Linear Parameter Varying Control of Time-Delayed Systems and an Application to Air-Fuel Ratio Control
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In this thesis one of the recently developed gain scheduling control methods, the linear parameter varying (LPV) technique is demonstrated. Starting from the basic definitions of an LMI, important derivations of time delayed control design conditions are derived. In subsequent steps, a motivating example is shown such that the stability and performance of the system is guaranteed in the full operating envelope. The thesis consists of methods and derivations to address time-delayed LPV plants. The synthesis conditions show that the proposed controllers are not only capable of compensating the delay bound but also its rate variation bound. A main benefit of the obtained controllers is that the scheduling of the parameters lead to a robust behavior even for large delay variation and rate. Numerical examples are used to compare the past methods and the current results on the analysis and control design of the same system. Finally the internal combustion engine air-fuel ratio problem is investigated with the help of the derived output-feedback controller design results. The same problem is addressed with a Smith Predictor based Internal Model Control technique to satisfy desired transient and steady-state response characteristics. The LPV control shows better performance compared to the IMC method for small values of the delay. Simulations are used to evaluate the results for larger values of the delay. For large values of the delay the bounds on the Lyapunov –Krasovskii approach introduce some conservatism in the control design and thus, performance specifications are compromised.