Program for symbolic and rule-based analysis and design of nonlinear systems

2005 ◽  
pp. 115-128 ◽  
Author(s):  
J. Birk ◽  
M. Zeitz
Keyword(s):  
Nonlinear Systems ◽  
Rule Based ◽  
Analysis And Design

Granular Synthesis of Rule-Based Models and Function Approximation Using Rough Sets

2010 ◽  
pp. 408-425 ◽  
Author(s):  
Carlos Pinheiro ◽  
Fernando Gomide ◽  
Otávio Carpinteiro ◽  
Isaías Lima
Keyword(s):  
Nonlinear Systems ◽  
Rough Sets ◽  
Estimation Procedure ◽  
New Method ◽  
Rule Based ◽  
Numerical Examples ◽  
Rule Sets ◽  
Computational Procedures ◽  
Granular Synthesis ◽  
And Function

This chapter suggests a new method to develop rule-based models using concepts about rough sets. The rules encapsulate relations among variables and give a mechanism to link granular descriptions of the models with their computational procedures. An estimation procedure is suggested to compute values from granular representations encoded by rule sets. The method is useful to develop granular models of static and dynamic nonlinear systems and processes. Numerical examples illustrate the main features and the usefulness of the method.

New Analysis/Design of Generalized Discrete PI Controller via Discrete Time Delay Control for Nonlinear Systems

2020 ◽  
Author(s):  
Suresh B. Reddy
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Pi Controller ◽  
Pid Controllers ◽  
Analysis And Design ◽  
Proportional Integral ◽  
Discrete Time Delay

Abstract Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) controllers are among the most common schemes for control since their formulation nearly a century ago. They have been very successful in many applications, even as we have migrated from analog implementations to digital control systems. While there is rich literature for design and analysis of PI/PID controllers for linear time-invariant systems with modeled dynamics, the tools for analysis and design for nonlinear systems with unknown dynamics are limited, despite their known effectiveness. This paper extends previous observations about a form of discrete Time Delay Control’s equivalence to a generalized PI controller for more general canonical systems, with additional complimentary feedback linearization of known dynamics, as desired. In addition, sufficient conditions for Bounded Input-Bounded Output (BIBO) as well as exponential stability are developed in this paper for the form of discrete TDC that is closest to generalized discrete PI equivalent controller, for multi-input multi-output nonlinear systems, including nonaffine cases. Accordingly, design procedures are suggested for such discrete TDC, and generalized discrete PI controller for nonlinear systems.

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