# 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

- 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.

## 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.