Linear parameter-varying control: Difference between revisions

Revision as of 18:49, 23 December 2017

Revision as of 04:08, 26 February 2018

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{{refimprovemore citations needed|date=January 2015}}

'''Linear parameter-varying control''' (LPV control) deals with the [[control systems|control]] of linear parameter-varying systems, a class of nonlinear systems which can be modelled as parametrized linear systems whose parameters change with their [[State (controls)|state]].

==[[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 [[Angle of attack|AoA]], [[Mach number|Mach]], [[dynamic pressure]], [[Center of mass|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]].

Scheduling multivariable controllers can be very tedious and time-consuming task. A new paradigm is the linear parameter-varying (LPV) techniques which synthesize of automatically scheduled multivariable controller.

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* It is also important that the selected scheduling variables reflect changes in plant dynamics as operating conditions change. It is possible in gain scheduling to incorporate linear [[robust control]] methodologies into nonlinear control design; however the global stability, robustness and performance properties are not addressed explicitly in the design process.

Though the approach is simple and the computational burden of linearization scheduling approaches is often much less than for other nonlinear design approaches, its inherent drawbacks outweigh its advantages and necessitates a new paradigm for the control of dynamical systems. New methodologies such as Adaptive control based on [[Artificial neural networks|Artificial Neural Networks]] (ANN), [[Fuzzy logic]] etc. try to address such problems, the lack of proof of stability and performance of such approaches over entire operating parameter regime requires design of a parameter dependent controller with guaranteed properties for which, a Linear Parameter Varying controller could be an ideal candidate.

==Linear parameter-varying systems==