Design PID Controllers Using Generalized Laguerre Functions

Abstract

This paper deals with a method of designing PID controllers. Generalized Laguerre functions were used for this task. Generalized Laguerre functions generate an orthogonal base in the time domain and the operator domain. This property of generalized Laguerre functions is beneficially used for the design of the PID controller. Parameters for generalized Laguerre function PID controllers are computed from the Laguerre series of the open loop and the Laguerre series of the ideal open loop. To satisfy this goal, the plant transfer function, the controller transfer function, and the ideal open loop transfer function are transformed into a generalized Laguerre functions base. Three examples are shown to present this method.

Keywords

• pid controller
• pi controller
• pd controller
• fractional order systems
• generalized laguerre functions
• orthogonal functions