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.

An Application to H2+ of Laplace Type Integral Transform and its Inverse

1985 ◽  
Vol 40 (3) ◽  
pp. 246-250 ◽  
Author(s):  
M. Primorac ◽  
K. Kovačević
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Integral Transform ◽  
Integral Transformation ◽  
Inverse Transform ◽  
Type Integral ◽  
Analytical Formulae ◽  
Molecular Computations ◽  
Laplace Type

Laplace type integral transformation (LIT) has been applied to wavefunctions. The effect of the inverse transform is also discussed. LIT wavefunctions are tested in the calculation of the ground-state energy of H2+, where the untransformed functions were 1s, 12s, 123s and 1234s- STO. The results presented here show that LIT wavefunctions are applicable in molecular computations. The analytical formulae for two-centre one-electron integrals over LIT wavefunctions are derived by use of a Barnett-Coulson-like expansion of rbN (rb + p)-v.

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.

Periodic Sampling Interval Repetitive Control and Its Application to Variable Spindle Speed Noncircular Turning Process

1998 ◽  
Vol 122 (3) ◽  
pp. 560-566 ◽  
Author(s):  
Reed D. Hanson ◽  
Tsu-Chin Tsao
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Design Method ◽  
Repetitive Control ◽  
Spindle Speed ◽  
Depth Of Cut ◽  
Time Varying ◽  
Turning Process ◽  
Noncircular Turning ◽  
Loop Stability

This paper addresses discrete-time, repetitive control for linear, periodic, time-varying systems. A periodic, repetitive control design method based on gain scheduling is proposed and the necessary and sufficient condition for closed-loop stability is presented. Utilizing the special structure of the repetitive controller, an efficient method for evaluating the closed-loop stability is developed. The algorithm is applied to the control of a piezoelectric fast-tool stage for variable spindle speed noncircular turning process. The tool performs dynamic variable depth of cut machining to generate noncircular workpiece profiles while the spindle carrying the workpiece rotates at a variable speed to inhibit machining instability (chatter). Experimental machining results are presented that demostrate the tracking performance of the period, time-varying controller design proposed, as well as the ability to increase machining stability using this approach. [S0022-0434(00)02402-3]

Constant Turning Force Adaptive Controller Design

1989 ◽  
Vol 111 (2) ◽  
pp. 125-132 ◽  
Author(s):  
Bor-Sen Chen ◽  
Yih-Fang Chang
Keyword(s):  
Control System ◽  
Force Feedback ◽  
Controller Design ◽  
Cutting Tools ◽  
Design Procedure ◽  
Adaptive Controller ◽  
Pi Controller ◽  
Cutting Process ◽  
Time Varying ◽  
Good Reliability

In the Constant Turning Force Adaptive Control system, the cutting process is nonlinear time-varying; besides, the stability cannot be assured by classical control theory since the cutting tools usually cut a workpiece at various cutting depths. In this paper, based on the small gain theorem, we propose a new method to design a PI controller with high robustness to stabilize the force feedback control system against the nonlinear time-varying gain perturbation in the cutting process. A simple design procedure will be presented and several illustrative simulation results are given. The practical experimental results of a converted lathe with the PI controller designed with this method also show a good robustness and good reliability.

scholarly journals Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

2016 ◽  
Vol 26 (2) ◽  
pp. 285-295 ◽  
Author(s):  
Lan Zhou ◽  
Jinhua She ◽  
Chaoyi Li ◽  
Changzhong Pan
Keyword(s):  
Control System ◽  
Output Feedback ◽  
Disturbance Rejection ◽  
Closed Loop ◽  
Repetitive Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Dimensional Model ◽  
Closed Loop System ◽  
Output Feedback Controller

Abstract This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based ROFMRCS that accurately presents the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A robust stability condition for the closed-loop system is given in terms of a linear matrix inequality. It yields the parameters of the repetitive controller, the output-feedback controller, and the EID-estimator. Finally, a numerical example demonstrates the validity of the method.

scholarly journals H∞ Controller Design for an Observer-Based Modified Repetitive-Control System

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lan Zhou ◽  
Jinhua She ◽  
Shaowu Zhou ◽  
Qiwei Chen
Keyword(s):  
Control System ◽  
Controller Design ◽  
Linear Time ◽  
Repetitive Control ◽  
State Observer ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Design Algorithm ◽  
Linear Time Invariant ◽  
Value Decomposition

This paper presents a method of designing a state-observer based modified repetitive-control system that provides a given H∞ level of disturbance attenuation for a class of strictly proper linear plants. Since the time delay in a repetitive controller can be treated as a kind of disturbance, we convert the system design problem into a standard state-feedback H∞ control problem for a linear time-invariant system. The Lyapunov functional and the singular-value decomposition of the output matrix are used to derive a linear-matrix-inequality (LMI) based design algorithm for the parameters of the feedback controller and the state-observer. A numerical example demonstrates the validity of the method.

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