|Tipo di tesi||Tesi di dottorato di ricerca|
|Titolo||Progettazione analitica e grafica di regolatori lineari mediante il metodo delle Formule di Inversione.|
|Titolo in inglese||Analytical and graphical design of linear compensators by using Inversion Formulae|
|Settore scientifico disciplinare||ING-INF/04 - AUTOMATICA|
|Corso di studi||Scuola di D.R. in INFORMATION AND COMMUNICATION TECHNOLOGIES (ICT)|
|Data inizio appello||2012-02-27|
|Disponibilità||Accessibile via web (tutti i file della tesi sono accessibili)|
Questa tesi di dottorato descrive i risultati di ricerca sulla progettazione di nuove metodologie per la sintesi di regolatori classici, utili sia in ambito didattico che industriale. Nella progettazione classica di reti correttrici, i margini di fase e di guadagno sono importanti indicatori frequenziali usati per valutare la robustezza e le prestazioni del sistema di controllo.
This Ph.D. thesis focuses on the results of a research activity on the design of new methods for the synthesis of classical regulators, useful in educational and industrial environments. In classical control design, the gain and the phase margins are important frequency-domain measures used to assess robustness and the performance of a control system. In the continuous time, several methods have been developed in order to meet these specifications. These can be divided into approximated and exact methods. The first ones are normally based on numerical or graphical trial-and-error solutions or fuzzy neural network. They are widely used in industry because they provide a reasonably good tuning of the compensator parameters using automated algorithms. However they are usually not easy to use for teaching purposes or for solving the problem exactly. This makes the synthesis procedure rather clumsy, and less suitable for educational purposes. It is very difficult to construct a written exercise, or test, of exam, in which the control design problem consists in classic trial-and-error design method. An alternative method that can be successfully employed both in an educational and in a practical context is based on the so-called Inversion Formulae. This method was introduced for the first time in 1982 for the numerical and graphical design of first order Lead and Lag controllers and nowadays it is taught in several Italian Universities. This thesis describes how Inversion Formulae technique has been extended to second order Lead-Lag and PID controllers. In particular, the graphical solution can be carried out by ruler and compass on the Nyquist diagrams of the plant and can be easily used in written exercises. Both the numerical and the graphical solutions have been also extended to the design of discrete regulators. This extension is relevant for industrial purposes, because nowadays compensators are often implemented by microprocessors and calculations are performed in the discrete time. The flexibility of the method has been used to design Lead-Lag controllers in order to meet other design requirements. Two of the three parameters of the considered form of Lead-Lag controller are designed to easily and exactly meet the phase margin and the gain crossover frequency. These frequency specifications are known to be related to the peak overshoot, the rise time and the bandwidth of the closed-loop system. The root locus and the contour locus methods have been used to synthesize the third parameter of the compensator in order to maximize the distance of the poles of the closed-loop characteristic equation from the imaginary axis. In this way the settling time of the system step response can be optimized. Moreover another tuning procedure to synthesize the third parameter of the compensator has been designed. This procedure aims to maximized the complementary modulus margin, which is related to a relevant indicator of the system robustness, that is the infinity-norm of the complementary sensitivity function. The results presented in this thesis can be seen as the starting point of a future research activity on the design of compensators.