Design of observer-based robust repetitive-control system

This paper presents a novel design method for discrete-time repetitive control systems (RCS) based on two-dimensional (2D) discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and linear matrix inequality (LMI) method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI of the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.

In view of the surplus torque and complexity of controlled plant in passive electrical load system, a novel approach based on single neuron PID adaptive control and repetitive control for repetitive periodic load control system is proposed. Radial basis function (RBF) neural network is used to identify the system on-line for the single neuron PID controller to adjust its weights and PID parameters by self- learning and self-adapting based on the desired output. The dynamic state performance can be improved by the single neuron adaptive PID control and the steady state performance is also improved by modified repetitive control. Computer simulation results show that the force/position hybrid control system can effectively reduce the surplus torque and improve the loading precision, and also it has fine dynamic and steady state performance and good robustness. The reliability of whole system is further improved.

This paper shows that design of a robustly stable repetitive control system is equivalent to that of a feedback control system for an uncertain linear time-invariant system satisfying the well-known robust performance condition. Once a feedback controller is designed to satisfy the robust performance condition, the feedback controller and the repetitive controller using the performance weighting function robustly stabilizes the repetitive control system. It is also shown that we can obtain a steady-state tracking error described in a simple form without time-delay element if the robust stability condition is satisfied for the repetitive control system. Moreover, using this result, a sufficient condition is provided, which ensures that the least upper bound of the steady-state tracking error generated by the repetitive control system is less than or equal to the least upper bound of the steady-state tracking error only by the feedback system

The modified repetitive control system is a type of servomechanism for periodic reference inputs. That is, the modified repetitive control system follows the periodic reference input with a small steady state error, even if a periodic disturbance or uncertainty exists in the plant. Using previously proposed modified repetitive controllers, even if the plant does not include time-delay, transfer functions from the periodic reference input to the output and from the disturbance to the output have infmite numbers of poles. To specify the input-output and the disturbance attenuation characteristic easily, Yamada et al. proposed the concept of a simple repetitive control system such that the controller works as a modified repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have fmite numbers of poles. In addition, Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. Recently, the p...

A new design method of the repetitive control system for linear systems with time-varying norm-bounded uncertainties is presented, which can design a low-pass filter of the repetitive controller and a stabilizing controller simultaneously in the repetitive control system. Using a Lyapunov functional for the repetitive control system, sufficient conditions are derived in terms of a linear matrix inequality (LMI), which ensure robust stability of the repetitive control system and achieve the prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance. Based on derived conditions, the problem of designing a stabilizing controller and finding the cut-off frequency of a low-pass filter is reformulated as an optimization problem with an LMI constraint of the free parameter. Then, an iterative algorithm is presented to calculate the largest cut-off frequency of a low-pass filter and design the corresponding state-feedback controller simultaneously. A numerical example is presented to illustrate the validity of the proposed method.

This paper investigates the problem of designing a robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> repetitive control system with periodic time-delay. Firstly, a continuous-discrete two-dimensional (2D) model with time-delay is constructed to describe the control and learning actions of the system. Then, by choosing an appropriate Lyapunov functional, LMI-based sufficient stability conditions for asymptotic stability and satisfactory H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> tracking performance of the 2D model is derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

The structured singular value method is applied to continuous-time SISO repetitive control systems in order to determine their stability and performance robustness in the presence of structured parametric modeling error in the plant. Performance measures for repetitive control systems are introduced and the robust performance analysis using structured singular values is modified, taking the alternating magnitude behaviour of the sensitivity function of a repetitive control system into account. The analysis procedure is simplified considerably in the case of large time delay by noting that the upper and lower envelopes of the structured singular value plots are obtained from corresponding finite dimensional systems without any time delay. The analysis procedures developed are applied to an example on repetitive control of an electrohydraulic material testing machine, available in the literature, to demonstrate their usefulness.

Effects of Non-Periodic Disturbances on Repetitive Control Systems

We give a parameterization of all causal stabilizing repetitive learning controllers for single-input and single-output linear minimum phase systems. The past studies on the parameterization of a repetitive learning control system were to obtain the parameterization of all internally stabilizing controllers for the control system such that the plant is connected 1/(1-e/sup -sT/) in series. Since 1/(1-e/sup -sT/) has no zeros in the closed right half plane, also the serial connections of 1/(1-e/sup -sT/) and a minimum phase system have no zeros in the closed right half plane. That is, the parameterization of all stabilizing controllers for a repetitive learning control system may be obtained by using the parameterization for a minimum phase system in Glaria and Goodwin (1994). Using the above mentioned idea, at first, the parameterization of all stabilizing repetitive learning controllers for the biproper minimum phase system is carried out. Next, since the exact repetitive learning controllers to stabilize the strictly stable proper system do not exist, the parameterization of all modified repetitive learning controllers using a low-pass filter in the repetitive learning controller is given.

The paper presents a limited angle torque motor used in optical scanning system. A method called repetitive control, in which the controlled variables follow periodic reference commands, is proposed to design the limited angle torque motor tracking control system. The compensator in the repetitive control system is synthesized by H/sub /spl infin// optimal control design theory. Experimental results show that the tracking performance of the repetitive controller is superior to that of the conventional controller.

The problem of designing output error controllers to track periodic reference signals for a class of uncertain linear time-delay systems subject to periodic disturbances is addressed. A repetitive controller, which is a type of output error controller, is developed for these systems and a sufficient condition for stability of the closed-loop system is derived by applying the Lyapunov–Krasovskii functional and linear matrix inequalities (LMIs). In order to relax the stability condition, the theory of the modified repetitive control (RC) system is extended to the systems represented by irrational transfer functions. Based on the extended theory of the modified RC system, a modified repetitive controller, another type of output error controller, is developed for these systems and sufficient conditions for stability of the closed-loop system are derived in terms of a frequency-domain criterion and LMI. Numerical simulations are presented to demonstrate the effectiveness of the proposed controllers.

A Design of Repetitive Control Systems – high Accuracy Servomechanisms for Periodic Inputs

In the present paper, we examine, a design method for 2-degree-of-freedom repetitive control systems. The 2-degree-of-freedom control has good characteristics, such as the input-output characteristics for the reference input and feedback control characteristics can be independently settled. 2-degree-of-freedom controllers consist of the feed-forward controller and the feedback controller. Design method of feedback controller for the repetitive control systems has been considered sufficiently, but design of feed-forward controllers for the repetitive control system has not been considered yet. In order to design feed-forward controller for the repetitive control system, we must solve the interpolation problem. In addition, the interpolation problem for feed-forward controller for the repetitive control system has many interpolation points. No method has been proposed to solve the interpolation problem for feed-forward controller for the repetitive control system. The purpose of this paper is to give a design method for feed-forward controllers and to propose a design method of 2-degree-of-freedom repetitive control systems.

This paper concerns the problem of designing a modified repetitive-control (RC) system for a class of servo system with nonintegral-chain form and unknown nonlinear dynamics, whose relative degree may be less than the system order. Our solution focuses on the unique features of equivalent input disturbance (EID) and extended state observer (ESO) approaches. An improved ESO is designed to estimate the EID together with the states by exploiting the known information of the plant model and the incorporation of the EID estimate into an RC law compensates for the influences of the actual disturbances. Both the stability criteria and optimization algorithm for controller parameters are provided. Finally, an application to speed control of a brushless DC motor system demonstrates the validity of the method.

Compensation in Repetitive Control System for Aperiodic Disturbances and Input Dead Zone