The proposed article deals with uncertain description of permanent-magnet DC motor Maxon RE 35 via parametric uncertainty and H-infinity controller design. There was analyzed influence of uncertainties of the particular motor parameters on the model behavior. Consequently there was designed an H-infinity controller via Matlab functions. The behavior of the obtained controller was analyzed on the step responses and course tracking of the closed loop with the nominal system and the system with perturbed parameters. and Obsahuje seznam literatury
This note proposes a quite general mathematical proposition which can be a starting point to prove many well-known results encountered while studying the theory of linear systems through matrix inequalities, including the S-procedure, the projection lemma and few others. Moreover, the problem of robustness with respect to several parameter uncertainties is revisited owing to this new theorem, leading to LMI (Linear Matrix Inequality)-based conditions for robust stability or performance analysis with respect to ILFR (Implicit Linear Fractional Representation)-based parametric uncertainty. These conditions, though conservative, are computationally very tractable and make a good compromise between conservatism and engineering applicability.
This paper considers a robust decentralized H2 control problem for multi-channel descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. Our interest is focused on dynamic output feedback. A necessary and sufficient condition for an uncertain multi-channel descriptor system to be robustly stabilizable with a specified H2 norm is derived in terms of a strict nonlinear matrix inequality (NMI), that is, an NMI with no equality constraint. A two-stage homotopy method is proposed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the efficiency of this method.