This chapter presents the identification of a web-winding system as a linear parameter-varying (LPV) system with the reel radius as the time-varying parameter. This system is nonlinear, time-varying and input-output unstable. Two identification methods are considered: in the first one, an LPV model is estimated in a single step using a novel approach based on sparse identification and set membership optimality evaluation. In the second one, several local linear time-invariant (LTI) models are identified using classical identification algorithms, and the overall LPV model is constructed as a weighted sum of the local models. The two methods are applied to experimental data measured on a real web-winding machine.

Chapter Contents:

• 4.1 Introduction
• 4.2 Sparse set membership identification of state-space LPV systems
• 4.3 Interpolated identification of state-space LPV systems
• 4.4 Web-winding system identification
• 4.4.1 The web-winding system
• 4.4.2 Experiment description
• 4.4.3 Sparse set membership LPV model
• 4.4.4 Interpolated LPV model
• 4.4.5 Model validation and results
• 4.5 Conclusion
• References

Inspec keywords: winding (process); set theory; linear parameter varying systems; nonlinear control systems; identification; input-output stability; time-varying systems

Other keywords: web-winding machine; reel radius; weighted sum; local linear time-invariant models; sparse identification; set membership optimality evaluation; nonlinear system; input-output instability; linear parameter-varying system; identification algorithms; LPV; time-varying parameter; local models

Subjects: Combinatorial mathematics; Nonlinear control systems; Control technology and theory (production); Combinatorial mathematics; Time-varying control systems; Production equipment; Control applications to materials handling; Linear control systems; Simulation, modelling and identification; Other manufacturing processes; Stability in control theory