Designing Minimum Variance Controller using VARX Model

In most industrial applications, attaining minimum output variance certifies the efficiency of system and results in increasing productivity and decreasing energy consuming. Therefore, minimum variance index is considered as one of the main subjects in control engineering field. A minimum variance controller is an optimal controller that provides (theoretically) the minimum possible variance. Designing this controller, however, requires exact models of both the system and disturbance. Due to existence of interactions among loops, modeling MIMO systems is often complicated. Existence of disturbance is another reason for this complication. In this paper, in order to avoid the need for an analytical model of system, VARX model has been used to simultaneous identification of the plant and disturbance. Then, the estimated model is used for designing a minimum variance controller. In this method, operating data of inputs and outputs of the system are the only requirements for identification of the VARX model. The proposed method has been tested on an experimental benchmark such as a four-tank system which has a nonlinearbehavior. The investigation results show that a minimum variance controller can be designed, based on an identified VARX model, for a MIMO system, without any need for an exact model of the system, while at the same time, capable of providing an acceptable minimum variance compared to that precisely obtained using the model-based ―Interactor-Matrix‖ method.