Guaranteed performance robust gain-scheduling control with uncertain scheduling parameters

One of the main objectives in control theory is to develop control strategies and synthesis conditions that not only guarantee closed-loop stability but also achieve guaranteed performance. In this research, novel Robust Gain-Scheduling (RGS) control synthesis conditions are developed for Linear Parameter-Varying (LPV) systems. In contrast to the conventional gain-scheduling synthesis methods, the scheduling parameters are assumed to be inexactly measured. This is a practical assumption since measurement noise is unavoidable in practical engineering applications.;The contributions of this dissertation are the characterization of novel synthesis conditions in terms of Parametrized Linear Matrix Inequalities (PLMIs) and Parametrized Bilinear Matrix Inequalities (PBMIs) for designing RGS controllers with guaranteed stability and performance. Multi-simplex modeling approach is utilized to model the scheduling parameters and their uncertainties in a convex domain. Synthesis conditions for RGS State-Feedback (SF), full-order Dynamic Output-Feedback (DOF), and Static Output-Feedback (SOF) controllers are developed in a unified framework. Matrix coefficient check approach is used to relax the PLMIs conditions into finite dimensional set of Linear Matrix Inequalities (LMIs) to obtain the optimal or suboptimal controller. The resulting controller not only ensures robustness against scheduling parameters uncertainties but also guarantees closed-loop performance under these uncertainties in terms of H2 and Hinfinity performance. By the virtue of introducing extra slack variables, controller synthesis is independent of Lyapunov variables, that assures improved performance and viability for multi-objective controller synthesis without introducing additional conservativeness. Since PBMIs problems are non-tractable in general, numerical algorithm is developed to solve the PBMIs conditions. Numerical illustrative examples and comparisons with the existing approaches confirm that the developed control approach outperforms the existing ones.;Furthermore, experimental validation of the developed RGS controllers has been conducted on the test bench of the Electric Variable Valve Timing (EVVT) actuator of automotive engines. Engine speed and vehicle battery voltage are used as noisy scheduling parameters. The experiments are performed at MSU Automotive Controls Lab at a room temperature of 25°. Experimental results demonstrate the effectiveness of the developed approach.