Determination of all fractional-order PID controllers that meet specific stability, robustness, and performance requirements
Lee, Yung K.
AdvisorWatkins, John Michael
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In this dissertation, a broad spectrum of research in fractional-order (FO) proportional-integral-derivative (PID) controllers is directed to fundamental control problems such as stability, performance, and robustness. First, nominal stability was considered by finding all the possible FO PID controllers that stabilize a closed-loop system with respect to arbitrary values of the fractional orders λ and μ of the FO PID controller. The findings are presented on the (Kp, Ki), (Kp, Kd), and (Ki, Kd) planes. In order to meet nominal performance specifications, a sensitivity function weight was introduced and FO PID controllers were sought to meet the weighted sensitivity constraint. This led to a complete set of possible values of FO PID parameters that satisfy the given performance specifications. Following the nominal stability and performance, robust stability and performance were investigated. For a robust stability requirement, a multiplicative weight was selected to bound all multiplicative errors of a closed-loop system. Such FO PID controllers allow the closed-loop to remain stable for all the sets of perturbed plants. Nominal performance and robust stability are the prerequisite conditions for the robust performance of a closed-loop system. Though, in robust stability analysis, the closed-loop system was designed only to remain stable, it was required not only to remain stable for all the uncertain plants but also to satisfy given performance specifications in the robust performance analysis. A substantial contribution of this research is the establishment of a complete set of solutions for FO PID controllers, with respect to nominal stability and performance and robust stability and performance. The use of frequency response of a system makes it possible to apply the results presented in this dissertation even when a system transfer function is not known or unavailable, as long as the experimental frequency data of a system can be obtained.
Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science