Online

Freiheit, Collin J.

Mechanical Engineering

2020

M.S.

Control systems are often subject to constraints imposed by physical limitations or safety considerations, and require means of constraint management to ensure the stability and safety of the system. For real-time implementation, constraint management schemes must not carry a heavy computational burden; however many of the current solutions are computationally unattractive, especially those with robust formulations. Thus, the design of constraint management schemes with low computational loads is an important and practical problem for control engineers. Reference Governor (RG) is an efficient constraint management scheme that is attractive for real-time implementation due to its low computational complexity and ease of implementation. However, in theory, RG is only able to enforce constant constraints for systems with time-invariant models. In this thesis, we extend the capabilities of RG to solve two separate problems. The solution to the first problem presented in this thesis is a novel RG scheme for overshoot mitigation in tracking control systems. The proposed scheme, referred to as the Reference Governor with Dynamic Constraint (RG-DC), recasts the overshoot mitigation problem as a constraint management problem. The outcome of this reformulation is a dynamic Maximal Admissible Set (MAS), which varies in real-time as a function of the reference signal and the tracking output. RG-DC employs the dynamic MAS to modify the reference signal to mitigate or, if possible, prevent overshoot. The second solution presented in this thesis is a RG scheme for constraint management of parameter-varying systems with slowly time-varying constraints. The solution, known as the Adaptive-Contractive Reference Governor (RG-AC) utilizes a contractive characterization of MAS that changes in real-time as a function of the system's time-varying parameters in a computationally attractive manner. This adaptive set is based off a first-order Taylor approximation of the parameter dependent matrices that describe the time-varying MAS. The work in this thesis is supported by simulation results which demonstrate the efficacy of both approaches, and also highlight their limitations.