Book ChapterDOI
Symbolic Computing Aided Design of Nonlinear PID Controllers
Jesús Rodríguez-Millán,Juan Cardillo +1 more
- pp 253-270
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TLDR
A symbolic computing tool is introduced, denoted by NLPID in the sequel, for the automatic design of linear and nonlinear PID controllers for nth order nonlinear control systems.Abstract:
In this paper we introduce a symbolic computing tool, denoted by NLPID in the sequel, for the automatic design of linear and nonlinear PID controllers for nth order nonlinear control systems. The nonlinear design algorithm is based upon Rugh's Extended Linearization Technique, and it was implemented using Mathematica® as symbolic computing platform. At its present stage of development NLPID uses Ziegler-Nichols tables to synthesize linear PID controllers, and therefore its ability to deal with first and second order plants could be limited.read more
Citations
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Book ChapterDOI
Improved non-standard discretization methods for nonlinear dynamical control systems
TL;DR: In this article, two modified versions of the Euler-Taylor-Picard discretization method for nonlinear dynamical control systems are described, in which an upper bound for the absolute difference of each pair of consecutive Picard iterations is derived.
Book ChapterDOI
Integrated Symbolic-Graphic-Numeric Analysis and Design in Nonlinear Control through Notebooks in Mathematica
TL;DR: Two sets of notebooks developed in Mathematica® are presented: a first one to analyze and classify local dynamics of secondorder parametrized nonlinear dynamical systems, and the second one to synthesize linear and extended nonlinear state-feedback controllers, PID controllers, and Luenberger observers for second-order nonlinear control systems.
Book ChapterDOI
Design of nonlinear lag-lead compensators by extended linearization using symbolic computation techniques
TL;DR: NLLag-Lead as discussed by the authors is a symbolic computation tool allowing to automate the design of linear and nonlinear lead, lag and lag-lead compensators, for nth ordersingle-input single-output nonlinear dynamical control systems.
Proceedings ArticleDOI
NLControl: a symbolic computation toolbox for nonlinear control by extended linearization
TL;DR: The symbolic computation tool NLControl is described, a computing aid to automate the design of linear/nonlinear controllers and observers to compensate smooth enough nth order nonlinear dynamical control systems by Jacobian and extended linearization.
References
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Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Book
Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
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Modern Control Theory
TL;DR: The relationship between state variable and transfer function descriptions of linear feedback control systems is discussed in this paper, along with the relationship between the Cayley Hamilton Theorem and state variable descriptions of systems.