Optimal multi-loop control system design subject to explicit constraints

A present method of tuning controller parameters in a multi-loop system is modified to maintain explicit constraints. This control system design is called optimal in the sense of performance and it is treated as a game including more than one interacting player representing the controller. Each player (controller) has to satisfy an objective function implying a squared error formulation. In practice, since every control signal cannot be followed by the physical system, the control signals of the plant have to be limited. Thus, explicit constraints are added to the game. On the one hand, the constraints are considered during the optimization of the objective functions, on the other hand, they are additionally reformulated as objective functions and optimized, too. It follows, that each player has to satisfy one, respectively two objective functions for this game. The solution of the game is the optimization of all multiple objective functions, leading to a multi-objective optimization problem, which is solved by a genetic algorithm. The modified method is applied to a model of a reverse osmosis desalination plant and a comparison of this method with the present method and a conventional decoupling method is shown.