On Modeling and Identification of Systems with General Backlash

The notion of general backlash is introduced where instead of 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. Hence the multi-valued mapping is represented by one equation. All the parameters in the model equation describing this hard nonlinearity are separated; consequently their estimation can be solved as a quasi-linear problem using an iterative parameter estimation method with internal variable estimation.