Optimal Time Control of Some Pulse-width-modulated Sampled-data Systems

Optimal Time Control of Some Pulse-width-modulated Sampled-data Systems PDF

Author: Elijah Polak

Publisher:

Published: 1961

Total Pages: 222

ISBN-13:

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The minimal time control problem for some pulsewidth-modulated-sampled-data (PWM) systems with second order plants is treated. Both linear and non-linear plants are considered; all having one thing in common: the optimal switching locus (OST) for a continuous relay system with the same plants is a monotonic curve in the phase plane. First it is shown how, by a reverse time mapping, it is possible to associate systematically with each initial state a finite canonical sequence which specifies the optimal PWM control over the entire transient process during which the state is taken to the origin. Then it is shown how, given an arbitrary initial state its associated canonical sequence can be constructed on the basis of the observed value of the state. A brief description of an electromechanical computer capable of implementing minimal time control for some of the systems considered is also given. (Author).

The Analysis of Nonlinear Feedback Sampled-data Systems

The Analysis of Nonlinear Feedback Sampled-data Systems PDF

Author: Mangalore Anantha Pai

Publisher:

Published: 1961

Total Pages: 226

ISBN-13:

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Various techniques are available for the analysis of nonlinear sampled-data systems. Most of these methods use either the phase plane approach or the describing function technique. Since the performance of such a system is described, at sampling instants, by means of a difference equation, an approach based on the difference equation would seem to be both natural and direct. The principle of complex convolution for a transform is explained and its geometrical interpretation is given. It is shown how the application of the convolution transform is both direct and simple with respect to solving nonlinear difference equations when the equation is given in scalar form. Dependence of the convergence of the solution on the initial value and the degree of nonlinearity is pointed out. It is concluded that for difference equations of second order and higher, this method involves too much laborious computation to justify its use. A simple method is presented for examining free oscillations in a sampled-data system containing either relay or a saturating amplifier. In addition, a certain analytical technique, analogous to that for differential equations, is developed to investigate the stability of forced oscillations for certain types of nonlinear difference equations. (Author).

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