MATCHED PROCESSORS FOR OPTIMUM CONTROL.
Item
-
Title
-
MATCHED PROCESSORS FOR OPTIMUM CONTROL.
-
Identifier
-
AAI8203278
-
identifier
-
8203278
-
Creator
-
FERIA, ERLAN HECTOR.
-
Contributor
-
Prof. Frederic Thau
-
Date
-
1981
-
Language
-
English
-
Publisher
-
City University of New York.
-
Subject
-
Engineering, Electronics and Electrical
-
Abstract
-
Optimum and suboptimum control laws for linear (in state) deterministic processes with quadratic (in state) performance criteria and quantized control are investigated using a 'Matched Processors (MPs) approach'. The optimum control law at each stage k is found to consist of M('m(N-k)) processors and a Comparator Decoder where: (a) M, N, and m are the number of control quantization levels, process stages, and process controls, respectively; (b) each of the M('m(N-k)) processors is a single output processor which has a quadratic dependence in the current process state, x(k), and in addition has parameters that depend in a unique control sequence from stage k to N - 1, U(,k,N-1) (this originates the names 'Matched Processor (MP)' for each of the M('m(N-k)) processors, 'Matched Processors (MPs) approach' for the design tool, and 'MPs control law' for the designed optimum control law); and (c) the Comparator Decoder chooses among the M('m(N-k)) MPs the one that yields the lowest output and then selects from the control sequence that was used in the design of the chosen MP the k-th stage control member, u*(k) (this is the optimum control action that must be applied to the process).;Although the implementation at each stage k of each of the M('m(N-k)) MPs is relatively easy to achieve in a digital computer, it is found that the implementation of all the M('m(N-k)) MPs is impossible for typical values of M, m, and N - k. To deal with this dimensionality problem we then make use of the structure of the MPs control law to define 'Reduced Order Matched Processors (ROMPs) control laws' which are shown to offer the possibility of having practical control laws with outstanding performance: a ROMPs control law is defined as any MPs control law which has had its order of MPs at any stage k, M('m(N-k)), reduced either by the simplification of the original MPs control law or by the outright deletion of some of its M('m(N-k)) MPs. In particular, we define I Stages Reduced Order Matched Processors (ROMPs) control laws with I (ELEM) (1,...,N) as a class of ROMPs control laws that have the following characteristics: (a) the order of their MPs at any stage k can not exceed M('mI); (b) the N Stages ROMPs control law is the same as the MPs control law; (c) the maximum on-line computation time and memory capacity required by the I Stages ROMPs control law steadily decrease as I decreases from N to 1; and (d) the I Stages ROMPs control law corresponding to a general stable scalar example is found to be an optimum control law for all possible values of I. The ROMPs control laws are then used to define ROMPs approaches which search for practical ROMPs control laws with desirable performance: a ROMPs approach is defined as any iterative approach that systematically searches for a physically realizable ROMPs control law with satisfactory on-line computation time and performance. In particular, an I Stages ROMPs approach is defined as an iteration technique that starting with I = 1, i.e. starting with a 1 Stage ROMPs control law, determines whether the considered I Stages ROMPs control law, besides having a practical on-line computation time and memory capacity, yields a performance that is close to the optimum and/or surpasses the performance of other offered suboptimum control laws. It is found that when the proposed I Stages ROMPs approach is applied to two practical processes (with small, intermediate, and large values of N) it yields I Stages ROMPs control laws with excellent on-line computation time, memory capacity, and performance.
-
Type
-
dissertation
-
Source
-
PQT Legacy CUNY.xlsx
-
degree
-
Ph.D.
-
Program
-
Engineering
