Abstract
This paper proposes an I-PD (integral preceded by proportional-derivative) controller design with a more rational method of plant-order reduction to the second order than the method previously proposed by the authors, where parameter-space search was employed. In the new method, first, the fractional balanced reduction is applied to the original single-input-single-output plant. Then, the reduced-order model is adjusted via the homotopy method in terms of the ν-gap metric. The method can also be applied to a plant that is not stable but stabilizable by state feedback in the same way. The resultant PID controller designed based on the optimal servomechanism using the second-order plant model provides preferable properties as a linear quadratic regulator (LQR), if the ν-gap can be made sufficiently small. Moreover, it can be extended to a model-following type by adding a reference model and a feedforward compensator to improve the output responses without decreasing the stability margins. The effectiveness and usefulness of the proposed method are demonstrated through design examples including an application to flight control and numerical simulations.
