Advances In Internal Model Principle Control Theory

In this thesis, two advanced implementations of the internal model principle (IMP) are presented. The first is the identification of exponentially damped sinusoidal (EDS) signals with unknown parameters which are widely used to model audio signals. This application is developed in discrete time as a signal processing problem. An IMP based adaptive algorithm is developed for estimating two EDS parameters, the damping factor and frequency. The stability and convergence of this adaptive algorithm is analyzed based on a discrete time two time scale averaging theory. Simulation results demonstrate the identification performance of the proposed algorithm and verify its stability. The second advanced implementation of the IMP control theory is the rejection of disturbances consisting of both predictable and unpredictable components. An IMP controller is used for rejecting predictable disturbances. But the phase lag introduced by the IMP controller limits the rejection capability of the wideband disturbance controller, which is used for attenuating unpredictable disturbance, such as white noise. A combination of open and closed-loop control strategy is presented. In the closed-loop mode, both controllers are active. Once the tracking error is insignificant, the input to the IMP controller is disconnected while its output control action is maintained. In the open loop mode, the wideband disturbance controller is made more aggressive for attenuating white noise. Depending on the level of the tracking error, the input to the IMP controller is connected intermittently. Thus the system switches between open and closed-loop modes. A state feedback controller is designed as the wideband disturbance controller in this application. Two types of predictable disturbances are considered, constant and periodic. For a constant disturbance, an integral controller, the simplest IMP controller, is used. For a periodic disturbance with unknown frequencies, adaptive IMP controllers are used to estimate the frequencies before cancelling the disturbances. An extended multiple Lyapunov functions (MLF) theorem is developed for the stability analysis of this intermittent control strategy. Simulation results justify the optimal rejection performance of this switched control by comparing with two other traditional controllers

Robust and Model Predictive Control for Boundary Control Systems

Tässä väitöskirjassa tarkastellaan robustia ja mallia ennakoivaa säätöä reunasäätöjärjestelmien kannalta. Robustin säädön osalta tunnettuja tuloksia, erityisesti sisäisen mallin periaate, yleistetään tälle systeemiluokalle. Approksimatiivisen robustin reguloinnin käsite esitellään reunasäätöjärjestelmien viitekehyksessä, koska sisäisen mallin periaatteen nojalla tarkasti reguloivan robustin säätäjän konstruointi ei käytännössä ole mahdollista, jos säädettävän systeemin ulostulo on ääretönulotteinen. Lisäksi esitellään käytännöllinen säätäjärakenne, jota käyttämällä robusti regulointi voidaan saavuttaa tässä approksimatiivisessa mielessä. Mallia ennakoivaa säätöä (MPC) tarkastellaan ääretönulotteisten systeemien luokalle, joka kattaa osan reunasäätöjärjestelmistä. Jatkuva-aikaista järjestelmää approksimoidaan diskreettiaikaisella käyttäen Cayley-Tustin muunnosta, ja MPC-ongelma muodostetaan diskreettiaikaiselle systeemille. Diskreettiaikaiselle MPC-ongelmalle todistetaan optimaalinen ja stabiloiva ratkeavuus, mikä yleistää vastaavan äärellisulotteisen MPC-tuloksen tarkasteltujen ääretönulotteisten systeemien luokalle.In this thesis, robust and model predictive control are considered for boundary control systems. In terms of robust control, the existing results, especially the internal model principle, are generalized to cover this class of systems. The concept of approximate robust regulation for boundary control systems is presented, as, due to the internal model principle, in practice it is not possible to construct an exact robust regulating controller if the output space of the controlled system is infinite-dimensional. A practical controller design is presented to achieve robust regulation in this approximate sense. Model predictive control (MPC) is considered for the class of regular linear systems which includes regular boundary control systems. The continuous-time system is approximated by a discrete-time one by using the Cayley-Tustin transform, and MPC is considered for the discrete-time system. Stability and optimality are proved for the proposed discrete-time MPC designs, which extends the corresponding finitedimensional MPC designs to the class of regular linear systems

Robust and Model Predictive Control for Boundary Control Systems

Tässä väitöskirjassa tarkastellaan robustia ja mallia ennakoivaa säätöä reunasäätöjärjestelmien kannalta. Robustin säädön osalta tunnettuja tuloksia, erityisesti sisäisen mallin periaate, yleistetään tälle systeemiluokalle. Approksimatiivisen robustin reguloinnin käsite esitellään reunasäätöjärjestelmien viitekehyksessä, koska sisäisen mallin periaatteen nojalla tarkasti reguloivan robustin säätäjän konstruointi ei käytännössä ole mahdollista, jos säädettävän systeemin ulostulo on ääretönulotteinen. Lisäksi esitellään käytännöllinen säätäjärakenne, jota käyttämällä robusti regulointi voidaan saavuttaa tässä approksimatiivisessa mielessä. Mallia ennakoivaa säätöä (MPC) tarkastellaan ääretönulotteisten systeemien luokalle, joka kattaa osan reunasäätöjärjestelmistä. Jatkuva-aikaista järjestelmää approksimoidaan diskreettiaikaisella käyttäen Cayley-Tustin muunnosta, ja MPC-ongelma muodostetaan diskreettiaikaiselle systeemille. Diskreettiaikaiselle MPC-ongelmalle todistetaan optimaalinen ja stabiloiva ratkeavuus, mikä yleistää vastaavan äärellisulotteisen MPC-tuloksen tarkasteltujen ääretönulotteisten systeemien luokalle.In this thesis, robust and model predictive control are considered for boundary control systems. In terms of robust control, the existing results, especially the internal model principle, are generalized to cover this class of systems. The concept of approximate robust regulation for boundary control systems is presented, as, due to the internal model principle, in practice it is not possible to construct an exact robust regulating controller if the output space of the controlled system is infinite-dimensional. A practical controller design is presented to achieve robust regulation in this approximate sense. Model predictive control (MPC) is considered for the class of regular linear systems which includes regular boundary control systems. The continuous-time system is approximated by a discrete-time one by using the Cayley-Tustin transform, and MPC is considered for the discrete-time system. Stability and optimality are proved for the proposed discrete-time MPC designs, which extends the corresponding finitedimensional MPC designs to the class of regular linear systems

Adaptive Optimal Control The Thinking Man's GPC

Exploring connections between adaptive control theory and practice, this book treats the techniques of linear quadratic optimal control and estimation (Kalman filtering), recursive identification, linear systems theory and robust arguments

About stabilization of non-minimum phase systems by output feedback

This thesis work has been motivated by an internal benchmark dealing with the output regulation problem of a nonlinear non-minimum phase system in the case of full-state feedback. The system under consideration structurally suffers from finite escape time, and this condition makes the output regulation problem very hard even for very simple steady-state evolution or exosystem dynamics, such as a simple integrator. This situation leads to studying the approaches developed for controlling Non-minimum phase systems and how they affect feedback performances. Despite a lot of frequency domain results, only a few works have been proposed for describing the performance limitations in a state space system representation. In particular, in our opinion, the most relevant research thread exploits the so-called Inner-Outer Decomposition. Such decomposition allows splitting the Non-minimum phase system under consideration into a cascade of two subsystems: a minimum phase system (the outer) that contains all poles of the original system and an all-pass Non-minimum phase system (the inner) that contains all the unavoidable pathologies of the unstable zero dynamics. Such a cascade decomposition was inspiring to start working on functional observers for linear and nonlinear systems. In particular, the idea of a functional observer is to exploit only the measured signals from the system to asymptotically reconstruct a certain function of the system states, without necessarily reconstructing the whole state vector. The feature of asymptotically reconstructing a certain state functional plays an important role in the design of a feedback controller able to stabilize the Non-minimum phase system