Full text
| |
| Author(s): |
Márcio Feliciano Braga
Total Authors: 1
|
| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação |
| Defense date: | 2015-03-27 |
| Examining board members: |
Pedro Luis Dias Peres;
Leonardo Antônio Borges Tôrres;
Edson Roberto de Pieri;
Juan Francisco Camino;
Paulo Augusto Valente Ferreira
|
| Advisor: | Pedro Luis Dias Peres; Ricardo Coração de Leão Fontoura de Oliveira |
| Abstract | |
This thesis investigates the problem of discretization of uncertain linear systems in two distinct scenarios. The first one supposes that the matrices of the system and the sampling rate are uncertain and time-invariant, described in terms of polytopes. The second case considers that all uncertain parameters, including the sampling interval, can vary in time and that the parameters of the system have known bounds for the rate of variation and are continuously monitored, in such a way that a new sample is collected whenever a significant change in the parameters occurs or when a maximum time interval since the previous sample is reached, thus characterizing the so-called event-based sampling. The aim is to design digital controllers for the discretized system and to guarantee the closed-loop robust stability of the original continuous-time system. A network-induced delay is also considered in the discretetime model. From the discretization point of view, extensions of the Taylor series expansion of an arbitrary degree ℓ applied to the original system are proposed as a solution to deal with expressions involving the exponential of uncertain matrices. The resulting discrete-time model consists of homogeneous polynomial matrices of degree ℓ with parameters belonging to the Cartesian product of unit simplexes, called multi-simplex, plus an additive norm-bounded term which represents the approximation residual error. More accurate models are obtained with the increase in the degree ℓ which, consequently, yields residues with lower norms, allowing to produce less conservative synthesis results. Conditions based on linear matrix inequalities for the synthesis of robust state-feedback and output-feedback digital controllers, H2 norm computation, and stability analysis for polynomial discrete-time systems with additive norm-bounded terms are also proposed. The conditions employ Lyapunov functions with polynomial dependency on the uncertain parameters to certify the closed-loop stability of the controlled system. In some cases, the matrix inequalities have a scalar parameter, becoming linear for fixed values of the parameter. The obtained results are gradually less conservative with the increase of the degree of the Lyapunov matrix and can be further enhanced with the help of a line search in the scalar parameter. Numerical experiments are presented to illustrate the versatility of the proposed methodology, applicable to a more general class of networked control problems than the existing methods in the literature. (AU) | |
| FAPESP's process: | 11/08312-6 - Discretization and Networked Control of Polytopic Systems with Uncertain Sampling Rates and Delay |
| Grantee: | Marcio Feliciano Braga |
| Support Opportunities: | Scholarships in Brazil - Doctorate |