A combined discrete variable structure control algorithm and its application to brushless DC servomotors

The purpose of this paper is to overcome the shortcoming that discrete variable structure control (VSC) system trajectory oscillates in a neighborhood of the origin.

Among all the proposed reaching laws, W. Gao's theory is most perfect. It makes great progress in revealing the motion mechanism of discrete‐time VSC systems. However, it has an obvious defect, i.e. the system trajectory oscillates in a neighborhood of the origin rather than converges to the origin. So, a new reaching law named variable rate reaching law to which the stability at the origin can be expected is proposed. The special feature of this new reaching law is that it is directly proportional to the norm of the state vector and can result in a sector‐shaped switching region. On the basis of analyzing the characteristic of the variable rate and the conventional reaching laws, a new combined control algorithm that discards the shortcomings of the two reaching laws and carries on their merits is formed, so satisfactory control performance can be achieved.

A new combined reaching law control algorithm, which uses the exponential rate reaching law in the reaching mode and in the front phase of the sliding mode, and uses the variable rate reaching law in the back phase of the sliding mode and in the steady‐state mode, is formed.

The paper is a very useful reference for control system designers.

The new control strategy is applied to the controller design for a brushless DC servomotor and good control performance is obtained.