Linear parameter varying control for autonomous systems: methods and application examples

2022-8-24
Çalış, Fatih
Linear parameter varying (LPV) systems are nonlinear systems which can be modelled as linear systems whose parameters change as a function of different "scheduling parameters". In other words, the dynamics of the LPV systems change during the operation hence they require a parameter dependent controller. Although classical gain-scheduling approaches satisfy some performance criteria for constant dynamics, they don't guarantee stability while the scheduling parameter is changing. On the other hand, H∞-norm based LPV control methods utilizing parameter dependent Lyapunov functions provide stability and performance guarantees for the closed-loop system throughout the whole operation. This controller synthesis problem is infinite-dimensional due to the dependency on the scheduling parameter, with the help of polytopic approach it turns into a finite-dimensional convex search with constraints in the form of linear matrix inequalities. In this thesis, LPV control is applied for lane keeping and a launch vehicle system. LPV system models are derived for both systems based on respective nonlinear models of the lateral vehicle dynamics and a rocket by linearization and selection of a suitable scheduling parameter. LPV controllers are designed using a linear matrix inequality (LMI) formulation of the stability conditions and performance constraints. The functionality of the designed controllers is validated by extensive high fidelity simulations.

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Citation Formats
F. Çalış, “Linear parameter varying control for autonomous systems: methods and application examples,” M.S. - Master of Science, Middle East Technical University, 2022.