Design of a MIMO PID Controller by Integral-Type Optimal Servomechanism and Fractional Balanced Reduction

摘要

The present paper proposes an efficient design method for a multiple-input multiple-output (MIMO) integral preceded by a proportional and derivative (I-PD) controller, which is a type of PID controller. In the proposed method, a given plant model is first reduced to a lower-order model using fractional balanced reduction, and an integral-type or robust optimal servomechanism is then designed for the reduced plant, which is expressed in a peculiar state-space form, where the state vector is composed of outputs, their derivatives, and control inputs. The resultant optimal feedback control law is immediately transformed into a MIMO I-PD control law. The optimal servomechanism, which is based on a linear quadratic regulator, provides a controller with desirable control performance, adequate stability margins, and easy trade-off between the control performance and stability margins attained through weight selection of the quadratic cost function. Although these features are not perfectly guaranteed in the resulting control system due to the model reduction, if the properties are adequately preserved, they make the controller design very simple and efficient. A design example illustrates the effectiveness of the proposed design method as well as its limitations.