Variable structure control

Variable structure control (VSC) is a form of discontinuous nonlinear control. The method alters the dynamics of a nonlinear system by application of a high-frequency switching control. The state-feedback control law is not a continuous function of time; it switches from one smooth condition to another. So the structure of the control law varies based on the position of the state trajectory; the method switches from one smooth control law to another and possibly very fast speeds (e.g., for a countably infinite number of times in a finite time interval). VSC and associated sliding mode behaviour was first investigated in early 1950s in the Soviet Union by Emelyanov and several coresearchers.^[1]

The main mode of VSC operation is sliding mode control (SMC). The strengths of SMC include:

Low sensitivity to plant parameter uncertainty
Greatly reduced-order modeling of plant dynamics
Finite-time convergence (due to discontinuous control law)

The weaknesses of SMC include:

Chattering due to implementation imperfections
Over-focus on matched uncertainties (i.e., uncertainties that enter into the control channel)

However, the evolution of VSC is an active area of research.^[2]

^ Emelyanov, S.V., ed. (1967). Variable Structure Control Systems. Moscow: Nauka.
^ Edwards, Cristopher; Fossas Colet, Enric; Fridman, Leonid, eds. (2006). Advances in Variable Structure and Sliding Mode Control. Lecture Notes in Control and Information Sciences. Vol. 334. Berlin: Springer-Verlag. ISBN 978-3-540-32800-1.

[E1967-1] Emelyanov, S.V., ed. (1967). Variable Structure Control Systems. Moscow: Nauka.

[EFF06-2] Edwards, Cristopher; Fossas Colet, Enric; Fridman, Leonid, eds. (2006). Advances in Variable Structure and Sliding Mode Control. Lecture Notes in Control and Information Sciences. Vol. 334. Berlin: Springer-Verlag. ISBN 978-3-540-32800-1.

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