Proportional-integral derivative realisation of optimal linear-quadratic regulators

The paper presents a new method for the realisation of optimal linear-quadratic regulators, for linear time-invariant systems, using the concept of proportional-integral derivative (p.i.d.) feedback. It is shown that an optimum complete-state-feedback regulator-system response can be alternatively obtained with incomplete feedback, by introducing the derivative-control action. Considering also the integral feedback, needed to cancel the unknown input disturbances, the method can be viewed as a design method for a class of optimal multivariable p.i.d. controllers with a prescribed closed-loop system response. The paper presents an analytical derivation and discusses the properties of such controllers. An illustrative numerical example is also included.