Design of variable structure controller for robot manipulators alleviating reaching phase and chattering phenomena

Abstract

The basic theory of a switching control system was proposed in the Soviet Union in 1950``s, and thereafter the term "variable structure system (VSS)" and "sliding mode control (SMC)" have been used for such systems. In the period of 1957--1962, the plant was a linear second-order systems with feedback based on an error signal and/or its derivative and it was assumed that the feedback factor could take one of two possible values. For such systems, the behavior of such systems was studied in the phase plane by Filippov, and the invariance condition of the overall system with respect to the disturbances and uncertainties was investigated by Drazenovic. In the 1970``s, the VSS has been also studied outside the Soviet Union by translating some of works written in Russian. Recently, the VSS has been developed as a general design scheme for a wide spectrum of system types including multi-input/multi-output (MIMO) systems, nonlinear systems, discrete models, robot manipulators, and so on. In addition, the objective of the VSS has been greatly extended to variety control problems such as stabilization, regulation, tracking, model following, and so forth. This kind of wide application is caused by several good features of the VSS. The most attractive feature of the VSS is an invariance property against system uncertainties and external disturbances. When the VSS is used as a control method for a plant, the overall system shows the same performance under the existence of disturbances and uncertainties if the system is in the sliding mode. Therefore, the system performance is insensitive to parameter variations. Although this invariance/robustness feature is very attractive, the VSS has some week points. Even though the VSS has an attractive property, it has two major disadvantages. The first disadvantage is that, as mentioned above, the VSS has invariance property. This property, however, can be guaranteed if the system is in the sliding mode. In other words, the output r...