Linearisation of backlash in control systems with random inputs

A general representation of mechanical backlash contains three zero-memory nonlinearities. When backlash occurs in a feedback control system with random input it may be linearised by replacing the zero-memory nonlinearities with their corresponding Booton equivalent gains. The technique yields reasonably accurate results in most cases, although it is shown that more accurate results are obtained for resetter backlash if an empirical linearisation procedure is used. The empirical technique approximates resetter backlash with a linear first-order lag, 1/(1 + s/A), where A is chosen on the basis of minimum mean-square error using an analogue. It is shown that A is a function of the power spectral density of the backlash input, which is assumed to be stationary and Gaussian-distributed. An example illustrates the application of the empirical linearisation method. Experimental results are also presented.