Robust control design with QFT

Načrtovanje regulatorja v frekvenčni domeni po Horowitzovi [2] metodi, oziroma metodi QFT, se je izkazala za učinkovito pri razvoju robustnih regulatorjev za doseganje standardnih zahtev frekvenčne domene tako pri sistemih z enim vhodom in enim izhodom (SISO) kot pri sistemih z več vhodi in več izhodi (MIMO). Razlog za učinkovitost metode QFT je neposredno upoštevan problem zmanjšanja negotovosti objekta. Namen naloge je predstaviti načrtovanje regulatorja s metodo QFT, ki je verjetno edina znana tehnika načrtovanja vodenja, kjer je zajeto hkratno upoštevanje faze in negotovosti objekta. Prednost metode je možnost doseganja robustne stabilnosti ter robustnega učinka z minimalnim učinkom povratne vezave [7]. Metoda QFT je grafično-analitični postopek načrtovanja vodenja, ki zahteva precej predpriprav pri oblikovanju vzorcev objekta ter empiričnih izkušenj, obenem pa daje načrtovalcu precej manevrskega prostora in direktnega vpogleda v spremembe regulatorja pri načrtovanju. Temeljna ovira metode je določanje mej objekta v Nicholsovem diagramu, saj izračun mej metode QFT eksponentno narašča z natančnostjo vzorca objekta. Za nazornejšo predstavitev metode je predstavljen eksperiment na realnem objektu, kjer je izvedeno vodenje sistema z regulatorjem načrtovanim s metodo QFT. Dobljeni rezultati so primerjani z rezultati vodenja sistema z regulatorjem načrtovanim po metodi H∞.The frequency domain controller design methodology by Horowitz [2], namely quantitative feedback theory (QFT), has proved to be very effective in terms of designing robust controllers to meet standard frequency domain specifications for both single input single-output (SISO) and multiple-input multiple-output (MIMO) systems. The reason for this is that QFT directly addresses the plant uncertainty reduction issue, the primary reason for feedbackhence allowing for the minimum energy to be demanded from a plant to meet certain performance specifications. The aim of the present work is to present the usage of the QFT method for the controller design. It is a graphic technique for designing feedback controllers which is probably the only known technique that simultaneously considers large parametric uncertainty and phase information. The ability to satisfy robust stability and different performance constraints with the minimum possible cost of feedback [7] is the biggest advantage of the method. The downside is that the method, though systematic and powerful in hands of an experienced control engineer, has only recently lent itself to a formal mathematical form as is the case with the more recent paradigms such as H∞ control and µ-synthesis. A major advantage of QFT is that the design is performed in the frequency domain. This enables a good insight into the plant operation and difficulties that may arise during the controller design. Uncertainties can be caused either by changing the plant characteristics or ambient conditions or by unknown external disturbances. QFT starts by defining the plant and then specifying its uncertainties. The defined uncertainties are then used to determine the differential gain and phase from the nominal ones, over the range of frequencies through which the plant operates. At each distinct frequency, differential gains and phases are used to generate the Plant template. The given example illustrates the steps taken in the QFT controller design. To allow for a more illustrative presentation we made an experiment with a real object with the controller designed according to the QFT method. In the work we show the complete procedure of the QFT design from the model analysis to the controller design. At the end we also compared the system performances of the QFT and H∞ controller design