Analysis of non-linear sampled-data systems with transportation lag

A detailed investigation is made into the effect of inherent transportation lag on the nature of limit cycles sustained in a second-order sampled-data system containing a relay type non-linearity. The effectiveness of the dither signals of sinusoidal. triangular and square wave shape to suppress limit cycles is studied in detail and the advantages arid disadvantages of each wave shape are discussed. The method of analysis is via the state transition technique and it is advantageously used to evaluate the response of the system until a final stendy-state value is attained by the controlled variable. The results conclusively prove that the wave shape and the nniplitude of the dithering signal have s pronounced influence on the manner of suppression of litnit cycles and the final steady-state error. It is clearly shown that systems with larger values of transportation lag call for stronger dithering signals in order to quench the limit cycles that would otherwise persist with a time period which is an integral multiple of the sampling period. I t is found, with regard to sinusoidal and triangular dither, that it is possible to exercise smooth control over the transient, response to any desired extent by merely varying the amplitude, provided the frequency of dither is at limit ten times the frequency of the signal of interest. Finally it is established that it should be possible to choose an optimum amplitude of the dithering signal in respect of settling time or any standard index of performance. © 1970 Taylor & Francis Group, LLC.