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Concept
Linear parameter-varying control
Summary
Linear parameter-varying control (LPV control) deals with the 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.
In designing feedback controllers for dynamical systems a variety of modern, multivariable controllers are used. In general, these controllers are often designed at various operating points using linearized models of the 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 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, 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.
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.
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.
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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