Output regulation of uncertain linear systems
Author(s)
Wang, Yang
Type
Thesis
Abstract
This thesis addresses the output regulation problem for uncertain single-input-single-output linear time-invariant systems. Specifically, we consider a case in which the plant is characterized by a largely uncertain stable transfer function and is affected by unknown periodic disturbances. The disturbance is modelled as the output of a suitable exosystem. Based on the adaptive feedforward control paradigm, adaptive control techniques and switching control theory, we propose four active feedforward control algorithms to solve the problem.
This thesis consists of three Parts. Specifically, Part I presents the problem formulation and literature review.
Then, in Part II, we start from the case in which the frequency of the disturbance is assumed to be known a priori. We propose an adaptive controller and a switching-based controller that both remove the longstanding assumption that the sign of either the real part or the imaginary part of the transfer function of a stable plant at the frequency of the disturbance must be known for adaptive feedforward control scheme to be applicable. The methods presented also avoid requirements of persistence-of-excitation and stability arguments based on averaging theory. Furthermore, the issue of non-singularity of the control law, which requires bounding the Euclidean norm of the estimates away from zero, is solved. These are the first significant contributions of this thesis.
Finally, in Part III, we remove the assumption about the prior knowledge of the disturbance frequency, and we extend the algorithms presented in Part II to this more challenging case by adopting a sequential strategy. Specifically, over a given time interval, only one of the two distinct actions --- estimation or regulation --- is performed. In the estimation mode, the frequency of the disturbance is identified in finite time by a non-asymptotic estimator, while in the regulation mode, the disturbance is rejected by either the adaptive controller or the switching-based controller with the frequency estimate held constant. Finally, a brand new state-norm-estimator-based switching logic is proposed to improve the transient behaviour and the robustness of the algorithms.
The effectiveness of all presented approaches is evaluated by extensive simulations. The numerical examples show that a reliable rejection/attenuation of the disturbance is achieved without/with the influence of bounded sensor noises.
This thesis consists of three Parts. Specifically, Part I presents the problem formulation and literature review.
Then, in Part II, we start from the case in which the frequency of the disturbance is assumed to be known a priori. We propose an adaptive controller and a switching-based controller that both remove the longstanding assumption that the sign of either the real part or the imaginary part of the transfer function of a stable plant at the frequency of the disturbance must be known for adaptive feedforward control scheme to be applicable. The methods presented also avoid requirements of persistence-of-excitation and stability arguments based on averaging theory. Furthermore, the issue of non-singularity of the control law, which requires bounding the Euclidean norm of the estimates away from zero, is solved. These are the first significant contributions of this thesis.
Finally, in Part III, we remove the assumption about the prior knowledge of the disturbance frequency, and we extend the algorithms presented in Part II to this more challenging case by adopting a sequential strategy. Specifically, over a given time interval, only one of the two distinct actions --- estimation or regulation --- is performed. In the estimation mode, the frequency of the disturbance is identified in finite time by a non-asymptotic estimator, while in the regulation mode, the disturbance is rejected by either the adaptive controller or the switching-based controller with the frequency estimate held constant. Finally, a brand new state-norm-estimator-based switching logic is proposed to improve the transient behaviour and the robustness of the algorithms.
The effectiveness of all presented approaches is evaluated by extensive simulations. The numerical examples show that a reliable rejection/attenuation of the disturbance is achieved without/with the influence of bounded sensor noises.
Version
Open Access
Date Issued
2019-01
Date Awarded
2019-05
Copyright Statement
Creative Commons Attribution NonCommercial Licence
Advisor
Parisini, Thomas
Publisher Department
Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)