Statistical study of pulse-width modulated control systems

✍ Scribed by S.C Gupta; E.I Jury

• Publisher: Elsevier Science
• Year: 1962
• Tongue: English
• Weight: 938 KB
• Volume: 273
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(62)91131-6

✦ Synopsis

This paper describes a statistical study of pulse-width modulated control systems. The pulse-wldth modulator is first considered for positive signals only. The output of this is then compared with the output of the approximate model where the pulsewidth modulator is replaced by sampler, a saturating nonlinear element, and a hold circuit based on equal area approximation. An example is worked to show that there is little error involved in the use of this approximation. Using this as the basis, the open loop case is worked out for Gausslan inputs. The results have been tabulated and graphed.

In the solution of the closed loop system, the difficulty of the calculation of the cross-correlation function is overcome by making another approximation based on the separability property of the Gaussian process. This facilitates the solution of the whole problem and the relationship of output mean square value to input mean square value is graphed for a simple example.