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'''Linear parametric varying control''' (LPV control). LPV systems are a very special class of nonlinear systems which appears to be well suited for control of dynamical systems with parameter variations. Before explaining about LPV control, it would be worth exploring the notion of [[gain scheduling]], its drawbacks and the need for an LPV method.
==Gain scheduling==
In designing feedback controllers for dynamical systems a variety of modern, [[Multivariable calculus|multivariable]] controllers are used. In general, these controllers are often designed at various operating points using [[Linearization|linearized]] models of the [[Scheduling|system dynamics]] and are scheduled as a function of a [[parameter]] or parameters for operation at intermediate conditions. It is an approach for the control of non-linear systems that uses a family of linear controllers, each of which provides satisfactory control for a different operating point of the system. One or more [[observable]] variables, called the [[Scheduling|scheduling variables]], are used to determine the current operating region of the system and to enable the appropriate linear controller. For example in case of aircraft control, a set of controllers are designed at different gridded locations of corresponding parameters such as AoA, [[Mach number|Mach]], [[dynamic pressure]], CG etc. In brief, gain scheduling is a control design approach that constructs a nonlinear controller for a nonlinear plant by patching together a collection of linear controllers. These linear controllers are blended in real-time via switching or [[interpolation]].
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===Drawbacks of classical gain scheduling===
* An important drawback of classical gain scheduling approach is that adequate performance and in some cases even stability is not guaranteed at operating conditions other than the design points.<ref>{{cite journal|last=S. Shamma|first=Jeff|title=Gain Scheduling: Potentital Hazards and Possible Remedies|journal=IEEE Control Systems|year=1992|volume=June|issue=3}}</ref>
* Scheduling multivariable controllers is often a tedious and time consuming task and it holds true especially in the field of aerospace control where the parameter dependency of controllers are large due to increased operating envelopes with more demanding performance requirements.
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===Parameter dependent systems===
In [[control engineering]], a [[state space]] representation is a [[mathematical model]] of a physical system as a set of input, <math>u</math> output, <math>y</math> and [[State variable|state]] variables, <math>x</math> related by first-order [[Differential equation|differential]] equations. The dynamic evolution of a [[nonlinear]], non-[[autonomous]] is represented by
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<references/>
==Further
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* {{cite book
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