The Nash Bargaining Model Used in an Optimally Designed PID Controller for Multiple Objectives

We propose a new design scheme of the PID controller optimized for multiple objectives. The game of designing the PID controller is considered in the context of the n-person bargaining game. In this game, a player is defined as having one of the desired properties: decreased ITSE (Integral of Time multiplied by Squared Error); fast response time and less overshoot. Utility functions corresponding to the players are also defined as objective functions related to their roles. A set of desired parameters of the PID controller (e.g. PID gains) is given by acquiring the Nash bargaining solution of the game. As the one-to-one correspondence exists between the players and the objective functions, it is easy to apply this design scheme to complex design problems. In this paper, an example of simulation results is illustrated to show the effectiveness of this scheme.