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]

See also

• Variable structure system
• Sliding mode control
• Hybrid system
• Nonlinear control
• Robust control
• Optimal control
• H-bridge – A topology that combines four switches forming the four legs of an "H". Can be used to drive a motor (or other electrical device) forward or backward when only a single supply is available. Often used in actuator in sliding-mode controlled systems.
• Switching amplifier – Uses switching-mode control to drive continuous outputs
• Delta-sigma modulation – Another (feedback) method of encoding a continuous range of values in a signal that rapidly switches between two states (i.e., a kind of specialized sliding-mode control)
• Pulse density modulation – A generalized form of delta-sigma modulation.
• Pulse-width modulation – Another modulation scheme that produces continuous motion through discontinuous switching.

References

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

Further reading

• Hasan K. Khalil (2002). Nonlinear Systems (3rd ed.). Upper Saddle River, NJ: Prentice Hall. ISBN 0-13-067389-7.
• Utkin, V.I. (1992). Sliding Modes in Control and Optimization. Springer-Verlag. ISBN 978-0-387-53516-6.
• Zinober, A.S.I., ed. (1990). Deterministic control of uncertain systems. London: Peter Peregrinus Press. ISBN 978-0-86341-170-0.
• Zinober, Alan S.I., ed. (1994). Variable Structure and Lyapunov Control. London: Springer-Verlag. doi:10.1007/BFb0033675. ISBN 978-3-540-19869-7.