Time-delay control with switching action using a frequency-shaped integral sliding surface

Sung Uk Lee1
1Nuclear Applications Technology Development Department, Korea Atomic Energy Research Institute, Daejeon, South Korea

Tóm tắt

The Time Delay Control with switching Action (TDCSA) method was recently proposed as a promising technique in a robust control area, where a plant has unknown dynamics with parameter variations and substantial disturbances are present. When TDCSA is applied to a nonlinear system with frequency resonances, TDCSA reveals a chattering problem or an undesired vibration. This undesired vibration and chattering problem comes from the switching action and high gains. Fast sliding mode dynamics or fast desired error dynamics improve the control performance, but excite the un-modeled resonance modes and cause an undesired vibration or chattering. To solve this problem, we proposed an integral sliding surface design method using frequency-shaping features. This method incorporates frequency-shaping LQ design techniques into an integral sliding surface. In this paper, the stability analysis of TDCSA using a frequency-shaped integral sliding surface is analyzed. Based on the experimental results, the frequency-shaped integral sliding surface was shown to be practicable for a single-link flexible arm. Motion control of a single-link flexible arm with un-modeled flexible modes was taken into account. The desired trajectory was tracked while minimally exciting the un-modeled flexible modes.

Tài liệu tham khảo

Lee, S. U. and Chang, P. H., “Control of a Heavy-Duty Robotic Excavator using Time Delay Control with Integral Sliding Surface,” Control Engineering Practice, Vol. 10, No. 7, pp. 697–711, 2002. Lee, S. U. and Chang, P. H., “The Development of Anti-Windup Scheme for Time Delay Control with Switching Action using Integral Sliding Surface,” Journal of Dynamic Systems, Measurement, and Control, Vol. 125, No. 4, pp. 630–638, 2003. Youcef-Toumi, K. and Ito, O., “A Time Delay Controller for Systems with Unknown Dynamics,” Journal of Dynamic Systems, Measurement, and Control, Vol. 112, No. 1, pp. 133–142, 1990. Slotine, J.-J. E. and Li, W., “Applied Nonlinear Control,” Prentice-Hall Englewood Cliffs, 1991. Koshkouei, A. J. and Zinober, A., “Robust Frequency Shaping Sliding Mode Control,” Proc. of IEE Conference on Control Theory and Applications, Vol. 147, No. 3, pp. 312–320, 2000. Moura, J. T., Roy, R. G., and Olgac, N., “Frequency-Shaped Sliding Modes: Analysis and Experiments,” IEEE Transactions on Control Systems Technology, Vol. 5, No. 4, pp. 394–401, 1997. David Young, K. and Özgüner, Ü., “Frequency Shaping Compensator Design for Sliding Mode,” International Journal of Control, Vol. 57, No. 5, pp. 1005–1019, 1993. Gupta, N. K., “Frequency-Shaped Cost Functionals-Extension of Linear-Quadratic-Gaussian Design Methods,” Journal of Guidance, Control, and Dynamics, Vol. 3, No. 6, pp. 529–535, 1980. Mehta, A. J. and Bandyopadhyay, B., “Frequency-Shaped Sliding Mode Control using Output Sampled Measurements,” IEEE Transactions on Industrial Electronics, Vol. 56, No. 1, pp. 28–35, 2009. Anderson, B. D. O., Moore, J. B., and Mingori, D., “Relations between FrequencyDependent Control and State Weighting in LQG Problems,” Optimal Control Applications and Methods, Vol. 8, No. 2, pp. 109–127, 1987. De Luca, A. and Siciliano, B., “Joint-based Control of a Nonlinear Model of a Flexible Arm,” Proc. of American Control Conference, pp. 935–940, 1988.