Ph.D. Thesis Proposal by
(Advisor: Professor Eric N. Johnson)
High Gain Control for Linear Systems with Unknown Higher Order Dynamics
9:00 AM, Tuesday, November 21, 2017
Montgomery Knight Building Room 325
High gain is desirable for many control systems that need to achieve both stability and a specific degree of performance. However, because higher-order dynamics (HOD) in the control systems in real world cause the undesirable limit cycle oscillation (LCO) or divergence, the applicable magnitude of gain is practically limited. This thesis proposes a new method of attaining maximum possible gain through the analysis and manipulation of LCO.
The existence of HODs within the control systems makes it difficult to analyze the system in the framework of the linear systems theory, which is not appropriate for the analysis of LCO either. Indeed, the HODs can be modeled as corresponding nonlinear analytic functions, enabling the LCO phenomena to be analyzed by the nonlinear systems theory specialized in the time periodic systems. This theory provides insights on the period and stability of the LCO inherent in the linear systems with HODs. Then we design linear compensators to adjust the LCO frequency that results in the reduction of the LCO amplitude to an acceptable level. As a result, we do not have to reduce the gain even in the presence of the LCO. If we do need to remove the LCO, we adjust the gain to an upper limit that does not cause the LCO. A hovering multi-rotor with complex motor/thrust dynamics is a good example to demonstrate the proposed idea. When the nonlinear flight dynamics of a multi-rotor is linearized near the hovering equilibrium, the system is equivalent to a low-order linear system with multiple HODs. A simple flight test can demonstrate the effectiveness of the linear compensator that modifies the LCO frequency and the critical gain that prevents from the generation of LCO.
Professor Eric N. Johnson, School of Aerospace Engineering (Advisor)
Professor Eric M. Feron, School of Aerospace Engineering
Professor J. V. R. Prasad, School of Aerospace Engineering
Professor Magnus B. Egerstedt, School of Electrical and Computer Engineering
Professor Federico Bonetto, School of Mathematics