FREQUENCY ANALYSIS OF A CONTROL LOOP CONTAINING A BI-STABLE ELEMENT,
Abstract
The performance of a control loop with a signum computer (bi-stable switch) in the forward portion is analyzed. The frequency response method (subject to usual restrictions that the input voltage to the non-linear element be sinusoidal) is used to determine the gain of the bi-stable element. This gain is approximately inversely proportional to the amplitude of the switching signal if the amplitude of the input is equal to or less than one-half the switching voltage amplitude and if the frequency of the input is less than the frequency of the switching voltage by at least a factor of five. If the amplitude of the input is small as compared to the amplitude of the switching signal, this approximation becomes better. In fact, as the ratio of this amplitude approaches zero, the gain approaches the limit of being exactly inversely proportional to the amplitude of the switching frequency for all signal frequencies less than the switching frequency. When considering the question of mode stability or limit cycle states, the frequency analysis method was no longer subject to the restriction that the input voltage to the non-linear element be sinusoidal. An exact method for determining the numbers of limit cycles and their periods of oscillation has been devised but is not included in this report. A graphical method is presented. Criteria for insuring oscillation in a specific mode have been determined for a certain class of control systems. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 11, 1958
- Accession Number
- AD0654332
Entities
People
- R. E. Gorozdos
Organizations
- Johns Hopkins University