Búsqueda de estructuras de reguladores en sistemas de control discreto que minimicen los efectos debidos a la utilización de aritmética de precisión finita

Abstract

Control algorithms (digital controllers) are dynamic discrete systems. Those systems are obtained designing discrete control system. So, it is necessary an implementation using software and/or digital hardware. The digital implementation forces the variables and filter coefficients to belong to a discrete set of values given by the length of the digital register (finite precision). Two-Complement Fixed-Point Arithmetic is the most used for the implementation of digital controllers because the microcontrollers and microprocessors using such arithmetic are cheap and fast. Using finite precision arithmetic in a controller implementation gives a non-linear control system although the initial specification was linear. This implementation causes new problems and the FWL (finite word length) effects. The analytic study of those effects is very difficult. If this effects are not taken into account, the system can not fulfill the initial specifications. The effects of finite word length (A/D conversion, coefficient quantization, limit cycles and quantization noise) has been studied numerous researchers in signal processing and in discrete control systems. In this thesis, research has been developed in the design of discrete-time control system where the controller are implemented by a microcontroller or a computer for the processing. In order to minimize the finite length arithmetic effects several implementations have been developed in the last years. Implementation of the transfer function can be perform using a given structured or can be divided in first and second order modules. The controller quantization of coefficients and the analysis of the limit cycles produced by the finite length arithmetic in the closed loop control systems are the general objectives in this research. This thesis introduce a new way to represent the discrete system very appropriated for finite length effect study. This representation has been used to develop the simulation workbench and the algorithm to look for limit cycles in the discrete control systems. As an example to show the procedure, a well-known digital control system has been designed. Alter the design, the behaviour of the system has been analyzed with different structures to implement the ideal controller, where the coefficients (the closed loop system are modified) and the coefficients and operations (limit cycles can appear) are quantized. The goal is to obtain a structure with minimum modification of the ideal system and with minimum effects from the limit cycles over the system response.