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Title: Digital Simulation of Dynamic Systems.
Author: Al-Afifi, J. I.
ISNI:       0000 0001 3404 1570
Awarding Body: University of Sussex
Current Institution: University of Sussex
Date of Award: 1978
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Starting with the observation that backcasting involves the prop~gation of the twin sources of errors (i.e. finite machine precision error and truncation erTor from integration method) in a different manneT than that of the propagation in forward integration, an investigation into the propagation of errors in. the numerical solutions of differential equations was carried out, this is covered in Chapter 2. The effect of backcasting (backward integration) on system characteristics such as stability, numeric stability and integration error, is then investigated. Previous examples discussed in the recent literature are re-analysed alongside some new examples to bring about an understanding of backcasting of dynamic systems. This is discussed in Chapter 3. Using the contrast between backcasting and forward running it was found possible to minimize integration error in the simple first order system by introducing elementary classical control principle (i.e. implementing a feedback process). The search for generalisation and the need for controlling errors in higher order systems led to the use of state space representation (e. g. as used in modern Control Theory). This has resulted in the developing of a considerably improved integration- process (involving simple Euler integration) applicable exactly to any order linear time-invariant (constant) system, where accuracy of the integration is only limited- by computer precision. Examples of 'problem' differential equations demonstrate this unequivocally. Clearly the ability to simulate 'constant' systems extremely efficiently makes the transfornation of time-varying and non-linear systems into series of 'constant' systems a practical and efficient method of simulation. Distinct advantages have become apparent In the process of discrete modelling ln comparison with continuous modelling, chapter 4 discusses this method in a structural way and compares it with previous methods (e.g. Runge-Kutta). Both the introductory chapter 1 and the concluding chapter 5 concentrate on the highly pragmatic and experimental approach which has been used, and stress that the thesis should be regarded as driven by the application of control principles to the simulation of dynamic systems in digital computers, which is itself a dynamic process .
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available