Effects of dither shapes in nonsmooth feedback systems: experimental results and theoretical insight

Abstract

Abstract-Dither signals are commonly used to compensate for nonlinearities in feedback systems in electronics and mechanics. Recently, theoretical results were proposed for the analysis of a particularly interesting class of nonsmooth systems, namely relay feedback systems with triangular dither. In this paper the class of dither signals is enlarged by considering square and trapezoidal dither: it is shown how the dither shape affects the behavior of nonsmooth feedback systems, differently from the case of dither in Lipschitz continuous systems. Experimental results support this fact and a theoretical insight is given in order to explain the phenomena.

Averaging of nonsmooth systems using dither

“…In particular, the dithered and the averaged solution may have qualitatively different behavior when the averaged nonlinearity is not Lipschitz continuous. Experimental confirmation of such behaviors on a DC motor are provided in Iannelli, Johansson, Jönsson, and Vasca (2003b). We have discovered similar phenomena for limit cycles of the averaged and the dithered systems in Iannelli (2002) and Iannelli et al (2003a,b).…”

Dither shape in the averaging of switched systems

“…The example does illustrate, however, how the dithered and the averaged solution bifurcate due to the fact that the averaged nonlinearity is discontinuous. We have discovered similar phenomena for limit cycles of the averaged and the dithered systems [7], [16], [17]. If assumption (iv) weakened such that the boundedness assumption on the density function is removed then the amplitude distribution function is no longer Lipschitz continuous and the conclusions of the theorem do not hold.…”

Practical stability and limit cycles of dithered relay feedback systems

“…Some examples have highlighted that the averaging approach cannot be simply extended to the case of square wave and more general zero-slope dither signals. Further investigations in this direction are the main object of some ongoing works [16,17] in which we deal with a wider class of switched systems and with more general dither signals.…”