PID controller design using fractional balanced reduction

This paper describes a PID controller design method composed of two stages. First a reduced-order plant model for a give plant is determined through fractional balanced reduction (FBR), and then an integral-type optimal servo (IOS) controller which is a kind of the linear quadratic regulator is designed. If the order of a given plant can be rationally reduced to twice the number of the outputs, the resultant controller becomes an I-PD (Integral preceded by Proportional-Derivative) one. The proposed I-PD controller design method is applicable not only to single-input-single-output (SISO) systems but also to multiple-input-multiple-output ones, since the FBR and the IOS which the method is based on are state-space design methods. Design examples and numerical simulations for a SISO third-order system, a two-input-two-output (2I2O) sixth-order system of the lateral-directional motion of a fighter aircraft and a 2I2O fifth-order unstable system of a micro aerial vehicle demonstrate the usefulness of the proposed method.