Adaptive time delay based control of non-collocated oscillatory systems (2311.14979v3)
Abstract: Time delay based control, recently proposed for non-collocated fourth-order systems, has several advantages over an observer-based state-feedback compensation of the low-damped oscillations in output. In this paper, we discuss a practical infeasibility of such observer-based approach and bring forward application of the time delay based controller, which is simple in both the structure and design. Moreover, robust estimation of the output oscillation frequency is used and extended by a bias canceling. The latter is required for positioning the oscillatory passive loads. This way, an adaptive version of time delay-based control is realized that does not require prior knowledge of the mass and stiffness parameters. The results are demonstrated on the oscillatory experimental setup with constraints in the operation range and control value.
- J. Vaughan, D. Kim, and W. Singhose, “Control of tower cranes with double-pendulum payload dynamics,” IEEE Transactions on Control Systems Technology, vol. 18, no. 6, pp. 1345–1358, 2010.
- J. Wang and W. T. van Horssen, “On resonances and transverse and longitudinal oscillations in a hoisting system due to boundary excitations,” Nonlinear Dynamics, vol. 111, pp. 5079–5106, 2023.
- B. Besselink, T. Vromen, N. Kremers, and N. Van De Wouw, “Analysis and control of stick-slip oscillations in drilling systems,” IEEE Trans. on Control Systems Technology, vol. 24, no. 5, pp. 1582–1593, 2015.
- M. Ruderman, “Robust output feedback control of non-collocated low-damped oscillating load,” in IEEE 29th Mediterranean Conference on Control and Automation (MED), 2021, pp. 639–644.
- M. Ruderman, “Time-delay based output feedback control of fourth-order oscillatory systems,” Mechatronics, vol. 94, p. 103015, 2023.
- C.-Y. Kao and B. Lincoln, “Simple stability criteria for systems with time-varying delays,” Automatica, vol. 40, no. 8, pp. 1429–1434, 2004.
- E. Fridman and U. Shaked, “Input–output approach to stability and l2-gain analysis of systems with time-varying delays,” Systems & Control Letters, vol. 55, no. 12, pp. 1041–1053, 2006.
- E. Fridman, “Tutorial on lyapunov-based methods for time-delay systems,” Eur. Journal of Control, vol. 20, no. 6, pp. 271–283, 2014.
- M. Ruderman, “One-parameter robust global frequency estimator for slowly varying amplitude and noisy oscillations,” Mechanical Systems and Signal Processing, vol. 170, p. 108756, 2022.
- B. Voß, M. Ruderman, C. Weise, and J. Reger, “Comparison of fractional-order and integer-order H-infinity control of a non-collocated two-mass oscillator,” IFAC-PapersOnLine, vol. 55, pp. 145–150, 2022.
- D. Luenberger, “An introduction to observers,” IEEE Transactions on Automatic Control, vol. 16, no. 6, pp. 596–602, 1971.