Variable structure system
Encyclopedia
A variable structure system, or VSS, is a discontinuous
nonlinear system of the form
where
is the state vector, 
is the time variable, and 
is a piecewise continuous function. Due to the piecewise continuity of these systems, they behave like different continuous nonlinear systems in different regions of their state space
. At the boundaries of these regions, their dynamics switch abruptly. Hence, their structure varies over different parts of their state space.
The development of variable structure control
depends upon methods of analyzing variable structure systems, which are special cases of hybrid dynamical system
s.
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 system of the form
where
is the state vector, is the time variable, and is a piecewise continuous function. Due to the piecewise continuity of these systems, they behave like different continuous nonlinear systems in different regions of their state spaceState 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...
. At the boundaries of these regions, their dynamics switch abruptly. Hence, their structure varies over different parts of their state space.
The development of variable structure control
Variable structure control
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...
depends upon methods of analyzing variable structure systems, which are special cases of hybrid dynamical system
Hybrid system
A hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior – a system that can both flow and jump...
s.
See also
- Variable structure controlVariable structure controlVariable 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...
- 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 sliding-mode control 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.