Modeling the effects of belt compliance, backlash, and slip on web tension and new methods for decentralized control of web processing lines

Scope and Method of Study: Non-ideal behavior of web process lines and new methods for regulation of web tension and web velocity are investigated. The non-ideal behavior considered includes the compliance and backlash in the transmission system and slippage of web over a roller. The effect of non-ideal elements on the controlled web tension is examined. Dynamic models are developed and analyzed to bring out the effect of non-ideal elements on controlled web tension. A method of mitigating the effect of backlash on controlled web tension is proposed. Effect of web slippage over a roller on span tension dynamics is investigated. The web tension and velocity dynamics are systematically laid down. Two decentralized control schemes viz., a non-adaptive scheme and an adaptive scheme are proposed for web tension/velocity regulation. Experimental study is conducted to validate the results.Findings and Conclusions: The dynamic model of belt-pulley transmission system is derived by considering the tight side of the belt as a spring. The singular perturbation analysis reveals that using only the measured load side speed as the feedback signal is not desirable. A method of setting the proportional and integral gains of the speed controller is proposed. Starting from the first principles, a dynamic model of backlash is derived. This model accounts for the momentum of load during no contact. Using the model, a bound on the error due to presence of backlash is derived. The proposed bound agrees with results of experiments. The dynamic model of rewind section of a transmission system containing belt-compliance and backlash is derived. Analysis of the dynamic model shows that the mean rewind tension is shifted when there is backlash in the transmission system. This result agrees with experimental data. Further, the experiments show that providing an additional braking input on the rewind shaft is successful in mitigating the effects of backlash. The dynamics of idle roller, material rolls, and web spans are systematically laid out and a decentralized control scheme for the entire web process line is proposed. A method of calculating the equilibrium inputs and setting the reference tensions is derived. An exponentially stable non-adaptive scheme and an asymptotically stable adaptive scheme are presented. These schemes explicitly account for the varying inertia of the unwind/rewind rolls and compensate for unmatched interconnections. Experimental results show that the proposed methods offer superior web tension regulation as compared to the existing decentralized PI-control scheme