Quasipolynomial Approach to Simultaneous Robust Control of Time-Delay Systems

A control law for retarded time-delay systems is considered, concerning infinite closed-loop spectrum assignment. An algebraic method for spectrum assignment is presented with a unique optimization algorithm for minimization of spectral abscissa and effective shaping of the chains of infinitely many closed-loop poles. Uncertainty of plant delays of a certain structure is considered in a sense of a robust simultaneous stabilization. Robust performance is achieved using mixed sensitivity design, which is incorporated into the addressed control law

STABILIZATION OF ROTARY INVERTED PENDULUM WITH DSP

V tem delu je predstavljena priprava programskih gradnikov na procesorju DSP TMS320F28335, ki so bili potrebni za razvoj okolja primernega izvajanju regulacijskih algoritmov. Sistem je bil zasnovan tako, da je prilagodljiv in primeren za nadaljnje eksperimente na področju vodenja in regulacij. Izvedeno je bilo načrtovanje in izvedba algoritmov vodenja za stabilizacijo inverznega rotacijskega nihala.This work presents preparation of the software for different modules on DSP TMS320F28335, which are needed to create an environment that is suitable for realization of regulation algorithms. The system has been designed in way of adaptability for further use. Design and realization of regulation algorithms for stabilization of rotary inverted pendulum have been performed

Robust pole placement for systems with delays

V disertaciji je predstavljena sinteza regulatorja za sisteme z zakasnitvami, ki temelji na razreševanju zaprtozančnih polinomskih enačb, ki odražajo lastnosti zaprtozančnega karakterističnega kvazi-polinoma. V delu so obravnavane tako notranje zakasnitve kot vhodne oz. izhodne transportne zakasnitve. Predlagana je celostna rešitev polinomske sinteze, ki omogoča izbiro poljubnega zaprtozančnega kvazi-polinoma s pomočjo uporabe opazovalnika zaprtozančnega sistema. Podoben pristop smo izbrali tudi v primeru kompenzacije transportne zakasnitve in sicer s strukturo kaskadnih opazovalnikov. V delu podrobno obravnavamo uporabo ter vpliv prostih polinomov, ki nastopijo v sistemu ob ustrezni izbiri strukture regulatorja. Proste polinome lahko uporabimo za optimizacijo kvazi-polinoma ali za optimizacijo robustnosti sistema po principu metrike Hinf. Optimizacijski problem robustnosti smo razširili na različne vidike obravnave sistema pod vplivom motenj v sistemu samem ali v zakasnitvah, ki so prisotne. Postopek optimizacije je bil izveden s pomočjo diferencialne evolucije. V delu je izpostavljen tudi poenostavljen postopek izbire ustreznega karakterističnega kvazi-polinoma ter učinkovit algoritem za izračun le nekaj skrajno desnih lastnih vrednosti sistemov z zakasnitvami, ki je pri obravnavi takšnih sistemov nepogrešljiv.This dissertation presents controller synthesis for time delay systems based on the solutions of sets of polynomial equations, which represent the essence of characteristic quasi-polynomial. In this work internal delays as well as input/output transport delays are addressed. We propose integrated solution of pole placement technique using a closed loop state observer, which allows arbitrary choice of quasi-polynomial. Similar approach was considered in the case of dealing with the compensation of transport delays by introducing a specific structure of cascade observers. We fully discuss the use and the influence of free polynomials, which occur in the system as a result of the appropriate structure of the controller. Free polynomials might be used for the optimization of the quasi-polynomial or for the optimization of the system robustness according to Hinf metrics. The robustness optimization problem was focused on different aspects of perturbations acting directly either on the system parameters or to the time delays present. The optimization process was performed using differential evolution. The work also deals with the proposed method for the simplified selection of suitable characteristic quasi-polynomial and the proposed effective algorithm for the computation of only few rightmost eigenvalues for time delay systems, which is indispensable in case of dealing with such systems

Quasipolynomial approach to simultaneous robust control of time-delay systems

A control law for retarded time-delay systems is considered, concerning infinite closed-loop spectrum assignment. An algebraic method for spectrum assignment is presented with a unique optimization algorithm for minimization of spectral abscissa and effective shaping of the chains of infinitely many closed-loop poles. Uncertainty of plant delays of a certain structure is considered in a sense of a robust simultaneous stabilization. Robust performance is achieved using mixed sensitivity design, which is incorporated into the addressed control law