LQG optimization of pid structured multi-model process control systems: One dof tracking and feedforward control

The solution of an optimal control problem is discussed where the single degree of freedom structure of the controller is chosen to have a very simple form. The controller may be chosen to be of reduced order, lead/lag, or PID forms, and the controller is required to minimize an LQG cost-index. The optimization is based upon a cost-function which allows separate costing of the terms due to the feedback and feedforward controllers. The system model can be uncertain and can be represented by a set of linear models over which the optimization is performed. This provides a form of robust optimal control that might even be applied to nonlinear systems that are approximated adequately by a set of linearized models. The aim is to find a single controller that has a simple form and stabilises the full set of models.