On Guaranteeing Global Stability with Sliding Mode Control, Theory and Experiment

Sliding mode control has been popular in recent years for designing control systems for nonlinear plants. One of the biggest advantages of this approach is that global stability may be guaranteed if the magnitude of modeling errors is known apriori. As these modeling error magnitudes increase, the sliding mode gain must be increased in order to guarantee global stability. This can lead to increased chattering. Boundary layer thickness is then typically increased to reduce chatter, which leads to poor trajectory following and performance. It is very important to know the explicit requirements in guaranteeing stability, and to test these conditions, so that the sliding mode gain can be as small as possible for a good design. This paper explicitly outlines the requirements for guaranteeing global stability for a nonlinear state-space plant. Application of these requirements to the control of a hydraulic powertrain is presented to show their implementation in an actual hardware environment.