Identification of Valve Stiction in Control Loops Using Refined Piecewise-Linear Hammerstein Models

This work is motivated by the modelling of sticky control valves via the piecewise linear Hammerstein (PWL-HMM) identification. In PWL-HMM, the nonlinear part of the valve, i.e. stiction, is described by a point-slope-based hysteresis model where a set of knots have to be defined for both the ascent and descent paths of the valve position signal. Traditionally, the knots are assumed to be uniformly distributed, as a result some irrelevant knots might be included in the model. We tackle this problem by proposing two methods, namely the constant threshold-based and BIC-based knot reductions, to identify such irrelevant knots and refine the PWL model of stiction. Numerical, experimental and industrial examples are provided to illustrate the effectiveness of the proposed knot refinement methods.