Algorithms for the design of control systems subject to singular value inequalities

1982 ◽  
pp. 112-134 ◽  
Author(s):  
D. Q. Mayne ◽  
E. Polak
Keyword(s):  
Control Systems ◽  
Singular Value

Structural Analysis of Nonlinear Control Systems Using Singular Value Decomposition: Part I — Approach

2003 ◽  
Author(s):  
Kwan-Woong Gwak ◽  
Glenn Y. Masada
Keyword(s):  
Structural Analysis ◽  
Singular Value Decomposition ◽  
Nonlinear Control ◽  
Control Systems ◽  
Singular Value ◽  
Mode Shapes ◽  
Nonlinear Control Systems ◽  
Control Input ◽  
Input Output ◽  
Value Decomposition

Structural information of a system/controller allows a designer to diagnose performance characteristics in advance and to make better choices of solution methods. Singular value decomposition (SVD) is a powerful structural analysis tool that has been applied to linear systems and controller designs, but it has not been used for nonlinear systems. In this paper, SVD is use to structurally analyze and to optimally design nonlinear control systems using the linear algebraic equivalence of the nonlinear controller. Specifically, SVD is used to identify control input/output mode shapes, and the control input/output distribution patterns are analyzed with the mode shapes. Optimizing control effort and performance is achieved by truncating some mode shapes in the linear mode shape combinations.

Sensitivity analysis of automatic flight control systems using singular-value concepts

1986 ◽  
Vol 9 (6) ◽  
pp. 621-626 ◽  
Author(s):  
Alfredo Herrera-Vaillard ◽  
James Paduano ◽  
David Downing
Keyword(s):  
Sensitivity Analysis ◽  
Control Systems ◽  
Flight Control ◽  
Singular Value

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.

Stability and Performance Robustness Analysis of Repetitive Control Systems Using Structured Singular Values

1996 ◽  
Vol 118 (3) ◽  
pp. 593-597 ◽  
Author(s):  
Levent Gu¨venc¸
Keyword(s):  
Time Delay ◽  
Control Systems ◽  
Repetitive Control ◽  
Singular Values ◽  
Parametric Modeling ◽  
Singular Value ◽  
Plant Performance ◽  
Structured Singular Value ◽  
And Performance ◽  
Performance Robustness

The structured singular value method is applied to continuous-time SISO repetitive control systems in order to determine their stability and performance robustness in the presence of structured parametric modeling error in the plant. Performance measures for repetitive control systems are introduced and the robust performance analysis using structured singular values is modified, taking the alternating magnitude behaviour of the sensitivity function of a repetitive control system into account. The analysis procedure is simplified considerably in the case of large time delay by noting that the upper and lower envelopes of the structured singular value plots are obtained from corresponding finite dimensional systems without any time delay. The analysis procedures developed are applied to an example on repetitive control of an electrohydraulic material testing machine, available in the literature, to demonstrate their usefulness.

Structural Analysis of Nonlinear Control Systems Using Singular Value Decomposition: Part II — Control of an Input-Constrained Thermal Process

2003 ◽  
Author(s):  
Kwan-Woong Gwak ◽  
Glenn Y. Masada
Keyword(s):  
Structural Analysis ◽  
Singular Value Decomposition ◽  
Nonlinear Control ◽  
Control Systems ◽  
Singular Value ◽  
Thermal System ◽  
Control Input ◽  
Input Constraints ◽  
Nonlinear Controller ◽  
Value Decomposition

In a Part I (Structural Analysis of Nonlinear Control System using Singular Value Decomposition: Part I—Approach), structural analysis algorithms for nonlinear control systems were developed applying singular value decomposition (SVD) on the linear algebraic equivalence of the nonlinear controller. In this paper, the proposed algorithms are applied to the temperature control of a thermal system which has control input constraints. Control input/output modes, weights of linear mode combination, colinearity, and mode truncation concepts introduced in Part I, are used to analyze and find the cause of input-constraint-violating-control of the nonlinear controller designed for the thermal system and to redesign the nonlinear controller to satisfy the input constraints and to reduce control effort.

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