Optimiranje sustava s referentnim modelom i parametarskom adaptacijom

U ovoj disertaciji dan je pregled metoda adaptivnog upravljanja sustavima višeg reda s promjenjivim ili nepoznatim parametrima. Detaljniji izvod algoritma dan je za adaptivno upravljanje s referentnim modelom i parametarskom adaptacijom, primjenom metode stabilnosti Ljapunova i hiperstabilnosti Popova. Razrađen je pojednostavljeni algoritam adaptivnog upravljanja, koji uključuje upotrebu samo nekoliko varijabli stanja podesivog sustava, referentni model nižeg reda od reda sustava te kompenziranje utjecaja nivoa upravljačkog signala na adaptacijski algoritam. Razvijen je analitički postupak određivanja težinskih koeficijenata pogrešaka na temelju parametara referentnog modela te predloženo određivanje ostalih koeficijenata algoritma adaptacije postupkom optimiranja. Modificirani algoritam adaptivnog upravljanja s referentnim modelom i parametarskom adaptacijom primijenjen je na istosmjerni elektromotorni pogon napajan tiristorskim usmjerivačem. Zadatak je algoritma kompenzacija utjecaja promjene momenta inercije na prijelaznu pojavu brzine vrtnje pogona. Djelovanje algoritma je testirano simuliranjem na računalu. Pojednostavljeni algoritam adaptacije s diskretnim referentnim modelom trećeg reda i upotrebom samo izlazne varijable sustava, realiziran je na digitalnom signalnom procesoru i primijenjen za upravljanje laboratorijskom maketom istosmjernog elektromotornog pogona. Kod simulacija je postignuto smanjenje pogreške u rasponu od 50 do 100 puta u odnosu na neadaptivni sustav, uz moment inercije dvostruko manji od nominalnog. Ispitivanje algoritma na laboratorijskoj maketi provedeno je uz dvostruko pojaćanje zatvorene petlje struje armature, koje približno odgovara dvostrukom smanjenju momenta inercije te prisustvo šuma u mjerenom signalu, kao i uz nelinearnosti i ograničenja ispitnog pogona. Izmjereno je smanjenje pogreške slijeđenja referentnog modela u odnosu na neadaptivni sustav od približno 4 puta.Various methods of adaptive control of a high-order system with variable or unknown parameters have been analysed. The design of the model reference adaptive control algorithm with parameter adaptation based on the Lyapunov stability and Popov hyperstability criterion has been discussed. A simplified adaptive control algorithm with few adjustable system state variables and a reference model of a lower order than the system has been developed. Compensation of the referent signal level influence on the adaptive system has been achieved by signal normalization. An analytic procedure for error weight coefficients determination based on reference model parameters, has been developed. Other adaptation coefficients have been determined by computer optimization. A modified reference model adaptive control algorithm with parameter adaptation has been applied for the control of the thyristor-supplied DC motor drive. Compensation of the angular speed response due to variations of the moment of inertia was the major task of the developed algorithm. An algorithm has been tested with computer simulation. The simplified adaptation algorithm with the third-order discrete reference model and system output variable has been implemented by means of a digital signal processor, and was used for the control of DC drive angular speed. The simulation results of the system with a moment of inertia two times smaller than the nominal value demonstrated a 50 to 100 fold decrease in transient error compared with the nonadaptive system. The adaptive algorithm has been tested on the laboratory model of a DC drive with signal noise and nonlinearities and limitations. The testing has been performed using a two fold gain over nominal value of the closed armature current loop, which is equivalent to moment of the inertia two times lower than the nominal value. The measured error signal has been 4 times decreased in respect to nonadaptive system