An approximate transient analysis of a second-order position-control system when backlash is present

An approximate transient analysis is derived for a second-orderposition-control system with backlash. The general characteristics of the transient oscillations are discussed, and the relationship between the amplitude of overshoot and time is given explicitly. It is shownthat there is a best choice for the ratio of the moments of inertia onopposite sides of the backlash if a maximum decrement of the transientoscillations is required. Furthermore, the conditions for which thesettling time for the system is a minimum are also derived. The effectof derivative of input on the transient response is considered. Resultsfrom an electronic analogue of the system confirm the theoretical work.