Transient Response of Repetitive Control Systems

1996 ◽  
Vol 118 (4) ◽  
pp. 795-797
Author(s):  
S. S. Garimella ◽  
K. Srinivasan
Keyword(s):  
Control System ◽  
Transfer Function ◽  
Decay Rate ◽  
Control Systems ◽  
Transient Response ◽  
Continuous Time ◽  
Relative Stability ◽  
Repetitive Control ◽  
Upper Bounds ◽  
Repetitive Controller

Upper bounds on transient response magnitudes for a SISO continuous-time repetitive control system are derived. Limiting the size of these transients is shown to be related to limiting the ∞-norm of a transfer function product of filters used in the repetitive controller. The decay rate of the transients is related to the peak of a function of frequency called the regeneration spectrum, which has previously been shown in the literature to be a measure of the relative stability of the system. Bounds derived here, although conservative, can be useful in the design of the repetitive controller, as illustrated by means of an example.

Stability Robustness of Repetitive Control Systems With Zero Phase Compensation

1990 ◽  
Vol 112 (3) ◽  
pp. 320-324 ◽  
Author(s):  
C. C. H. Ma
Keyword(s):  
Control System ◽  
Large Class ◽  
Control Systems ◽  
Repetitive Control ◽  
Tracking Performance ◽  
Three Solutions ◽  
Phase Compensation ◽  
Saturation Nonlinearity ◽  
Stability Robustness ◽  
Zero Phase

It is shown that a special zero phase control (ZPC) system introduced by Tomizuka is L∞ stable against a large class of common nonlinearities. However, it still suffers from the generic nonrobustness problem associated with a linear repetitive control system when subjected to a saturation nonlinearity. For the special ZPC system, however, three solutions exist for the problem, two of which do not degrade the repetitive tracking performance.

scholarly journals Padé-Approximation-Based Preview Repetitive Control for Continuous-Time Linear Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jia-Yu Zhao ◽  
Zhao-Hong Wang ◽  
Jian-De Yan ◽  
Yong-Hong Lan
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Padé Approximation ◽  
Repetitive Control ◽  
State Equation ◽  
The State ◽  
Space Representation ◽  
Pade Approximation ◽  
Time Linear ◽  
Repetitive Controller

This paper concerns a Padé-approximation-based preview repetitive control (PRC) scheme for continuous-time linear systems. Firstly, the state space representation of the repetitive controller is transformed into a nondelayed one by Padé approximation. Then, an augmented dynamic system is constructed by using the nominal state equation with the error system and the state equation of a repetitive controller. Next, by using optimal control theory, a Padé-approximation-based PRC law is obtained. It consists of state feedback, error integral compensation, output integral of repetitive controller, and preview compensation. Finally, the effectiveness of the method is verified by a numerical simulation.

Analysis and Design of Repetitive Control Systems Using the Regeneration Spectrum

1991 ◽  
Vol 113 (2) ◽  
pp. 216-222 ◽  
Author(s):  
K. Srinivasan ◽  
F.-R. Shaw
Keyword(s):  
Control System ◽  
System Design ◽  
Control Systems ◽  
Repetitive Control ◽  
Characteristic Root ◽  
Rational Approach ◽  
Control System Design ◽  
Analysis And Design ◽  
Sensitivity Functions ◽  
Insight Into

The absolute and relative stability of continuous-time SISO repetitive control systems is examined here using a function of frequency termed the regeneration spectrum. The regeneration spectrum is easily computed and is related to important features of the characteristic root distribution of such systems, for large values of the time delay. The regeneration spectrum is combined with other frequency domain measures of control system performance such as the sensitivity and complementary sensitivity functions to obtain improved insight into the tradeoffs in repetitive control system design. The result is a more rational approach to repetitive control system design and is illustrated by an example.

Laplace-type integral transform for time-varying periodic repetitive controller design

2018 ◽  
Vol 233 (2) ◽  
pp. 204-213
Author(s):  
Wu-Sung Yao ◽  
Po-Wen Hsueh
Keyword(s):  
Control System ◽  
Integral Transform ◽  
Controller Design ◽  
Integral Transformation ◽  
Repetitive Control ◽  
Periodic Signal ◽  
Time Varying ◽  
Type Integral ◽  
Laplace Type ◽  
Repetitive Controller

In this article, Laplace-type integral transformation is introduced to construct the recursive algorithm of the repetitive controller to regulate time-varying periodic signal. A theoretical analysis of Laplace-type integral transformation operator is adopted for time-varying repetitive controller design, where the stability and performance of the proposed repetitive control system are addressed. The implementation of the repetitive control strategy is investigated by a simulated example of the cycle ergometer. Results are given to illustrate that the proposed method is effectively used to analysis repetitive control system for the time-varying periodic signal regulation.

Effects of Desired Transmissibility Functions on the Performance and Design of Control Systems for Microgravity Isolation Systems

1995 ◽  
Author(s):  
N.-C. Tsai ◽  
A. Sinha
Keyword(s):  
Control System ◽  
Transfer Function ◽  
Control Systems ◽  
Closed Loop ◽  
Relative Displacement ◽  
Absolute Acceleration ◽  
Active Isolation ◽  
Space Experiments ◽  
Acceleration Feedback ◽  
Isolation Systems

Abstract This paper examines the performance of active isolation systems for micrograviry space experiments as a function of desired transmissibilities which are chosen to be either much below or close to what can be tolerated. The control system utilizes two feedback signals: absolute acceleration and relative displacement of the mass. The controller transfer function for acceleration feedback is chosen to avoid marginally stable pole-zero cancellations. The controller transfer function for relative displacement feedback is determined to achieve the desired transmissibility function. The issue of stability and properness of this controller transfer function are addressed. The required input forces and “equivalent” closed-loop stiffness are examined for various examples of desired transmissibilities.

Algebraic Method for the Synthesis of Astatic Continuous-Time Control Systems

2019 ◽  
Vol 20 (5) ◽  
pp. 274-279 ◽  
Author(s):  
D. P. Kim
Keyword(s):  
Transfer Function ◽  
Control Systems ◽  
Characteristic Polynomial ◽  
Performance Indicators ◽  
Continuous Time ◽  
Setting Time ◽  
Monic Polynomial ◽  
Algebraic Method ◽  
Synthesis Process ◽  
Time Control

An algebraic method for the synthesis of astatic continuous-time control systems is considered. The method is based on the construction of the desired transfer function (DTF) from given performance indicators (setting time, overshoot, etc.) and a given plant transfer function. The construction of DTF is based on the use of the desired normalized transfer function (NTF). The desired NTF is the transfer function whose denominator is a monic polynomial with unit free term and whose performance indicators, except for the setting time, coincide with those of the DTF. Therefore, one can obtain the DTF by constructing the desired NTF and then by applying the inverse transform with transformation ratio equal to the ratio of the setting time of the system to be synthesized to that of the system with the desired NTF. The desired NTF is assembled from standard NTFs. There are various standard NTFs: binomial, arithmetic, and geometric. The type of an NTF is determined by its characteristic polynomial; an NTF is said to be binomial if its characteristic polynomial is the Newton binomial and arithmetic or geometric if the roots of its characteristic polynomial form an arithmetic or a geometric progression, respectively. When constructing the desired NTF, three conditions must be met: the physical feasibility of the controller, solvability, and robustness. These three conditions determine the degrees of the characteristic equation of the system to be synthesized and the degrees of the unknown polynomials that are introduced in the synthesis process. After that, according to the given performance indicators, the type of the desired NTF is determined. Here we find only the denominator of the desired NTF. If the system to be synthesized is rth-order astatic and the plant does not contain right poles and zeros, then the numerator of the desired NTF is equal to the sum of the last r terms of the characteristic polynomial. After the system DTF has been obtained, the transfer function of the controller is determined by equating the transfer function of the closed-loop system with the DTF.

scholarly journals Calculation, modeling and description features of cascade systems in MATLAB

2020 ◽  
pp. 39-51
Author(s):  
Nikolay Bilfeld ◽  
Yulia Volodina
Keyword(s):  
Control System ◽  
Transfer Function ◽  
Transient Response ◽  
Cascade Control ◽  
Cascade System ◽  
Cascade Systems ◽  
Analytical Expression ◽  
Cascade Control System

A simulation of a cascade system, during which the problem of determining the transfer function of a cascade system for analytical reception of the transient response occurred, is performed. It is proven that the equivalent object used in many modelling works and the cascade system are not the same. Transients obtained by using an equivalent object are different from real transients in a cascade control system. The analytical expression of the description of cascade system is received as a result of researches.

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