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A Simplified Numerical Approach to Feedback Controller Design
Author(s) -
Bechtel Tom B.
Publication year - 2004
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450820622
Subject(s) - control theory (sociology) , controller (irrigation) , simplex , pid controller , state space representation , mathematical optimization , computer science , function (biology) , state space , state (computer science) , scheme (mathematics) , simplex algorithm , code (set theory) , mathematics , control (management) , algorithm , control engineering , engineering , linear programming , artificial intelligence , temperature control , mathematical analysis , statistics , geometry , set (abstract data type) , evolutionary biology , agronomy , biology , programming language
A generalized parameter optimization method for computing feedback controller parameters is proposed. The method utilizes the downhill simplex method (DSM), a pattern search algorithm, to determine the optimal parameters that minimize an objective function or performance index. The system model, expressed in terms of state‐space equations is integrated with respect to time at each DSM iteration in order to determine the states. A fourth‐order Runge‐Kutta scheme is used for integrating the state equations. A penalty function approach is used for problems with inequality constraints on the state variables or controls. Though relatively inefficient in terms of the number of function evaluations, DSM requires only that the user provide the model equations, and not their derivatives. Additionally, the DSM code is very compact. Thus, a small and straightforward program allows for controller parameter determination for a variety of state‐space and classical PID feedback control design problems.