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UBC Theses and Dissertations

Application of geometric programming to PID controller tuning with state constraints Carver, Leonard James

Abstract

In the thesis, geometric programming is considered as a numerical optimization technique. The problem of minimizing the integral square error of a system characterized by a second order plant with proportional- integral-derivative (PID) controller is investigated. Constraints are imposed upon the state of the system In order to obtain feasible solutions and conditions that are amenable to the geometric programming technique. The application of geometric programming requires the use of approximation procedures to eliminate untenable conditions in the objective and constraint functions. The techniques utilized render solutions that are easily obtainable, usually amounting to solving a set of linear equations and requiring no differentiation of terms. In addition, there is rapid convergence to an optimum. The accuracy of the results is dependent upon the validity of the approximations.

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