Robust Control of Dynamical Systems Using Linear Matrix Inequalities and Norm-Bounded Uncertainty
- PDF / 491,553 Bytes
- 10 Pages / 595.276 x 790.866 pts Page_size
- 104 Downloads / 155 Views
Robust Control of Dynamical Systems Using Linear Matrix Inequalities and Norm-Bounded Uncertainty Victor A. F. de Campos · José J. da Cruz · Luiz C. Zanetta Jr.
Received: 10 October 2012 / Revised: 10 October 2013 / Accepted: 18 December 2013 © Brazilian Society for Automatics–SBA 2014
Abstract This work presents the application of linear matrix inequalities (LMIs) to the robust adjustment of controllers with pre-defined structure to improve the damping of dynamical systems. The uncertainty is described using normbounded models. Results of some tests show that gain and zeros adjustments are sufficient to guarantee robust stability and performance with respect to various operating points. Making use of the flexible structure of LMIs, we propose an algorithm that guarantees the damping factor specified for the closed-loop system, always using a controller with flexible structure. The technique used here is the pole placement, whose objective is to place the poles of the closed-loop system in a specific region of the complex plane, for a set of operating conditions. Results of tests with an electrical power system are presented and compared to another robust control technique that makes use of polytopic models. Keywords Linear matrix inequalities · Pole placement · Norm-bounded uncertainty · Robust control
1 Introduction Robust control of dynamical systems has been the subject of many researches during the last decades. Applications V. A. F. de Campos (B) Universidade Federal do ABC, R Abolição, s/n, Santo André, SP, Brazil e-mail: [email protected] J. J. da Cruz · L. C. Zanetta Jr. Escola Politécnica da USP, Av Prof Luciano Gualberto, 148, tr 3, São Paulo, SP, Brazil e-mail: [email protected] L. C. Zanetta Jr. e-mail: [email protected]
of robust control to more complex systems have been arising in the last years. H∞ control was applied to a single machine power system in Taranto and Chow (1995), while μsynthesis was used to ensure robust stability and performance of power systems in Djukanovic et al. (1999). Techniques like LQG/LTR (loop transfer recovery) were also explored (Son and Park 2000). Nevertheless, the most flexible technique in terms of grouping different requisites involves the use of linear matrix inequalities (LMIs). LMIs have been used in many control applications (Boyd et al. 1994), and as examples of their applications to more complex systems we have Rao and Sen (2000), Ramos et al. (2005), and Pal and Chaudhuri (2005). In these works, however, the controller generated by the LMI algorithm is full order; the adjustment of controllers with pre-defined structure is handled in a few papers, like Scavoni et al. (2001), although it is of practical importance to real applications. Chilali and Gahinet (1996) and Chilali et al. (1999) apply LMIs to robust pole placement in generic systems, but the controllers generated are full order, and the formulation does not permit to define the structure of the controller. Chilali and Gahinet (1996) develop a robust pole placement algorithm, that conside
Data Loading...
