Design of a Robust Discrete Time Sliding Mode Repetitive Controller (original) (raw)

Dual-mode structure digital repetitive control

Automatica, 2007

A flexible repetitive control (RC) scheme named "dual-mode structure repetitive control" (DMRC) is presented in this article. A robust stability criterion for DMRC systems is derived in terms of two parameters: odd-harmonic RC gain and even-harmonic RC gain. Several useful corollaries for the stability are addressed to reveal the compatibility of DMRC. The general framework of DMRC offers the flexibility in the development of various RC controllers. Without additional complexity and loss of tracking accuracy, DMRC can achieve faster error convergence rate than conventional RCs. DMRC requires the same data memory size as that of conventional RC one. An application example of DMRC controlled PWM inverter illustrates the validity of our proposed DMRC scheme. Comparisons of DMRC, conventional RC and odd-harmonic RC highlight the advantages of the presented DMRC approach. ᭧ . His research interests mainly involve power electronics and electric machines drives, advanced control and its applications and renewable energy generation. Dr. Zhou has authored or co-authored more than 30 published technical articles in the relevant areas.

New Repetitive Control with Improved Steady-state Performance and Accelerated Transient

In repetitive control, the enhanced servo performance at the fundamental frequency and its higherorder harmonics is usually followed by undesired error amplifications at other frequencies. In this paper, we discuss a new structural configuration of the internal model in repetitive control, wherein designers have more flexibility in the repetitive loop-shaping design, and the amplification of non-repetitive errors can be largely reduced. Compared to conventional repetitive control, the proposed scheme is especially advantageous when the repetitive task is subject to large amounts of non-periodic disturbances.

Robust design of repetitive control system

Repetitive controller is usually designed by assuming constant period of reference/disturbance signal, which leads to the selection of fixed sampling period. However, in practical, reference signal and disturbance are varying in period. Therefore, sampling period is carefully adjusted to overcome period variation, which makes characteristic of the plant is also changing. Robust design is employed to obtain pre-compensator which stabilizes closed loop repetitive system for all values of sampling period in the known interval. The design consists of two steps; constructing a nominal pre-compensator and designing robust pre-compensator which works well for large range of sampling period variation. In the design, time-varying plant parameters due to sampling period variation are treated as parametric uncertainties. The new form of pre-compensator which works with this robust design is also proposed.

A repetitive controller for discrete-time passive systems

Automatica, 2006

This work proposes and studies a new repetitive controller for discrete-time systems which are required to track or to attenuate periodic signals. The main characteristic of the proposed controller is its passivity. This fact implies closed-loop stable behavior when it is used with discrete-time passive plants. The work also discusses the energetic structure, the frequency response and the time response of the proposed controller structure. Some examples are included to illustrate its practical use. CONTENTS VII Conclusion 23 References 23 This work was supported in part by the Comisión Interministerial de Ciencia y Tecnologia (CICYT) under project DPI2004-06871-C02-02. Ramón Costa-Castelló and Robert Griñó are with the

Repetitive Control based on Integral Sliding Mode Control of Matched Uncertain Systems

International Journal of Advanced Computer Science and Applications

This paper proposed an integral sliding mode control scheme based on repetitive control for uncertain repetitive processes with the presence of matched uncertainties, external disturbances and norm-bounded nonlinearities. A new method based on the combination of repetitive control and sliding mode approach is studied in order to use the robustness sensibility property of the sliding mode control to matched uncertainties and disturbances and to cancel gradually tracking error for periodic processes. A sufficient condition of the existence of sliding mode is studied based on basic repetitive control and a sliding mode controller is synthesized through linear matrix inequalities, which guarantees the stability along the periods of the controlled closed-loop process and the reachability of the sliding surface is ensured. Then, an adaptive integral sliding mode controller is synthesized to improve performances of the proposed control scheme. The effectiveness of the proposed controlled design schemes is proved by the use of a third order uncertain mechanical system and the simulation results using the new approaches give good performances.

Design of Robust Repetitive Control With Time-Varying Sampling Periods

IEEE Transactions on Industrial Electronics, 2014

This paper proposes the design of robust repetitive control with time-varying sampling periods. First, it develops a new frequency domain method to design a low-order, stable, robust, and causal IIR repetitive compensator using an optimization method to achieve fast convergence and high tracking accuracy. As such, a new stable and causal repetitive controller can be implemented independently to reduce the design complexity. The comprehensive analysis and comparison study are presented. Then, this paper extends the method to design a robust repetitive controller, which compensates time-varying periodic signals in a known range. A complete series of experiments is successfully carried out to demonstrate the effectiveness of the proposed algorithms.

Design of Robust Higher-Order Repetitive Controller Using Phase Lead Compensator

IEEE Access, 2020

The performance of conventional repetitive controller (RC) deteriorates under frequency variations and system uncertainties. Due to limited bandwidth, it is also a trivial task to stabilize the conventional RC. This paper proposes a higher-order repetitive controller (HORC) with linear phase lead as a stabilizing compensator and zero-phase tracking error (ZPTE) compensator. The periodic signal generator, used by the HORC, offers relatively high gains in the neighborhood of tuned frequency and its harmonics. Stability conditions for higher-order repetitive (HOR) control system, including the phase lead compensator, are presented. The proposed solution is applied to repetitive current control of a two-level gridconnected inverter. Simulation and experimental results show that the HORC designed using the phase lead compensation is robust to frequency variation in reference/disturbance and system uncertainties. INDEX TERMS Repetitive controller, frequency variation, higher-order repetitive controller, phase lead.

Discrete-time repetitive control system with multiple periods

In this paper, a new approach to regulate any periodic signals with multiple periods is proposed and a useful discrete-time controller called multiple repetitive controller is presented. The contributions are as follows. First, the proposed multiple repetitive controller not only can be implemented with much less memory elements than the previous ones but also can provide much faster convergence of the controlled error to zero. Secondly, the proposed repetitive controller not only can assure the stability of the closed loop system but also can assign all poles of the system on a disk with a given radius whose center is the origin. Thirdly, the proposed controller is obtained in an explicit form and the design method requires to solve no equation. The design effort is very small even if the periods are very large. Finally, the proposed scheme is applied to DC servo motor system, and the effectiveness is demonstrated by simulation.

Repetitive Control Design for the Possible Digital Feedback Control Configurations

Advances in the Astronautical Sciences, 2018

Digital repetitive control (RC) seeks to make a feedback control system converge to zero tracking error at each sample time following a periodic command. Many spacecraft sensors perform repeated periodic scanning maneuvers. Zero tracking error might best be accomplished by observing previous period error and computing the needed correction from the system inverse. Unfortunately, discrete time equivalents of continuous time models usually have zeros introduced outside the unit circle, making the inverse model unstable. The asymptot-ic pattern of zero locations is known in general for each pole excess. One can cancel all dynamics inside the unit circle, but one cannot cancel the zeros outside. The authors and co-workers have developed several RC methods to design FIR filters that compensate these zeros, each making its own pattern of additional zeros outside. Previous literature considers many pole excesses, but normally only considers a continuous time feedback system converted to discrete time. More general applications need to handle general digital feedback control systems , with digital controller, but continuous time plant, possible anti-aliasing filter , possible sensor noise filter, etc. It is the purpose of this paper to examine what the possible patterns of zero locations can be for these different situations. New situations occur with repeated original zero pattern outside the unit circle, or neighboring zeros outside, or the union of zero patters for two different pole excesses. Each RC approach addresses these situations differently. Generally, the RC based on inverse frequency response tends to produce the best result, but the other approaches develop understanding of the source of observed compen-sator zero patterns.

Comparison of four discrete-time repetitive control algorithms

IEEE Control Systems, 1993

our different algorithms used for cancellation of periodic F disturbances are presented and compared. The theoretical advantages and disadvantages, computational complexity, execution time, and method of implementation are discussed for each method. Experimental data is presented from the use of these algorithms in compensating for repetitive disturbances present in the tracking servo of a computer disk drive. Four Methods-Options and Trade-offs The terms "repetitive control" and ''learning control" are often used to describe specialized control algorithms designed to cancel errors which are periodic in time. Many systems are subject to such errors. This typically occurs when the system repeats a trajectory over and over (Le., milling machines, robots, thermal cycling, etc.) or when the system is subject to disturbances that are periodic (Le., rotating machinery, power systems, satellites, etc.). The objective here is to compare four different methods so that the reader will have a good idea of options and trade-offs. Data from the use of these four algorithms on a disk drive enables us to draw conclusions about the properties of the controllers. Repetitive controllers can be classified as being either intemal model based or extemal model based. Controllers using the intemal model are linear and have periodic signal generators in them. The extemal model views the cancellation signal as being injected from outside of the basic plant/controller feedback loop. For intemal model type controllers we chose a Q-filter algorithm developed by Chew and Tomizuka [l], [2] and Tsao and Tomizuka [ 121 as well as a modification of the algorithm used by Sidman [6], [7]. For extemal model type controllers, we chose a parameter adaptation scheme used by Tomizuka and Kempf [ 101 and Sadegh and Gugliemo [5] as well as a variation of the leaming algorithm developed by Messner and Horowitz [4]. Experimental Apparatus All of the repetitive controllers discussed were implemented in a "plug-in" fashion, meaning the repetitive compensator is