Parametric Identification of Systems with General Backlash

The notion of general backlash is introduced where instead of the straight lines determining the upward and downward parts of backlash characteristic general curves are considered. An analytic form of general backlash characteristic description is proposed, which is based on appropriate switching and internal functions. Consequently, this multi-valued mapping is represented by one difference equation. All the parameters in the equation describing this hard nonlinearity are separated; hence the general backlash identification can be solved as a quasi-linear problem using an iterative parameter estimation method with internal variable estimation. Also the identification of cascaded systems consisting of a general input backlash followed by a linear dynamic system is presented. Simulation studies of general backlash identification and that of cascaded systems with general input backlash are included.