Observer-based controller for Lipschitz nonlinear systems

An observer-based controller for Lipschitz nonlinear systems is presented. The necessary and sufficient condition to ensure stability of state-observer as well as nonlinear system with state-feedback control law is derived. According to the separation principle, the closed-loop stability is guaranteed based on dual problems concerning stability of state-observer and stability of state-feedback parts. Also, the stability region for locally Lipschitz nonlinearities is obtained. A practical synthesis approach to achieve controller parameters is then given which yields the closed-loop convergence with less conservative results. The effectiveness of the proposed synthesis method is finally demonstrated by simulation results.     

Output-feedback sampled-data polynomial controller for nonlinear systems

This paper presents the stability analysis and control synthesis for a sampled-data control system which consists of a nonlinear plant and an output-feedback sampled-data polynomial controller connected in a closed loop. The output-feedback sampled-data polynomial controller, which can be implemented by a microcontroller or a digital computer, is proposed to stabilize the nonlinear plant. Based on the Lyapunov stability theory, stability conditions in terms of sum of squares are obtained to guarantee the stability and to aid the design of a polynomial controller. A simulation example is given to demonstrate the effectiveness of the proposed control approach.     

Robust self-tuning PID controller for nonlinear systems

In this paper, we propose a robust self-tuning PID controller suitable for nonlinear systems. The control system employs a preload relay (P_Relay) in series with a PID controller. The P_Relay ensures a high gain to yield a robust performance. However, it also incurs a chattering phenomenon. In this paper, instead of viewing the chattering as an undesirable yet inevitable feature, we use it as a naturally occurring signal for tuning and re-tuning the PID controller as the operating regime digresses. No other explicit input signal is required. Once the PID controller is tuned for a particular operating point, the relay may be disabled and chattering ceases correspondingly. However, it is invoked when there is a change in setpoint to another operating regime. In this way, the approach is also applicable to time-varying systems as the PID tuning can be continuous, based on the latest set of chattering characteristics. Analysis is provided on the stability properties of the control scheme. Simulation results for the level control of fluid in a spherical tank using the scheme are also presented.     

严格反馈型非仿射非线性系统的自适应模糊控制

针对一类具有严格反馈形式的非仿射非线性受扰系统,提出了基于backstepping方法的自适应模糊控制.该算法仅要求模糊逻辑系统逼近误差范数有界,引入监督控制补偿系统逼近误差和外界干扰,保证闭环系统所有信号一致有界,跟踪误差一致渐近稳定.将R(o)ssle混沌系统作为仿真对象,仿真结果表明了该方法的有效性.     

非线性切换系统基于观测器的容错控制器设计

针对一类具有执行器故障的非线性切换系统,研究基于系统状态估计和故障重构的容错控制问题.首先,在具有平均驻留时间(ADT)的切换信号下,设计一种切换PI观测器作为状态-故障估计器,以达到对系统状态和故障同时渐近估计的目的;其次,基于线性矩阵不等式,给出非线性切换系统观测器存在的充分条件;再次,基于PI观测器给出的状态和故障估计,提出一种非线性切换系统的容错控制器设计方法;最后,以一个电子电路为仿真实例进行分析,验证了所提出方法的可行性和适用性.     

A robust adaptive controller for Hammerstein nonlinear systems

Hammerstein nonlinear systems have appeared useful in modeling nonlinear processes encountered in engineering practice. Control algorithms may lead to unsatisfactory performance if the parametric model does not agree with the plant. To this end, this paper proposes a new robust adaptive control approach for discrete-time Hammerstein nonlinear systems which are more close to some industrial plants. The adaptive control law and recursive parameter estimation are updated by introducing the estimate of the model error as a feedback. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under mild conditions. Simulation examples including a continuous stirred tank reactor (CSTR) system are given to show the effectiveness of the obtained results.     

A robust Markov game controller for nonlinear systems

This paper proposes a reinforcement learning (RL)-based game-theoretic formulation for designing robust controllers for nonlinear systems affected by bounded external disturbances and parametric uncertainties. Based on the theory of Markov games, we consider a differential game in which a ‘disturbing’ agent tries to make worst possible disturbance while a ‘control’ agent tries to make best control input. The problem is formulated as finding a min–max solution of a value function. We propose an online procedure for learning optimal value function and for calculating a robust control policy. Proposed game-theoretic paradigm has been tested on the control task of a highly nonlinear two-link robot system. We compare the performance of proposed Markov game controller with a standard RL-based robust controller, and an H_∞ theory-based robust game controller. For the robot control task, the proposed controller achieved superior robustness to changes in payload mass and external disturbances, over other control schemes. Results also validate the effectiveness of neural networks in extending the Markov game framework to problems with continuous state–action spaces.     

Functional observer-based fuzzy controller design for continuous nonlinear systems

This paper presents a novel method of synthesising controllers for nonlinear systems represented by Takagi--Sugeno fuzzy model using functional observer. The proposed method uses minimum order observer for estimating the control input of each rule as a function of states. Existence conditions of the functional observer-based controller are provided in the form of rank equality conditions. The stability conditions of the observer are obtained using quadratic Lyapunov function, and the conditions are presented in the form of linear matrix inequalities. Observer parameters can be obtained by solving these inequalities. Finally, systematic synthesis procedures for constructing the observer are presented. Examples with simulation output are given to demonstrate this method and to compare its performance with a conventional full-state observer-based controller.     

An adaptive support vector regressor controller for nonlinear systems

In this study, a novel online support vector regressor (SVR) controller based on system model estimated by a separate online SVR is proposed. The main idea is to obtain an SVR controller based on an estimated model of the system by optimizing the margin between reference input and system output. For this purpose, “closed-loop margin” which depends on tracking error is defined, then the parameters of the SVR controller are optimized so as to optimize the closed-loop margin and minimize the tracking error. In order to construct the closed-loop margin, the model of the system estimated by an online SVR is utilized. The parameters of the SVR controller are adjusted via the SVR model of system. The stability of the closed-loop system has also been analyzed. The performance of the proposed method has been evaluated by simulations carried out on a continuously stirred tank reactor (CSTR) and a bioreactor, and the results show that SVR model and SVR controller attain good modeling and control performances.     

输入饱和下非线性系统的事件触发控制器设计

本文研究了具有输入饱和的非线性系统事件触发控制策略设计问题.首先,针对输入饱和下非线性系统,建立混杂系统模型.其次,当非线性函数满足Lipschitz条件下,给出闭环混杂系统局部一致渐近稳定性的稳定判据,并设计了事件触发饱和控制器.然后,当非线性函数满足扇区条件时,给出闭环混杂系统框架下满足局部一致渐近稳定性的LMI条件,并设计了事件触发饱和控制器.进一步地,在事件触发饱和控制器作用下,分析了非线性系统的半全局鲁棒镇定性.最后,结合两个仿真实例说明了所提出事件触发控制策略的有效性.     

A fuzzy PID controller for nonlinear and uncertain systems

 In order to control systems that contain nonlinearities or uncertainties, control strategies must deal with the effects of these. Since most control methods based on mathematical models have been mainly focused on stability robustness against nonlinearities or uncertainties, they are limited in their ability to improve the transient responses. In this paper, a nonlinear fuzzy PID control method is suggested, which can stably improve the transient responses of systems disturbed by nonlinearities or unknown mathematical characteristics. Although the derivation of the control law is based on the design procedure for general fuzzy logic controllers, the resultant control algorithm has analytical form with time varying PID gains rather than linguistic form. This means the implementation of the proposed method can be easily and effectively applied to real-time control situations. Control simulations are carried out to evaluate the transient performance of the suggested method through example systems, by comparing its responses with those of the nonlinear fuzzy PI control method developed in [9].     

A third-order sliding mode controller for nonlinear multivariable systems

This paper proposes a third-order sliding mode controller for nonlinear multivariable systems with uncertain parameters and subject to external disturbances. The controller achieves fast convergence rate, high tracking accuracy, and a reduced level of chattering. The stability of the controller and its global ultimately uniform convergence is proved by the Lyapunov stability theory. Simulation results on a single inverted pendulum system are given to illustrate the effectiveness of the proposed control scheme by comparing it with methods such as a second-order supertwisting controller, a third-order supertwisting controller, and an integral terminal third-order sliding mode controller.     

TS-based sampled-data model predictive controller for continuous-time nonlinear systems

This paper proposes a new fuzzy model predictive control approach for continuous-time nonlinear systems in terms of linear matrix inequalities (LMIs). The proposed approach is based on the Takagi–Sugeno fuzzy modeling, a quadratic Lyapunov function, and a sampled-data parallel distributed compensation controller with constant sampling time. The goal is designing the sampled-data controller such that at each sampling time, the stability of the closed-loop system is guaranteed and an infinite horizon cost function is minimised. The main advantage of the proposed approach is to eliminate the approximations induced from discretizing the original system and cost function upper bound minimisation. Consequently, a lower bound of the cost function is obtained and the performance of the proposed model predictive controller is improved compared to the recently published papers in the same field of interest. In addition, the Euclidean norm constraint of the control input vector is derived in terms of LMIs. To illustrate the merits of the proposed approach, the proposed technique is applied to a continuous stirred tank reactor system.     

A nonlinear hybrid controller for swinging-up and stabilizing the Furuta pendulum

The conventional switching strategy for solving the inverted pendulum control problem is based on two steps: swinging-up and stabilization. In this note, first, a new strategy for swinging the Furuta pendulum up towards the desired upright position is designed using the Speed-Gradient method, which uses only directly measured coordinates. Then, a nonlinear controller, based on the Forwarding approach, stabilizes the upright position. As a new contribution the latter leads to a nonlinear stabilizer around the upright position, whose Lyapunov function yields a larger size estimation of the domain of attraction than the one obtained with the traditional linear approach. This estimation allows us to use it in a global switching strategy in the practical implementation and guarantees almost-global asymptotic stability of the equilibrium. Successful experimental results are reported with the available laboratory Furuta pendulum.     

不确定非线性系统的高阶滑模控制器设计

针对一类不确定非线性SISO系统,结合系统有限时间稳定理论与积分滑模控制理论,提出了一种新的高阶滑模控制器设计方法,改善了现有高阶滑模控制中存在的缺陷.积分滑模保证了系统初始时刻就具有抗扰能力,同时采用有限时间稳定观测器实现了高阶滑模的输出反馈控制.仿真结果表明该控制器可使系统在有限时间内收敛,并有效地减小了系统抖振.     

A simple robust controller for a class of nonlinear systems

A new robust state‐feedback controller is designed to solve the tracking problem of a class of nonlinear uncertain systems. The contributions of our paper are threefold: Firstly, a new robust state‐feedback controller with a simple structure is derived. Owing to its simplicity, less computation is needed. What is more, for polynomial‐type uncertainties, a much simpler controller can be derived directly without the need of computing partial derivatives. Secondly, a technique that leaves positive functions used in the nonlinear damping terms to be chosen freely is introduced which may enable us to find out a good one among all candidate positive functions to reduce the control effort and to design a ‘softer’ controller. Thirdly, the assumption made in non‐adaptive robust control schemes where the bounding functions are required to be exactly known is relaxed, and the assumption on the reference signal is relaxed too. When our robust controller is applied, the simulations show that better performance can be achieved with less control effort. Copyright © 2000 John Wiley & Sons, Ltd.     

异步电机的非线性自适应反步控制器设计

针对描述异步电机的动态特性方程,在一些系统参数未知的情况下,应用分离子系统的方法和反向递推技术,设计了非线性自适应控制器.实现了电机对给定转速信号和磁通量信号的输出渐近跟踪控制,保证了整个系统的全局有界稳定性.仿真结果验证了该自适应控制策略的有效性.