Identification of cascade systems with backlash

Abstract

This article deals with identification of cascade dynamic systems including backlash. A new form of backlash description is leading to mathematical models of the cascade system with output backlash and the sandwich system with internal backlash, which have all the model parameters separated. The identification based on these models is solved as a quasi-linear problem using iterative algorithms with internal variable estimation. More illustrative examples are included.

Identification of nonlinear dynamic systems with input saturation and output backlash using three-block cascade models

“…In analogy with the Wiener model, the cascade model structure consisting of a linear dynamic block followed by a nonlinear dynamic block was often used for the identification of nonlinear dynamic systems with output dynamic nonlinearities, e.g., in [24][25][26]. However, in some cases of more complex nonlinear dynamic systems with actuator nonlinearities such as saturations, the twoblock cascade model may be not precise enough and it is appropriate to choose a three-block cascade model with combination of nonlinear static, linear dynamic, and nonlinear dynamic blocks.…”

Identification of Nonlinear Cascade Systems with Noninvertible Piecewise Linear Input and Backlash Output Nonlinearities

“…, n L , v(t), x(t), g 1 (t) and g 2 (t) are not available and must be estimated, an iterative parameter estimation process has to be considered. The techniques presented in [18][19][20], which are based on the use of the preceding estimates of model parameters for the estimation of internal variables and vice-versa, can be easily extended to this three-block model. We replace the internal variables in (16) by their estimates defined as …”

“…3 with inputs x(t) and outputs y(t). The backlash can be described by the following first order nonlinear difference equation [18] (9) where g 1 (t) and g 2 (t) are internal variables defined as…”

“…Therefore, a special case of two-block models consisting of the cascade of linear dynamic and nonlinear dynamic blocks has to be used. For example, the cascade model structure consisting of a linear dynamic block followed by a nonlinear dynamic block was often used for the identification of nonlinear dynamic systems with output backlash [16][17][18].…”

Modeling and Identification of Nonlinear Cascade and Sandwich Systems with General Backlash

“…There are some contributions in the literature on the identification of systems with backlash, however it is assumed that the backlash is "straight" ie, straight lines approximate the upward and downward curves of the characteristic; see eg [3][4][5][6][7][8][9]. This simplifies the system description, however, in some cases it leads to inaccuracies.…”