Variable structure control
Encyclopedia
Variable structure control, or 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). Variable structure control (VSC) and associated sliding mode behaviour was first investigated in early 1950s in the Soviet Union by Emelyanov and several coresearchers.
Presently, the main mode of VSC operation is sliding mode control
(SMC). The strengths of SMC include:
The weaknesses of SMC include:
However, the evolution of VSC is presently an active area of research.
Classification of discontinuities
Continuous functions are of utmost importance in mathematics and applications. However, not all functions are continuous. If a function is not continuous at a point in its domain, one says that it has a discontinuity there...
nonlinear control
Nonlinear control
Nonlinear control is the area of control engineering specifically involved with systems that are nonlinear, time-variant, or both. Many well-established analysis and design techniques exist for LTI systems ; however, one or both of the controller and the system under control in a general control...
. The method alters the dynamics of a nonlinear system by application of a high-frequency switching control. The state
State space (controls)
In control engineering, a state space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations...
-feedback
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...
control law is not a continuous function
Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
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). Variable structure control (VSC) and associated sliding mode behaviour was first investigated in early 1950s in the Soviet Union by Emelyanov and several coresearchers.
Presently, the main mode of VSC operation is sliding mode control
Sliding mode control
In control theory, sliding mode control, or SMC, is a nonlinear control method that alters the dynamics of a nonlinear system by application of a discontinuous control signal that forces the system to "slide" along a cross-section of the system's normal behavior. The state-feedback control law is...
(SMC). The strengths of SMC include:
- Low sensitivity to plantPlant (control theory)A plant in control theory is the combination of process and actuator....
parameter uncertainty - Greatly reduced-order modeling of plant dynamics
- Finite-time convergence (due to discontinuous control law)
The weaknesses of SMC include:
- ChatterChatterChatter may refer to:* Chatter or machining vibrations* Contact bounce or chatter, a common problem with mechanical switches and relays* Chatter , the volume of communication to or from suspected terrorists...
ing due to implementation imperfections - Over-focus on matched uncertainties (i.e., uncertainties that enter into the control channel)
However, the evolution of VSC is presently an active area of research.
See also
- Variable structure system
- Sliding mode controlSliding mode controlIn control theory, sliding mode control, or SMC, is a nonlinear control method that alters the dynamics of a nonlinear system by application of a discontinuous control signal that forces the system to "slide" along a cross-section of the system's normal behavior. The state-feedback control law is...
- Hybrid systemHybrid systemA hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior – a system that can both flow and jump...
- Nonlinear controlNonlinear controlNonlinear control is the area of control engineering specifically involved with systems that are nonlinear, time-variant, or both. Many well-established analysis and design techniques exist for LTI systems ; however, one or both of the controller and the system under control in a general control...
- Robust controlRobust controlRobust control is a branch of control theory that explicitly deals with uncertainty in its approach to controller design. Robust control methods are designed to function properly so long as uncertain parameters or disturbances are within some set...
- Optimal controlOptimal controlOptimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
- H-bridgeH-bridgeAn H bridge is an electronic circuit that enables a voltage to be applied across a load in either direction. These circuits are often used in robotics and other applications to allow DC motors to run forwards and backwards...
– 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 amplifierSwitching amplifierA class-D amplifier or switching amplifier is an electronic amplifier where all power devices are operated as binary switches. They are either fully on or fully off. Ideally, zero time is spent transitioning between those two states....
– Uses switching-mode control to drive continuous outputs - Delta-sigma modulationDelta-sigma modulationDelta-sigma modulation is a method for encoding high-resolution or analog signals into lower-resolution digital signals. The conversion is done using error feedback, where the difference between the two signals is measured and used to improve the conversion...
– 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 modulationPulse-width modulationPulse-width modulation , or pulse-duration modulation , is a commonly used technique for controlling power to inertial electrical devices, made practical by modern electronic power switches....
– Another modulation scheme that produces continuous motion through discontinuous switching.