### Abstract

Generalized optimal linear quadratic trackers and their applications to control systems are investigated in this dissertation With the deployment of the frequency-domain shaping on the time-domain performance index function the frequency-domain design concept can be merged into the optimization methodology in the time domain However for the strictly proper system without having any extra input or output signal inducing the frequency-domain proportional-integral-derivative (PID) weighting function on the item of time-domain output tracking performance is equivalent to augmenting PID filter at the output terminal of the given strictly proper plant theoretically Consequently the augmented plant arises in a proper system model with extra input and output signals Nevertheless how to resolve the optimal tracking for this generic system model has not been properly addressed in literature Specifically if an arbitrary time-varying command signal with enormous variations at some isolated time instants is involved the design methodology for the optimal tracking of this kind of system arises in more challenge Nevertheless in this dissertation we first derive generalized optimal linear quadratic analog and digital trackers for the deterministic continuous-time and discrete-time general system models respectively Then some new applications of the generalized optimal linear quadratic trackers on control systems are investigated These include: (i) A new approach for computing the control zeros of the given non-square systems (ii) A new optimal PID filter-shaped proportional-plus-integral (PI) state-feedback linear quadratic design for non-square non-minimum phase system to achieve a minimum phase-like tracking performance However a square non-minimum plant is still non-minimum phase even though through appending PID filter(s)/controller(s) at either the input terminal output terminal or both terminals To solve for the above-mentioned issues in this dissertation we have designed a new PI current-output observer-based optimal linear quadratic tracker for square non-minimum phase system with an unknown external disturbance (iii) A new PI observer-based optimal linear quadratic tracker for the proper system using PI observer to estimate the system state and the unknown external disturbance Some illustrative examples are given to demonstrate the effectiveness of the proposed methodologies and (iv) A one-learning-epoch optimal linear quadratic tracker with an input-constrained for the repetitive proper system with unknown process disturbance and unknown measurement noise For completeness disturbance estimation and performance compensation of unknown stochastic system with disturbances and positive input constraint are presented in this dissertation Its novelties and contributions include: (i) Developing an improved observer/Kalman filter identification (OKID) method which uses the current output measurement to estimate the current state (ii) Proposing a modelling of a delay-free linear model for the unknown nonlinear time-delay system (iii) Constructing a well-performed system output estimation by utilizing the current output-based Kalman filter (iv) Formulating a universal approach for constructing artificial system models based the current output-based Kalman filter (v) Conducting of quantitative analysis to determine the stochastic and deterministic components of the unknown system of interest (vi) Presenting a mechanism for virtual measurement which allows us to use the output of the constructed artificial system model as virtual measurement to replace those missing and/or abnormal output measurements during the phases of testing and/or practical operation (vii) Developing a modified observer-based model predictive control (MPC) with input constraints for the unknown nonlinear time-delay stochastic system with positive input constraints (viii) Developing a universal mechanism for creating simulator and tracker design for positive input-constrained unknown nonlinear input time-delay stochastic sampled-data systems and (ix) Carrying out the closed-loop type long-time prediction of future input-output sets along the associated virtual measurements of the proposed artificial system with the modified MPC Finally a case study on the real stochastic nonlinear input time-delay blast furnace temperature control is demonstrated to show the effectiveness of the proposed methodologyDate of Award | 2016 Jul 25 |
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Original language | English |

Supervisor | Jason Sheng-Hon Tsai (Supervisor) |