Variable structure control explained

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.

Further reading

• Book: Hasan K. Khalil . 2002 . 3rd . Nonlinear Systems . 0-13-067389-7 . . Upper Saddle River, NJ.
• Book: Utkin, V.I. . Sliding Modes in Control and Optimization . Springer-Verlag . 1992 . 978-0-387-53516-6 .
• Book: Zinober . A.S.I. . Deterministic control of uncertain systems . Peter Peregrinus Press . London . 1990 . 978-0-86341-170-0 . Alan S.I. Zinober.
• Book: Zinober . Alan S.I. . Variable Structure and Lyapunov Control . Lecture Notes in Control and Information Sciences . Springer-Verlag . London . 1994 . 193 . 978-3-540-19869-7 . 10.1007/BFb0033675.
• Book: Steinberger . M. . Horn . M. . Fridman . L. . Variable-Structure Systems and Sliding-Mode Control . Studies in Systems, Decision and Control . Springer-Verlag . London . 2020 . 271 . 978-3-030-36620-9 . 10.1007/BFb0033675.

Notes and References

1. Book: Variable Structure Control Systems. Emelyanov. S.V.. Nauka. Moscow. 1967.
2. Book: Advances in Variable Structure and Sliding Mode Control. Edwards. Cristopher. Fossas Colet. Enric. Fridman. Leonid. Springer-Verlag. Berlin. 2006. Lecture Notes in Control and Information Sciences. 334. 978-3-540-32800-1.