scholarly journals STABILITY STUDY OF PULSE-WIDTH MODULATED AND NONLINEAR SAMPLED-DATA SYSTEMS

1961 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Pulse Width ◽  
Stability Study ◽  
Data Systems ◽  
Sampled Data ◽  
Pulse Width Modulated

Minimum Time Control of Second Order Pulse-Width-Modulated Sampled-Data Systems

1962 ◽  
Vol 84 (1) ◽  
pp. 101-109 ◽  
Author(s):  
E. Polak
Keyword(s):  
Pulse Width ◽  
Phase Plane ◽  
Sampling Period ◽  
Second Order ◽  
Data Systems ◽  
Sampled Data ◽  
Relay System ◽  
Pulse Width Modulated ◽  
Minimal Time ◽  
Time Control

This paper treats the minimal time control problem for two second order pulse-width-modulated sampled-data systems, one with a double integrator type plant and one with a plant described by an integral and a time constant. Such plants are encountered in systems with hydraulic components. It is shown rigorously that for minimal time control the phase plane can be divided into two regions: a striplike region around the optimal switching trajectory for a continuous relay system with the same plants, in which the pulse width must be adjusted for optimal action; and the rest of the phase plane in which an optimal p.w.m. system of the type described behaves like a continuous optimal relay system, the pulse duration being equal to the sampling period. A brief description of an electromechanical computer capable of implementing minimal time control for these systems is also given.

On the Periodic Modes of Oscillation in Pulse-Width-Modulated Feedback Systems

1962 ◽  
Vol 84 (1) ◽  
pp. 71-81 ◽  
Author(s):  
E. I. Jury ◽  
T. Nishimura
Keyword(s):  
Limit Cycles ◽  
Pulse Width ◽  
Pulse Width Modulation ◽  
General Procedure ◽  
Discrete Systems ◽  
Forced Oscillations ◽  
Sampled Data ◽  
Feedback Systems ◽  
Pulse Width Modulated ◽  
Data Feedback

A general procedure for obtaining information on the periodic modes of oscillation in PWM and nonlinear sampled-data feedback systems is considered in this paper. Based on the equivalence of PWM in the state of limit cycles to the finite pulsed systems with the periodically varying sampling pattern, the methods of analysis applied to the latter are extended to obtain these limit cycles. In particular, the final value theorem is applied to obtain the fundamental response equation which gives rise to the limit cycles for the various specified modes. The theory is applied to systems with and without integrator and the results are checked by the phase-plane approach. Two kinds of nonlinearities, namely, pulse-width modulation and saturating gain, are discussed among the various nonlinearities, and examples are presented for each of these cases. Furthermore, both self-excited and forced oscillations are examined as well as the possible existence of limit cycles for certain specified modes. This approach to examining the periodic modes is not restricted to the type of non-linearity or the order of the system and thus can be applied to various forms of nonlinear discrete systems. However, it is based on the assumption that the mode of the limit cycle is specified, as can be done in certain cases, and thus the method of this paper permits the study of the conditions that sustain those oscillations.

Stability Study of PWM Feedback Systems

1964 ◽  
Vol 86 (1) ◽  
pp. 80-86 ◽  
Author(s):  
E. I. Jury ◽  
T. Nishimura
Keyword(s):  
Fundamental Equation ◽  
Sufficient Conditions ◽  
Feedback System ◽  
Stability Study ◽  
Data Systems ◽  
Sampled Data ◽  
Feedback Systems ◽  
Data Feedback ◽  
Maximum Period ◽  
Fundamental Equations

A fundamental equation which yields the limit-cycle feature of PWM feedback system is derived in this paper. The application of this equation to obtain the response of the autonomous as well as the forced PWM system is indicated. The application of this fundamental equation to other types of nonlinear sampled-data feedback systems is also demonstrated. The maximum mode of the limit cycles that can exist in relay-mode oscillations of PWM systems as well as the limitations on the maximum period is obtained in this paper. Based on the foregoing derivations, the sufficient conditions for eliminating all saturated oscillations is derived. The experimental study performed on the digital computer confirms the theoretical results. Stability curves for certain PWM systems are being calculated which will aid considerably in this design. The basic advantage of PWM controllers on relay sampled-data systems with regard to sensitivity and stability is well pointed out in this paper as well as a few examples illustrating the application of the fundamental equations derived.

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