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.

Structural Analysis and Optimization of Nonlinear Control Systems Using Singular Value Decomposition

2004 ◽  
Vol 127 (1) ◽  
pp. 105-113 ◽  
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 for linear systems, but it has not been applied to nonlinear systems. In this paper, SVD is used 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 using the mode shapes. Optimizing control effort and performance is achieved by truncating some mode shapes in the linear mode shape combinations. The proposed method is applied to the temperature control of a thermal system, and design guidelines are provided to overcome input-constraint-violating solutions.

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.

Regularization Embedded Nonlinear Control Designs for Input-Constrained and Ill-Conditioned Thermal System

2004 ◽  
Vol 126 (3) ◽  
pp. 574-582 ◽  
Author(s):  
Kwan-Woong Gwak ◽  
Glenn Y. Masada
Keyword(s):  
Singular Value Decomposition ◽  
Nonlinear Control ◽  
Singular Value ◽  
Input Constraint ◽  
Nonlinear Controller ◽  
Truncated Singular Value Decomposition ◽  
Temperature Tracking ◽  
Nonlinear Controllers ◽  
Value Decomposition ◽  
Control Designs

New regularization embedded nonlinear control designs are proposed for the temperature control of an input-constrained and ill-conditioned thermal process. A classic nonlinear controller applied to such a process is shown to provide good temperature tracking but generates physically unreasonable actuator solutions, i.e. input-constraint-violation. The reason of input-constraint-violating control solutions—ill-conditionedness—is shown by applying singular value decomposition (SVD) on the linear algebraic equivalence of the nonlinear controllers (LAENC). Based on the analogy of LAENC and regularization method for the linear algebraic equations, Tikhonov, truncated singular value decomposition (TSVD) and modified TSVD (MTSVD) methods are embedded in the design of feedback linearizing controllers (FBL) and sliding mode controllers (SMC). These regularization embedded nonlinear controllers (RENLC) provide good temperature tracking and generate physically reasonable and actuator-constraint-satisfying solutions for the ill-conditioned system, in spite of the modeling errors inherent in applying regularization. The optimal Tikhonov parameter is found using an L-curve. Quantitative comparisons of the residuals and standard deviations of the control inputs are used as criteria to select the optimal truncated singular value decomposition (TSVD) parameter.

Sign in / Sign up

Export Citation Format

Share Document