## Electrical and Computer Engineering ETDs

#### Publication Date

7-14-1972

#### Abstract

The theory needed to define and obtain an optimized digital simulation of a given continuous system is presented in this dissertation. The frequency domain approach to simulation is used and a nonlinear function minimization algorithm, implemented on a digital computer, is incorporated to obtain the optimum simulation.

The discrete transfer function obtained from z-transform theory is used to represent the digital system. The frequency domain response of this discrete transfer function can then be expressed simply as a function of frequency, for frequencies up to one-half the sampling frequency. A frequency domain error measure, in the complex plane, is defined to be the sum of the squared magnitudes of the difference in the frequency domain responses of the continuous and discrete systems at a finite number of frequencies. The coefficients of the discrete system are adjusted, by means of the function minimization algorithm, to minimize the defined error.

Similar optimization procedures have been previously described. These methods, in some instances, produce an unstable, or nearly unstable, simulation of a stable continuous system. A technique is introduced here of constraining the discrete system coefficients to insure a stable simulation of a stable system. In addition, these parameters may be further restrained to keep the transient behavior of the discrete system similar to that of the system simulated. Essentially these constraints limit the time domain error while the frequency domain error is minimized.

To evaluate the effectiveness of the above procedure, it is compared with the bilinear transformation and the impulse, step, and ramp invariant methods of obtaining a discrete simulation of both a first and second order continuous system. These comparisons are made in the time domain, for impulse, step, ramp, and sinusoidal inputs, as well as in the frequency domain. In addition, the effects of the constraints on the optimization technique are shown. In some instances, a small percentage increase in the frequency domain error will allow orders of magnitude decreases in the time domain errors.

#### Sponsors

The Atomic Energy Commission

#### Document Type

Dissertation

#### Language

English

#### Degree Name

Electrical Engineering

#### Level of Degree

Doctoral

#### Department Name

Electrical and Computer Engineering

#### First Committee Member (Chair)

Ahmed Erteza

#### Second Committee Member

Arnold Herman Koschmann

#### Third Committee Member

Sam D. Stearns

#### Third Advisor

Shlomo Karni

#### Recommended Citation

Schroeder, Donald Howard. "A New Optimization Procedure for Digital Simulation." (1972). https://digitalrepository.unm.edu/ece_etds/469