Order Reduction of Controller Using Singular Perturbation Approach

INTRODUCTION Designing control system by using the H∞ or μ -synthesis leads to a high-order controller due to using the frequency weighting filter to envelop the uncertainty factors. In most practical circumstances, it is desirable to reduce the controller order. Moreover, any controller order reduction method should take into account closed-loop stability and other specific performance aspects. There are many researchers who have proposed several methods to achieve low-order controller. Generally, these methods can be classified into four groups, that is, modal truncation, balanced truncation, singular perturbation and projection method. For some conditions, the modal truncation make up a good approximation. The error bound of the difference between the high-order and the low-order controller in the H∞ -norm can be minimized by using the projection method, but computationally expensive. Recent control literatures show that an important role is played by the balanced realization truncation order-reduction techniques in model and controller reduction procedures, but the error of the reduction tends to have smaller errors at high frequencies and larger errors at low frequencies. It is undesirable for many applications. On the other hand, the singular perturbation method displays the opposite character. In this paper we propose a controller order reduction method using the singular perturbation approximation where the state-space of the high-order controller is first transformed to the balanced coordinates. To verify the performance of the low-order controller, it is applied to the vibration reduction problem of the structural having four transverses and four torsionals coupled vibration modes. The concept of the singular perturbation approximation method have been published in the literatures [1-5]. To maintain as much as posible the properties of the high-order controller transfer function in the lowand medium-frequencies, a weighting fuction is used. From the simulation results, the low-order controller is effective to reduce the vibration of the structure and the order of the controller can be reduced up to 7th-order from 30th-order.