ABSTRACT
This chapter investigates variable structure control (VSC) as a high-speed switched feedback control resulting in a sliding mode. For example, the gains in each feedback path switch between two values according to a rule that depends on the value of the state at each time instant. The purpose of the switching control law is to drive the plant’s state trajectory onto a prespecified (user-chosen) surface in the state space and to maintain the plant’s state trajectory on this surface for all subsequent time. This surface is called a switching surface and the resulting motion of the state trajectory a sliding mode. When the plant state trajectory is “above” the surface, a feedback path has one gain and a different gain if the
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trajectory drops “below” the surface. This surface defines the rule for proper switching. The surface is also called a sliding surface (slidingmanifold) because, ideally speaking, once intercepted, the switched control maintains the plant’s state trajectory on the surface for all subsequent time and the plant’s state trajectory then slides along this surface. The plant dynamics restricted to this surface represent the controlled system’s behavior. The first critical phase of a VSC design is to properly construct a switching surface, so that the plant, restricted to the surface, has desired dynamics, such as stability to the origin, tracking, regulation, and so on.
