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.

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.

scholarly journals A Design Method for Robust Stabilizing Modied Repetitive Controllers for Multiple-Input/Multiple-Output Time-Delay Plants

1970 ◽  
Vol 7 (1) ◽  
pp. 32-42
Author(s):  
Zhongxiang Chen ◽  
Tatsuya Sakanushi ◽  
Kou Yamada ◽  
Yun Zhao ◽  
Satoshi Tohnai
Keyword(s):  
Control System ◽  
Time Delay ◽  
Design Method ◽  
Multiple Input Multiple Output ◽  
Repetitive Control ◽  
Control Design ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Output Time ◽  
Reference Input

The modified repetitive control system is a type of servomechanism for a periodic reference input. When modified repetitive control design methods are applied to real systems, the influence of uncertainties in the plant must be considered. In some cases, uncertainties in the plant make the modified repetitive control system unstable, even though the controller was designed to stabilize the nominal plant. Recently, the parameterization of all robust stabilizing modified repetitive controllers was obtained by Yamada et al. In addition, Yamada et al. proposed the parameterization of all robust stabilizing modified repetitive controllers for time-delay plants. However, no paper has proposed the parameterization of all robust stabilizing modified repetitive controllers for multiple-input/multiple-output time-delay plants. In this paper, we expand the result by Yamada et al. and propose the parameterization of all robust stabilizing modified repetitive controllers for multipleinput/multiple-output time-delay plants.

LQR Control Design of Discrete-Time Networked Cascade Control Systems With Time Delay

2011 ◽  
Author(s):  
Rohit K. Belapurkar ◽  
Rama K. Yedavalli
Keyword(s):  
Control System ◽  
Control Systems ◽  
Discrete Time ◽  
Time Delays ◽  
Control Design ◽  
Aircraft Engine ◽  
Cascade Control ◽  
Engine Control ◽  
Lqr Control ◽  
Turboshaft Engine

Series cascade control systems, in which, the output of one process drives a second process are studied extensively in literature. Traditional control design methods based on transfer function approach are used for design of cascade control systems with disturbances in inner loop and time delays in outer loop process. Design of current turboshaft engine control systems are based on cascade control system framework. Next generation aircraft engine control systems are based on distributed architecture, in which, communication constraints like time delays can degrade control system performance. Stability of networked cascade control systems for turboshaft engines in a state space framework is analyzed in the presence of time delays. Two architectures of networked cascade control systems are presented. Stability conditions for discrete-time cascade control systems are presented for each of the architecture with time delays which are more than the sampling time.

Control Systems

2019 ◽  
pp. 31-40
Author(s):  
Pierre-Loïc Garoche
Keyword(s):  
Control System ◽  
Differential Equations ◽  
Control Theory ◽  
System Design ◽  
Ordinary Differential Equations ◽  
Control Systems ◽  
Control Design ◽  
Control System Design ◽  
Typical Development ◽  
Typical Process

This chapter sketches the typical development of control systems and refers the reader to classical books for more details on control system design. Historically, control design started in the continuous world: a system had to be controlled, and its dynamics was captured by the equations of physics, for example, using ordinary differential equations. Then, control theory provides means to build a controller: another system, used in combination with the system to be controlled, is able to move the system to the requested state. The chapter thus begins by presenting a typical process leading to the development of a controller in the aerospace domain. It then gives an idea of each step.

Analyzing Robust Stability of an Interval Control System on the Basis of Vertex Polynomials

2019 ◽  
Vol 20 (5) ◽  
pp. 266-273 ◽  
Author(s):  
S. A. Gayvoronskiy ◽  
T. A. Ezangina ◽  
I. V. Khozhaev ◽  
A. A. Nesenchuk
Keyword(s):  
Control System ◽  
Control Systems ◽  
Characteristic Polynomial ◽  
Robust Stability ◽  
Root Locus ◽  
Phase Equation ◽  
The Third ◽  
Stability Degree ◽  
Polynomial Coefficients ◽  
Interval Extension

In the paper, a characteristic polynomial of an interval control system, whose coefficients are unknown or may vary within certain ranges of values, is considered. Parametric variations cause migration of interval characteristic polynomial roots within their allocation areas, whose borders determine robust stability degree of the interval control system. To estimate a robust stability degree, a projection of a polytope of interval characteristic polynomial coefficients on a complex plane must be examined. However, in order to find a robust stability degree it is enough to examine some vertices of a coefficient polytope and not the whole polytope. To find these vertices, which fully determine a robust stability degree, it is proposed to use a basic phase equation of a root locus method. Considering the requirements to placing allocation areas of system poles an interval extension of expressions for angles included to the phase equation. The set of statements, allowing to find a sum of pole angles intervals in the case of degree of oscillating robust stability, were formulated and proved. From these statements, a set of double interval angular inequalities was derived. The inequalities determine ranges of angles of all root locus edge branches departure from every pole. Considered research resulted in a procedure of finding coordinates of verifying vertices of a coefficients polytope and vertex polynomials according to these vertices. Such polynomials were found for oscillating robust stability degree analysis of interval control systems of the second, the third and the forth order. Also, similar statements were derived for aperiodical robust stability degree analysis. Numerical examples of vertex analysis of oscillating and aperiodical robust stability degree were provided for interval control systems of the second, the third and the fourth order. Obtained results were proved by examining root allocation areas of interval characteristic polynomials examined in application examples of proposed methods.

Computer-Aided Control System Design and Control Performance for Active Vibration Control Systems Based on μ Synthesis Theory

1994 ◽  
Vol 6 (4) ◽  
pp. 304-311
Author(s):  
Kenzo Nonami ◽  
◽  
Qi-fu Fan ◽  
Keyword(s):  
Control System ◽  
Vibration Control ◽  
System Design ◽  
Control Systems ◽  
Active Vibration Control ◽  
Singular Value ◽  
Control System Design ◽  
Robust Performance ◽  
Computer Aided ◽  
Active Vibration

The <I>H</I>∞ control theory is currently the most powerful method for robust control theory, and is useful as well as practical because a great amount of software related to computer-aided control system design is available. However, it has some disadvantages in that the <I>H</I>∞ control system is a conservative one and cannot deal with robust performance. This is due to maximum singular values. Doyle proposed a structured singular value instead of a maximum singular value. This is called ∞ synthesis theory and actively deals with robust performance using D-K iteration. This paper is concerned with computeraided design of active vibration control systems based on the μ synthesis theory. First, the paradigm of the μ synthesis theory is described concerning μ, robust performance, and D-K iteration. Next, the relationships between the μ controller, robust performance, nominal performance, and robust stability are discussed for vibration control systems.

scholarly journals Examination of a repetitive process control system

2019 ◽  
Vol 287 ◽  
pp. 08002
Author(s):  
Nina G. Nikolova
Keyword(s):  
Control System ◽  
Process Control ◽  
Control Systems ◽  
Process Control System ◽  
Robust Performance ◽  
Repetitive Process ◽  
Process Control Systems ◽  
Improved Performance ◽  
Robust Process

In the present work, the application of repetitive filters in the robust process control systems is examined. The functionality of the proposed system and the improved performance, robust performance and filtering properties has been proven.

Discrete Sliding Mode Control Design With Invariant Sliding Sectors

2000 ◽  
Vol 122 (4) ◽  
pp. 776-782 ◽  
Author(s):  
Xinghuo Yu ◽  
Shuanghe Yu
Keyword(s):  
Sliding Mode Control ◽  
Control Systems ◽  
Discrete Time ◽  
Sliding Mode ◽  
Design Procedure ◽  
Control Design ◽  
Higher Order ◽  
Mode Control ◽  
Simulation Results ◽  
Discrete Sliding Mode Control

In this paper, a new concept of invariant sliding sector is proposed for the design of discrete time sliding mode control. A methodology is developed which ensures the existence of the invariant sliding sector and conditions to guarantee the existence of the invariant sliding sector are derived. The second-order discrete sliding mode control systems are used to inform the discussion. Simulation results are presented to demonstrate the usefulness of the concept and effectiveness of the methodology proposed. It should be noted that most of the design procedure could be extended to higher order discrete sliding mode control systems. [S0022-0434(00)02004-9]

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