Adaptive Pulse Width Control for Precise Positioning Under the Influence of Stiction and Coulomb Friction

For the robustness experiment, the friction is increased by increasing the sealing pressure. The PID control exhibits a large overshoot during the transient state, while the other controllers exhibit no overshoot, as shown in Figs. 4 and 5. In the SMC, errors are reduced very slowly and the steady-state error is relatively large as shown in Fig. 5. Settling times of the PID control, the TDC, and the TDSMC are 3.32 s, 2.96 s, and 1.94 s, respectively, as shown in Figs. 4{b) and 5(^). The PID control and the TDC perform very poorly and their settling times are increased by 90.8 and 105.6 percent, respectively, from their nominal values. On the other hand, the TDSMC performs very well and its settling time is increased only by 9 percent from the nominal value. Therefore, the TDSMC has the best performance robustness. Conclusions The TDSMC which is a combination of the TDC and the SMC is proposed for the system with unknown dynamics and disturbances. This method uses the idea of switching of the sliding mode control while reducing the chattering associated with it. Experiments on the position control of a DC motor system with stick-slip friction, were conducted to evaluate performances of the control algorithms. Experiments show that the TDSMC exhibits the best performance robustness and that the TDC and the TDSMC perform better than the PID control with an anti-windup filter and the integral sliding mode control. 227. Youcef-Touini, K., and Bobbet, J., 1991, "Stability of Uncertain Linear Systems With Time Delay," ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL, Vol. 113, pp. 558-567. Youcef-Toumi, K., and Ito, O., 1990, "A Time Delay Controller for Systems With Unknown Dynamics," ASME JOURNAL OF DYNAMIC SYSTEMS, MEASURE- MENT, AND CONTROL, Vol. 112, Youcef-Toumi, K., and Reddy, S., 1992, "Analysis of Linear Time Invariant Systems With Time Delay," ASME JOURNAL OF DYNAMIC SYSTEMS, MEASURE- MENT, AND CONTROL, Vol. 114, Youcef-Toumi, K., and Wu, S.-T., 1992, "Input/Output Linearization Using Time Delay Control," ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL, Vol. 114, pp. 10-19

Coulomb Friction Modelling in Numerical Simulations of Vibration and Wear Work Rate of Tube Bundles,"

where yj is the displacement of the y* mode of vibration. Conclusions A force-balance friction model for the simulation of multidegree-of-freedom mechanical systems is presented. Different from others, this model can be applied to systems with twodimensional sticking/slipping friction acting on a surface. No iteration is needed in the simulation to detect the stick/slip state. The present friction model is an extension of Kamopp's model (1985). It is compared with a piecewise continuous solution using classical Coulomb friction. The results demonstrate that the present friction model is reliable in detecting stick/slip states and is effective in reducing numerical chattering due to the discontinuities in friction calculations. The present friction model has recently been used to model sticking/slipping friction forces in a finite element model of a tube, impacting and rubbing against loose-fitting supports (Tan and Rogers, 1996). Acknowledgments The work reported here was supported by Atomic Energy of Canada Limited, as part of its program of work on heat exchanger tube vibration and wear prediction, and NSERC, through a Collaborative R&D grant. The authors also wish to acknowledge the support of the UNB