An investigation is made into the approximate synthesis of optimal feedback controllers from the maximum principle necessary conditions. The overall synthesis can be separated into two phases: the computation of optimal open-loop controls (control programs) and trajectories from the necessary conditions, and the processing of this data to obtain an approximate representation of the optimal control as a state function. A particular technique for approximating the optimal feedback control from the optimal open-loop controls and trajectories is proposed and examined in Part I of the thesis. Parameters in a prechosen suboptimal controller structure are computed such that a sum of integral square deviations between the suboptimal and optimal feedback controls is minimized. The deviations are computed and summed over a certain set of trajectories which "cover" the system operating region. Experimentation with various controller structures is quite feasible since the controller parameters are computed by solving linear algebraic equations. Examples are given to illustrate the application of the technique and ways in which suitable controller structures may be found. If general purpose functions are to be used for this purpose, piecewise polynomial functions are recommended and techniques for their use are discussed. The synthesis method advocated is evaluated with respect to control sensitivity and instrumentation and compared to alternative procedures. Part II is concerned with the computation of optimal control programs, the most time consuming numerical task in the synthesis procedure. A new numerical optimization technique is presented which extends the function space Newton-Raphson method (quasilinearization) to a more general terminal condition. More significantly, a generalized Ricatti transformation is employed, and as a consequence, the integration of the unstable coupled canonical system is eliminated. Examples are given as evidence of the improved numerical qualities of the new algorithm. This method is one example of a class of algorithms, defined and developed in the thesis, called second variation methods. Some methods in this class have previously appeared in the literature but they are developed in the thesis from a unified point of view. The recognition of this class allows the relationships between the various methods to be seen more clearly as well as allowing techniques developed for use in one algorithm to be used in others. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Methods for studying the behaviour of on-off feedback systems, with the emphasis on steady-state periodic phenomena, are presented in this thesis. The two main problems analyzed are (1) the determination of the periods of self and forced oscillations in single-, double-, and multiloop systems containing an arbitrary number of on-off elements; and (2) the investigation of the asymptotic stability in the small of single-loop systems containing one on-off element which may or may not have a linear region of operation. To study the periodic phenomena in on-off systems, methods of determining the steady-state response of a single on-r-off element are first described. Concepts pertaining to the steady-state behaviour are then introduced: in this respect it has been found that generalizations of the concepts of the Hamel and Tsypkin loci and also of the phase characteristic of Neimark are useful in the study of self and forced oscillations. Both the Tsypkin loci and the phase characteristic concepts are used to determine the possible periods of self and forced oscillations in single- and double-loop systems containing an arbitrary number of on-off elements; these concepts are also applied to multiloop systems. On-off elements containing a linear region of operation, called a proportional band, are then described: both the transient and periodic response are presented. An approximate method for determining the periodic response is given. The concept of the Tsypkin loci is used to determine the possible periods of self and forced oscillations in a single-loop system containing one on-off element with a proportional band. The asymptotic stability in the small, or local stability, of the periodic states of single-loop systems containing one ideal on-off element has been considered by Tsypkin. In this thesis, Tsypkin's results have been generalized to include the cases of on-off elements containing a proportional band. The stability of such systems is determined by the stability of equivalent sampled-data systems with samplers having finite pulse widths. Finally, this stability problem is solved by a direct approach, one that makes use of the physical definition of local stability; the results obtained by this method agree with those derived by the sampled-data approach. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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Call number: LD2668 .T4 1960 S75

Call number: LD2668 .T4 1962 W36

Call number: LD2668 .T4 1966 H489 / Master of Science

Call number: LD2668 .T4 1966 F771 / Master of Science

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy