation of computation time delay fault

Computation time delay in digital control systems reduces its robustness as well as degrades its performance. In this paper, the computation time delay is assumed to be constant and smaller than the sampling time and is treated as a fault to be detected, using an appropriate controller to minimize its effects. Thus, a discrete-time sliding mode control that improves the systems’ performance when a computation time delay fault is found is proposed herein. A robust sliding mode observer-based is used to generate the residuals. Using the accumulated residual functions, a new scheme for fault detection and for controller adaptation is proposed. The technique is used to control a Rotary Motion Inverted Pendulum System to illustrate the design procedures and the effectiveness of the method.     

Sliding mode control of switched systems: A geometric algebra approach

Geometric algebra (GA) is proposed as a mathematical framework for revisiting fundamental aspects of sliding mode control (SMC) in nonlinear, switch-controlled, single input systems. Sliding mode existence conditions, the switching policy, the invariance conditions, the associated equivalent control, and the characterization of ideal sliding dynamics, are all re-examined using a geometric algebra (GA) standpoint. Two illustrative examples, from switched power electronics, are presented using the GA language.     

离散时间系统的滑模控制器设计与仿真研究

针对不确定性离散时间系统,分析和设计了一类变结构控制器。当存在外界干扰和不确定性时,系统状态也是全局有界稳定的。一个新的切换面作为系统的输出信号被提出,特别用来设计滑模控制器。系统状态一旦进入到准滑动模态,就对设备参数变化和外界干扰显示出强的鲁棒性,因为控制器的设计完全考虑了边界层的影响。外推法被用来估计不确定离散时间系统的不确定值。两种方法均有效地消除了系统的抖振,确保了系统的稳定性,且保证了变结构控制系统良好的品质。最后,仿真结果证实了所提出方法的有效性。