Ph.D. received on: 8/7/1997

E-mail: menini@disp.uniroma2.it

Tutor: Prof.  Osvaldo Maria Grasselli, University of Roma Tor Vergata
 
 

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Dynamic control of sampled-data systems with continuous-time requirements   ___________________________________________________________________________________________________________

Advisor:

Prof. Osvaldo Maria Grasselli, University of Roma Tor Vergata

Summary:

Sampled-data systems are studied, in this thesis, in their true nature of hybrid systems, being both continuous-time and discrete-time dynamic systems. In particular, the problem of input-output decoupling for single-rate systems and the problem of robust asymptotic tracking and regulation, in the presence of physical parameters uncertainties, have been dealt with.
 As for the problem of input-output decoupling, unitary feedback systems have been considered, or, equivalently, open loop systems, constituted by the cascade connection of the discrete-time compensator and the continuous-time plant. The main result consists in the proof that continuous-time input-output decoupling is achievable if and only if the given continuous-time plant can be decoupled by means of a static precompensator. Such a result, therefore, allows the problem to be solved by means of purely continuous-time techniques. Several conditions for the existence of static precompensators achieving input-output decoupling for continuous-time plants have been studied, in the case of square systems. It is stressed that, in the case of square systems, the problem of obtaining input-output decoupling with stability can be solved easily.
 As for the the problem of robust asymptotic tracking and regulation, the necessity of a purely continuous-time internal model of the exogenous signals has been proven in the case in which exponential convergence of the error and of the state response is required, and a design procedure for the synthesis of a hybrid compensator solving the problem has been given. The use of a new technique in the mentioned necessity proof allows to improve the existing results, valid in the case of dead-beat convergence requirements. Lastly, the case of multi-rate systems has been considered. The design technique proposed for such a class of systems substantially differs from the one valid for single-rate systems only in its discrete-time component, which is constituted by a periodic subcompensator.
 The main common feature of the two problems considered in this thesis, is the need for hybrid compensators, which is implied by the continuous-time requirements of the considered control problems, excluding those systems which can be decoupled by means of static precompensators, in the case of the input-output decoupling problem, and those systems which, if the hold devices are taken into account, already contain a complete internal model of the exogenous signals, in the case of the asymptotic tracking and regulation problem.

 
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