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.

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.

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.

Zero Phase Error Tracking Controllers With Optimal Gain Characteristics

1993 ◽  
Vol 115 (3) ◽  
pp. 311-318 ◽  
Author(s):  
Y. Funahashi ◽  
M. Yamada
Keyword(s):  
Control System ◽  
Phase Error ◽  
Tracking Performance ◽  
Output Data ◽  
Tracking Controllers ◽  
Tracking Controller ◽  
Phase Property ◽  
Feedforward Controller ◽  
Step Type ◽  
Zero Phase

Recently, a digital feedforward controller, called a Zero Phase Error Tracking Controller (ZPETC), has been proposed. In this controller, the overall frequency response between the desired output and the controlled output exhibits zero phase shift for all frequencies by using a few steps of the future desired output data. In this paper, two extensions of ZPETC’s are proposed: a ZPETC with deadbeat tracking performance and an L2-Optimal ZPETC. These ZPETC’s can provide the overall control system with not only the above phase property but also the excellent tracking performance for a desired output and the superior gain property, respectively. Moreover, a ZPETC with both the excellent tracking performance for a step-type and ramp-type desired output and the superior gain property, called an L2-Optimal ZPETC with deadbeat tracking performance, is presented.

Discrete-Time Repetitive Control System Design Using the Regeneration Spectrum

1993 ◽  
Vol 115 (2A) ◽  
pp. 228-237 ◽  
Author(s):  
F.-R. Shaw ◽  
K. Srinivasan
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
System Performance ◽  
Controller Design ◽  
Repetitive Control ◽  
Design Procedure ◽  
Controlled System ◽  
Stability Robustness ◽  
Analysis And Synthesis ◽  
The Stability

The stability, transient response, and stability robustness of discrete-time repetitive control systems characterized by large values of the time delay inherent in such systems are examined here using a function of frequency termed the regeneration spectrum. The ability to infer different aspects of controlled system performance from the regeneration spectrum, and its ease of computation, makes it a valuable tool for controller analysis and synthesis. A design procedure for discrete-time repetitive control systems, based on the regeneration spectrum, is outlined and a controller form suggested to effectively handle the trade-off between the different aspects of controlled system behavior. The controller design procedure is applied to an electrohydraulic material testing application characterized by strong nonlinearities, and shown experimentally to be effective in improving the controlled system performance.

Anti-Windup Control of Second-Order Plants With Saturation Nonlinearity

1993 ◽  
Vol 115 (4) ◽  
pp. 715-720 ◽  
Author(s):  
Ming C. Leu ◽  
Sangsik Yang ◽  
Andrew U. Meyer
Keyword(s):  
Control System ◽  
Control Systems ◽  
Real World ◽  
System Performance ◽  
Function Method ◽  
Second Order ◽  
Describing Function ◽  
Saturation Nonlinearity ◽  
Integral Action ◽  
Describing Function Method

All real-world control systems have saturation nonlinearity in final control elements (including actuators). When controllers involve integral action, reset windup can cause instability as well as make system performance unsatisfactory. Based on the describing function method and the generalized Popov criterion, this paper presents analysis of the global stability of a control system having a saturating second-order plant, both with and without using a deadbeat limiting scheme to constrain its controller output. The improvement of system performance by incorporating the anti-windup feature in the controller is illustrated by computer simulations.

Robust Performance Repetitive Control Systems

1998 ◽  
Vol 123 (3) ◽  
pp. 330-337 ◽  
Author(s):  
Jianwu Li ◽  
Tsu-Chin Tsao
Keyword(s):  
Control System ◽  
Control Systems ◽  
Robust Stability ◽  
Repetitive Control ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Control Design ◽  
Robust Performance ◽  
Feedback Form ◽  
Pure Delay

This paper addresses analysis and synthesis of robust stability and robust performance repetitive control systems. The repetitive control design problem is formulated as a standard feedback form in the linear fractional transformation form such that the standard numerical optimization software can be used to obtain the solution. The main idea of the robust repetitive control system design lies in introducing a fictitious complex uncertainty to replace the long delay chain in the internal model of the repetitive control system. This drastically reduces the order of the augmented plant for controller synthesis and hence generates a low order compensator, which in conjunction with the pure delay renders a repetitive controller that can be implemented efficiently in real time. The proposed approach can be applied to both the continuous and discrete-time domain repetitive control design for unstable open-loop plant. Sufficient conditions for the robust stability and robust performance repetitive control systems are presented. Conservatism analysis shows that the sufficient conditions become necessary when the pure delay approaches infinity. The robust repetitive control is applied to an electrohydraulic actuator for tracking periodic trajectories. Experimental results are presented to illustrate the design procedure and control system performance.

A Design Method for Two-Degree-of-Freedom Multi-Period Repetitive Control Systems with the Specified Frequency Characteristic

2011 ◽  
Vol 497 ◽  
pp. 255-269
Author(s):  
Zhong Xiang Chen ◽  
Kou Yamada ◽  
Nobuaki Nakazawa ◽  
Iwanori Murakami ◽  
Yoshinori Ando ◽  
...  
Keyword(s):  
Control System ◽  
Control Systems ◽  
Frequency Characteristic ◽  
Design Method ◽  
Repetitive Control ◽  
Output Characteristic ◽  
Degree Of Freedom ◽  
Disturbance Attenuation ◽  
Input Output ◽  
Two Degree Of Freedom

Multi-period repetitive controllers improve the disturbance attenuation characteristic of themodified repetitive control system that follows the periodic reference input with small steady stateerror. Recently, the parameterization of all stabilizing multi-period repetitive controllers was studied.However, when the parameterization of all stabilizing multi-period repetitive controllers is used, theinput-output characteristic and the feedback characteristic cannot be specified separately. From thepractical point of view, it is desirable to specify the input-output characteristic and the feedback characteristicseparately. In addition, the parameterization is useful to design stabilizing controllers. Fromthis view-point, the parameterization of all stabilizing two-degree-of-freedom multi-period repetitivecontrollers those can specify the input-output characteristic and the disturbance attenuation characteristicseparately was solved by Yamada et al. However, when we design a stabilizing two-degree-offreedommulti-period repetitive controllers using the parameterization proposed by Yamada et al, thefrequency characteristic of the control system cannot be settled so easily. From the practical point ofview, the frequency characteristic of the control systems are required to be easily settled. This problemcan be solved by obtaining the parameterization of all stabilizing two-degree-of-freedom multi-periodrepetitive controllers with the specified frequency characteristic. In this paper, we propose the parameterizationof all stabilizing two-degree-of-freedom multi-period repetitive controllers with thespecified frequency characteristic.

scholarly journals A New Design Method of High-Order Modified Repetitive Control Systems for Reference Inputs with Uncertain Period-Time

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zhongxiang Chen ◽  
Kou Yamada ◽  
Tatsuya Sakanushi
Keyword(s):  
Control System ◽  
Control Systems ◽  
Closed Loop ◽  
Design Method ◽  
Repetitive Control ◽  
High Order ◽  
Stabilizing Controllers ◽  
Control Precision ◽  
Free Parameters ◽  
High Control

This paper considers the design of high-order modified repetitive control systems for periodic reference inputs with uncertain period-time. The objective of this work was to develop a new design method so that the closed-loop high-order modified repetitive control system is robustly stable with high control precision for periodic reference inputs with uncertain period-time. The parametrization of all stabilizing controllers containing three free parameters is proposed based on the Youla-Kucera parameterization. Moreover, to obtain the free parameters, the constraint conditions were converted into stability conditions in the form of Bilinear Matrix Inequalities that can be solved using the available software. In addition, the high control precision is guaranteed by designing the free parameters after the control characteristic of this control system. The validity and effectiveness of the proposed design method were verified by numerical examples.

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