Robust discrete-time sliding mode control for tracking and model following of uncertain nonlinear systems

This paper proposes a discrete-time controller for robust tracking and model following of a class of nonlinear, multi-input multi-output, systems. For this purpose, a discrete-time sliding mode controller (DTSMC) is used to ensure the stability, robustness and an output tracking against the modelling uncertainties, even at relatively large sampling periods. In this way, Takagi–Sugeno (T–S) fuzzy modelling is used to decompose the nonlinear system to a set fuzzy-blended locally linearised subsystems. Implementation of the second Lyapunov theory for mismatched uncertain nonlinear T–S fuzzy models results in a set of linear matrix inequalities, which is used to design the sliding surface. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show that the proposed method guarantees the stability of closed-loop system and achieves small tracking error in the presence of parametric uncertainties at large sampling periods.     

Robust tracking control for uncertain fuzzy systems with time delay and external disturbances

In this article, robust tracking and disturbance rejection problem for Takagi–Sugeno fuzzy systems with time delay and external disturbances are discussed. Specifically, proportional-integral controller with an enhanced equivalent-input-disturbance technique is constructed to force the output trajectories to track the bounded reference input signal even in the presence of external disturbances. Further, the resulting fuzzy control system can be represented as an augmented system with state delay and uncertainties and the output tracking problem is transformed into stabilization problem of the augmented system. In the stabilization analysis, the considered fuzzy system does not share the same membership functions with the proposed control. Moreover, the delay-dependent stabilization criteria for the addressed fuzzy system are presented in the form of linear matrix inequalities by the virtue of augmented Lyapunov–Krasovskii functional. To be specific, the symmetric matrices involved in the Lyapunov–Krasovskii functional need not be positive definite. Ultimately, three numerical examples are offered to support the validity of the established theoretical results.     

基于动态参考规划的鲁棒Tube模型预测跟踪控制

为实现扰动和约束作用下对系统的最优鲁棒跟踪, 提出一种动态参考规划(DRP)方法, 设计鲁棒Tube模型预测控制器(RTMPC)将系统状态驱动到以最优跟踪点为中心的扰动不变集内. 基于DRP的RTMPC控制方法, 以多步参考为决策变量, 确保在线优化递归可行性的同时, 增加在线优化的自由度; 另外, 通过设定目标函数惩罚标称状态轨迹和参考稳态之间、以及最后一步参考稳态和设定点之间的加权欧式距离, 可实现最优鲁棒跟踪.     

Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input

The stabilisation problem for a class of Takagi–Sugeno (TS) fuzzy bilinear systems (FBSs) with time-varying state and input delays is investigated in this article. A fuzzy controller is designed to stabilise TS FBSs with time-varying state and input delays via the parallel distributed compensation method. Based on a Lyapunov–Krasoviskii function, the delay-dependent stabilisation conditions are proposed in terms of a linear matrix inequality to guarantee the asymptotic stabilisation of time-delay FBSs with disturbance input. Two numerical examples with delays in the state and input are given to demonstrate that the proposed stability condition is less conservative than some existing results. Finally, the validity and applicability of the proposed control scheme are successfully demonstrated in the control of a Van de Vusse reactor with delay.     

A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

A boiler‐turbine unit is a primary module for coal‐fired power plants, and an effective automatic control system is needed for the boiler‐turbine unit to track the load changes with the drum water level kept within an acceptable range. The aim of this paper is to develop a nonlinear tracking controller for the Bell‐Åström boiler‐turbine unit. A Takagi‐Sugeno fuzzy control system is introduced for the nonlinear modeling of the Bell‐Åström boiler‐turbine unit. Based on the Takagi‐Sugeno fuzzy models, a nonlinear tracking controller is developed, and the proposed control law is comprised of a state‐feedforward term and a state‐feedback term. The stability of the closed‐loop control system is analyzed on the basis of Lyapunov stability theory via the linear matrix inequality approach and Schur complement. Moreover, model uncertainties are also considered, and it is proved that with the proposed control law the tracking error converges to zero. To assess the performance of the proposed nonlinear state‐feedback state‐feedforward control strategy, a nonlinear model predictive control strategy and a linear strategy are presented as comparisons. The effectiveness and the advantages of the proposed nonlinear state‐feedback state‐feedforward control strategy are demonstrated by simulations.     

Robust nonlinear variable selective control for networked systems

This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi–Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H₂ performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.     

离散时间部分状态反馈模型参考自适应控制

本文针对线性不确定性系统, 给出了部分状态反馈直接模型参考自适应控制设计方案以及详细的系统稳 定性、输出跟踪性能分析. 控制器设计基于降维观测器和参数化方法. 此方案采用反馈控制, 反馈信号不仅仅依赖 全状态信息或者输出信号, 而是任意不超过系统维数的可测信号. 因此, 部分状态反馈控制是包含状态反馈、输出 反馈控制的新的控制方案, 缓解了状态反馈对状态信息的限制, 降低了输出反馈控制结构的复杂性. 通过引入辅助 信号, 本文证明了输出匹配条件的存在性、所有闭环系统信号的有界性以及渐近输出跟踪性能. 仿真结果验证了该 方案的有效性.     

State tracking model reference adaptive control for switched nonlinear systems with linear uncertain parameters

Model reference adaptive control(MRAC)is considered for a class of switched nonlinear systems in which the unknown parameters appear linearly.The linear uncertain parameters in each subsystem can be expressed as a vector and the uncertain vectors in different subsystems are estimated individually by different vector variables.Update laws are designed such that the parameter estimation will ’freeze’ until its corresponding subsystem is active.Controllers for subsystems are given to ensure asymptotic states tracking under arbitrary switchings.Two examples are presented to validate the proposed method.     

微手系统的鲁棒无源跟踪控制

近年来, 微手系统作为机器人技术的一个热门研究领域, 受到了越来越多的关注. 由于微手系统是复杂且具有非线性的, 因此在实际应用当中很难达到精确跟踪的性能. 为了解决微手系统的精准控制问题, 本文讨论了微手系统的鲁棒无源跟踪控制. 首先, 运用基于演算子理论的鲁棒右互质分解方法, 建立了微手系统的动态模型. 然后, 通过结合无源补偿算子, 设计了无源鲁棒控制器, 保证了系统的鲁棒稳定性和无源性. 进而提出了基于双Bezout恒等式的鲁棒跟踪控制方案, 使整个非线性系统具有较强的鲁棒性和良好的跟踪性能. 最后, 通过仿真进一步验证了所提出方法的有效性     

Robust tracking control of an induction motor

This paper address the tracking control problem of a induction motor driving a mechanical load. Based on the nonlinear dynamics of the induction motor, a robust tracking controller is developed which can compensate for parametric uncertainties and additive bounded disturbances throughout the entire electromechanical system. A uniform ultimate bounded (UUB) result is obtained for the rotor position tracking error. Simulation results with full state measurements and a flux observer are presented to illustrate the effectiveness of the proposed controller.     

离散线性信息融合最优跟踪控制

提出一种有限时间离散线性最优跟踪控制问题的新解法--信息融合估计解法.基于信息融合估计理论,推导出协状态融合滤波方程和控制量融合估计值,由此获得最优融合控制律及二次性能指标最小值.从理论上证明了信息融合估计解法与传统解法的等同性,从信息融合的角度建立了有限时间离散线性最优跟踪控制系统,从而统一了最优控制问题和最优估计问题,电机系统的控制仿真结果验证了该解法的有效性以及与传统解法的等同性.     

Robust reliable control for a near space vehicle with parametric uncertainties and actuator faults

Based on fuzzy control techniques, this article is concerned with the problem of robust reliable control for a near space vehicle (NSV) with parametric uncertainties and actuator faults. The nonlinear dynamics of a NSV is represented by the Takagi–Sugeno fuzzy models, and then the actuator fault model and fuzzy state-space observer are developed. Next, the fuzzy observer-based robust reliable control strategy is proposed. It is proved that the fuzzy control systems for the NSV is reliable in the sense that the closed-loop system is asymptotically stable and the actuator components can operate well in the presence of some actuator faults. The developed theoretical results are in the form of linear matrix inequalities, which can be readily solved via standard numerical software. Finally, simulation results are given to illustrate the applicability of the proposed approach.     

Mobility assistance system for an electric wheelchair using annotated maps

An electric wheelchair is very useful for physically challenged or elderly people. A electric wheelchair can be equipped with a computer and sensors such as cameras and LIDARs to make it a robotic wheelchair. This opens the possibility to reduce the burden and increase the comfort of the users with use of robotics technology. In this paper, we begin with a dynamic shared control and propose to use a map with annotations to increase the user’s comfort while keeping safety. We provide a system with localization, which can relate the current position of the wheelchair to the annotations. Both quantitative evaluation and subjective survey demonstrate the effectiveness of the proposed method.     

一类互联机器人系统的鲁棒分散跟踪控制

研究互联机器人系统在受到模型不确定性和外部干扰情况下的鲁棒轨迹跟踪问题.针对系统中存在的不确定动力学问题,在不确定项的连续界函数已知的情况下,基于Lyapunov设计方法提出一种鲁棒分散控制器的设计方法,实现互联机器人系统位置和速度的渐近跟踪.仿真算例表明了该方法的有效性.     

Discrete model reference adaptive control with an augmented error signal

A method is developed for designing discrete model reference adaptive control systems when one has access to only the plant's input and output signals. Controllers for single-input, single-output, nonlinear, nonautonomous plants are developed via Lyapunov's second method. The augmented error signal method is employed to ensure that the normally used true error signal approaches zero asymptotically without requiring anticipative values of the plant output signal. Such anticipative signals are replaced by others easily obtained from low pass digital filters operating on the plant's input and output signals.     

Simultaneous fault estimation and fault-tolerant tracking control for uncertain nonlinear discrete-time systems

This paper deals with simultaneous fault estimation and control for a class of nonlinear systems with parameter uncertainty, which is described by Takagi–Sugeno (T–S) fuzzy model with parameter uncertainties and unknown disturbance. In this paper, a fuzzy reference model is used to generate error dynamic for tracking control. By considering actuator fault as an auxiliary state vector, we construct an augmented error system and propose a fault estimator/controller to achieve simultaneous fault estimation and fault-tolerant tracking control. H_∞ approach is used in the design of estimator/controller to attenuate the effect of the unknown disturbance and parameter uncertainties. The design conditions are formulated into a set of linear matrix inequalities (LMIs), which can be efficiently solved. Finally, a pitch-axis nonlinear missile model is used to illustrate the effectiveness of the proposed method.     

Speed tracking control using an ANFIS model for high-speed electric multiple unit

The high-speed electric multiple unit (EMU) is a complex, uncertain and nonlinear dynamic system. The traditional approach to operating the high-speed EMU is based upon manual operation. To improve the performance of high-speed EMU, this paper develops a control dynamic model to capture the motion of the high-speed EMU and then uses it to design a desirable speed tracking controller for EMU. We exploit a data-driven adaptive neurofuzzy inference system (ANFIS) to model the running process. Based on the ANFIS model, we propose a generalized predictive control algorithm to ensure the high-precision speed tracking of the high-speed EMU. The simulation results on the actual CRH380AL (China railway high-speed EMU type-380AL) operation data show that the proposed approach could ensure the safe, punctual, comfortable and efficient operation of high-speed EMU.     

Relaxed fuzzy control synthesis of nonlinear networked systems under unreliable communication links

This paper proposes relaxed conditions for control synthesis of discrete-time Takagi–Sugeno fuzzy control systems under unreliable communication links. To widen the applicability of the fuzzy control approach under network environments, a novel fuzzy controller, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the multi-steps-past normalized fuzzy weighting functions, is provided to make much more use of the information of the underlying system. Moreover, a new kind of slack variable approach is also developed and thus the algebraic properties of these multi-instant normalized fuzzy weighting functions are collected into some augmented matrices. As a result, the conservatism of control synthesis of discrete-time Takagi–Sugeno fuzzy control systems under unreliable communication links can be significantly reduced. Two illustrative examples are presented to demonstrate the effectiveness of the theoretical development.