Premium
Nonlinear Extensions of Classical Controllers Using Symbolic Computation Techniques: A Dynamical Systems Unifying Approach
Author(s) -
RodriguezMillan Jesus,
Bokor Jozsef
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19980781592
Subject(s) - control theory (sociology) , nonlinear system , linearization , feedback linearization , computation , controller (irrigation) , mathematics , filter (signal processing) , nonlinear control , representation (politics) , pid controller , computer science , algorithm , control engineering , artificial intelligence , engineering , temperature control , physics , control (management) , quantum mechanics , politics , law , political science , agronomy , computer vision , biology
In previous works we reported the development of symbolic computation tools to automate the design of nonlinear state feedback controllers [1], nonlinear PID controllers [2], nonlinear lag‐lead compensators [3], and nonlinear obsevers [4] using the extended linearization method [5]. In this paper we show that a careful analysis of the state variables representation of these classical controllers indicates that all of them are particular cases of the nonlinear extension of a mth order linear filter, consisting of a kth order input derivative operator followed by an output mth order linear dynamical system. Using this two blocks decomposition approach, the design of nonlinear extensions of nth order controllers can be decomposed into two independent subalgorithms: a kth order PD controller algorithm, and a mth order state vector feedback algorithm. Hence, an appropriate, assembly of our symbolic computation tools NL Feedback and NLPID could, in principle, allow to use the extended linearization method to synthesize nonlinear extension of arbitrary nth order linear filter (controllers).