Restricted structure control of multiple model systems with Series 2 degrees of freedom tracking and feedforward action

The solution of a scalar optimal control problem is discussed where the feedback, series tracking and feedforward controllers are chosen to have a very simple structure or format. Each controller term may be chosen to be of reduced order, lead/lag, or proportional, integral, derivative forms, and the controller is required to minimize a linear–quadratic gain (LQG) cost-index. The optimization is based upon a cost-function which also allows separate costing of the terms due to the feedback, tracking and feedforward controllers. The system model can be uncertain and can be represented by a set of models over which the optimization is performed. This provides a form of robust optimal control that might even be applied to non-linear systems that can be approximated by a set of linearized models. The theoretical problem considered is to obtain the causal, stabilizing, feedback, series-tracking and feedforward controllers, of a prespecified form, that minimize an LQG criterion over the set of possible linear plant models. The underlying practical problem of importance is to obtain a simple method of tuning low-order controllers, given only an approximate model of the process. The results are illustrated in a power generation control problem for a system represented by 12 different linearized plant models. The single feedback controller that is obtained has a simple form and stabilizes the full set of models.