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Variable structure control

Wikipedia contributorsAdapted for Fathomly · View authors
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Source updated March 20, 2025

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.

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.

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This article is adapted from the Wikipedia article “Variable structure control”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Related topics

Variable structure system

A variable structure system, or VSS, is a discontinuous nonlinear system of the form x ˙ = φ {\displaystyle {\dot {\mathbf {x} }}=\varphi (\mathbf {x} ,t)} where x ≜ [ x 1 , x 2 , … , x n ] T ∈ R n {\displaystyle \mathbf {x} \triangleq [x_{1},x_{2},\ldots ,x_{n}]^{\operatorname {T} }\in \mathbb {R} ^{n}} is the state vector, t ∈ R {\displaystyle t\in \mathbb {R} } is the time variable, and φ ( x , t ) ≜ [ φ 1 ( x , t ) , φ 2 ( x , t ) , … , φ n ( x , t ) ] T : R n + 1 ↦ R n {\displaystyle \varphi (\mathbf {x} ,t)\triangleq [\varphi _{1}(\mathbf {x} ,t),\varphi _{2}(\mathbf {x} ,t),\ldots ,\varphi _{n}(\mathbf {x} ,t)]^{\operatorname {T} }:\mathbb {R} ^{n+1}\mapsto \mathbb {R} ^{n}} 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.

Sliding mode control

In control systems, sliding mode control is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "slide" along a cross-section of the system's normal behavior. The state-feedback control law is not a continuous function of time.

Hybrid system

A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior, a system that can both flow and jump (described by a state machine, automaton, or a difference equation). Often, the term "hybrid dynamical system" is used instead of "hybrid system", to distinguish from other usages of "hybrid system", such as the combination neural nets and fuzzy logic, or of electrical and mechanical drivelines.