## Document Type

Dissertation

## Date of Award

Spring 5-31-1976

## Degree Name

Degree of Engineer in Electrical Engineering

## Department

Electrical Engineering

## First Advisor

Marshall Chuan Yung Kuo

## Second Advisor

John Mihalasky

## Third Advisor

K. Denno

## Fourth Advisor

Raj Pratap Misra

## Abstract

It is well known that in actual control systems there are uncontrolled parameter changes caused by aging of elements, temperature, pressure and effects of externalmedium, among others, which may impair the performance ofthe system. Hence, there is the need to develop systems that weakly react to these parameter fluctuations. Sensitivity theory has been developed to study some of these problems. Most of the investigations in this area, however, deal with problems in continuous systems modeled by ordinary differential equations. Even the recent publications on sensitivity problems in distributed parameter control systems are largely concerned with systems modeled by first order partial differential equations.

In this dissertation, the study of parameter sensitivity is extended to higher order distributed parameter control systems. The dynamic system of interest is represented by a non-linear higher order vector partial differential equation and its associated matrix sensitivity equation. The problem posed is that of minimizing a cost functional consisting of both the performance and trajectory sensitivity indices subject to the state and sensitivity equations of the system. By means of variational techniques, the necessary conditions for optimality are obtained. The sufficient conditions are also derived using the theory of convexity.

The theory developed is applied to two classes of reliability models of wide-applicability. These are represented by the standby redundant system and the semi-infinite parabolic PDE. The resulting co-state equations, together with the system's equations, are discretized in both space and time. Algorithms are then developed to integrate these equations. The results are presented in the form of state and sensitivity profiles for a given set of conditions. The variation of the functional performance index with respect to changes in system parameter is also presented.

The study concludes with a series of numerical examples to illustrate the theory and technique in modeling various sensitivity problems in distributed parameter control systems. In particular, the problem of achieving a compromise among a set of design objectives is emphasized.

This dissertation is essentially an extension of low sensitivity design theory to distributed parameter systems.

## Recommended Citation

Ayiku, Moses Nee Buernor, "Distributed parameter sensitivity theory to solve certain reliability problems" (1976). *Dissertations*. 1304.

https://digitalcommons.njit.edu/dissertations/1304