General parallel structure digital repetitive control

This article presents a parallel structure digital repetitive control (PSDRC) scheme, where the internal models of all harmonics are decomposed into multiple parallel connected groups. Compared with conventional repetitive controller, the proposed parallel structure enables repetitive controller to regulate the error convergence rate at each group of harmonic frequencies independently and offers faster total error convergence rate. Moreover, PSDRC can achieve zero-error tracking or perfect disturbance rejection for all harmonics without occupying more data memory. A stability criterion with rigorous proof for PSDRC system is addressed, which is compatible with those existing stability criteria for existing RC schemes. An application example of three-phase pulse-width modulation inverter is provided to demonstrate the effectiveness of the proposed PSDRC scheme.     

Digital repetitive plug-in controller for odd-harmonic periodic references and disturbances

This work develops a digital repetitive plug-in controller for odd-harmonic discrete-time periodic references and disturbances. The controller presents a novel structure and it has a lower data memory occupation than the usual repetitive controllers because it takes advantage of the particular characteristics of the signals to track or attenuate. A sufficient criterion of stability, several hints for its practical application and an example are also included in the work.     

Analysis and design of a robust odd-harmonic repetitive controller for an active filter under variable network frequency

Frequency variations in the electrical network may cause a dramatic performance decay in repetitive controlled active filters intended to remove odd-harmonic distortion in single-phase AC loads. This work presents an odd-harmonic repetitive controller for a shunt active power filter that addresses such a performance problem. This is achieved by means of an adaptive change of the sampling period of the digital controller. However, this action implies structural changes that may result in an overall destabilization of the closed-loop system. Hence, a small-gain theorem-based robust control design technique allows to obtain a controller which assures BIBO stability in the required sampling period interval. Experimental results validate the proposal.     

High-order repetitive control for discrete-time linear switched systems

This paper is concerned with the design of a high-order repetitive control (RC) law for a class of discrete-time linear switched systems with repetition-varying reference trajectories. First, a high-order RC law, which embeds the characteristic of known variation of the reference trajectories, is proposed to the system, and a two-dimensional (2D) model is presented to describe the control and learning actions of the repetitive control system by using the lifting technique. By choosing appropriate multiple Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the proposed results.     

机器人系统非线性分散重复学习轨迹跟踪控制

采用一类具有"小误差放大、大误差饱和"功能的非线性饱和函数来改进传统重复学习控制(Repetitive control, RC)机器人系统动力学控制, 形成一类新的非线性分散重复学习控制(Nonlinear decentralized repetitive control, NRC),使得在不增加驱动力矩的条件下获得了更快的响应速度和更高的轨迹跟踪精度. 应用Lyapunov直接稳定性理论和LaSalle不变性原理证明了闭环系统的全局渐近稳定性. 三自由度机器人系统数值仿真结果表明了所提出的非线性分散重复学习控制具有良好的控制品质.     

Quasi-sliding mode based repetitive control for nonlinear continuous-time systems with rejection of periodic disturbances

A Quasi-Sliding Mode (QSM) based tracking control method for tackling Multiple-Input Multiple-Output (MIMO) nonlinear continuous-time systems with un-matching system uncertainties and exogenous disturbances is proposed. The presented Repetitive Control (RC) scheme ensures robust system stability when the system is subject to non-periodic uncertainties and exogenous disturbances. The complete rejection of periodic exogenous disturbances and a perfect tracking of non-periodic reference trajectories are achievable. In this paper, a practical application to a mass-spring-damper system is used to illustrate the validity of the proposed QSM based RC method.     

Discrete terminal sliding mode repetitive control for a linear actuator with nonlinear friction and uncertainties

A robust discrete terminal sliding mode repetitive controller is proposed for a class of nonlinear positioning systems with parameter uncertainties and nonlinear friction. The terminal sliding mode control (TSMC) part is designed to improve the transient characteristics of the system, as well as the robustness against parameter uncertainties, nonperiodic nonlinearities, and disturbances. The repetitive control (RC) part is then integrated to eliminate the effects of the periodic uncertainties present in the system. Moreover, a pure phase lead compensator is incorporated into the RC to improve the tracking at high frequencies. A robust stability analysis and an analysis of the finite time convergence properties of the proposed controller are also provided in this paper. Simulation testing and an experimental validation using a linear actuator system with nonlinear friction and parameter uncertainties are conducted to verify the effectiveness of the proposed controller.     

Separated design of robust model predictive control for LPV systems with periodic disturbance

To eliminate the steady-state error of systems with periodic disturbance, the repetitive control (RC) is a useful approach. For practical applications, the controller is designed to both steer system output to a given set-point (or track a given reference signal) and reject periodic disturbance. The learning procedure of RC and the control action to steer system output to a set-point may influence each other and prolong the convergence time RC. In order to reduce this interaction, this paper proposes a separated design approach. A linear parameter varying (LPV) system is considered. A repetitive predictive control (RPC) and a robust model predictive control (RMPC) are separately designed, respectively, corresponding to reject the periodic disturbance and steer system output to the set-point. The convergence of the proposed RPC sub-controller is derived. The numerical examples show that the proposed design is effective.     

Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control

This paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional‐derivative control strategy is presented, where the derivative gain is to make the closed‐loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.