Settling Time Optimization of a Critically Damped System with Input Shaping for Vibration Suppression Control

Authors

  • M. D. Duong School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Vietnam
  • Q. T. Dao School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Vietnam
  • T. H. Do School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Vietnam
Volume: 12 | Issue: 5 | Pages: 9388-9394 | October 2022 | https://doi.org/10.48084/etasr.5242

Abstract

The input shaping technique is widely used as feedforward control for vibration suppression of flexible dynamic systems. The main disadvantage of the input shaping technique is the increasing system time response since the input shaper contains time delay parts. However, with the same reference input, the actuator effort in the case of using an input shaper is smaller than the one in the case without an input shaper. Thus, it is possible to decrease the system response time by designing the feedback controller to maximize the actuator effort. This paper proposes a design approach to design the Proportional-Derivative (PD) controller for position control of the actuator so that the settling time of the flexible system with input shaper is minimized. The actuator system with a PD controller is equivalent to a critically damped system, and the condition for the controller gains is established. In addition, the settling time and actuator effort with shaped step input are calculated. The controller gains can be determined by solving the settling time optimization problem with the actuator effort constraint. The effectiveness of the proposed approach is verified via experiments with an overhead crane model.

Keywords:

flexible system, input shaping, PD controller, settling time optimization, overhead crane

Downloads

Download data is not yet available.

References

I. Esen and M. A. Koç, "Dynamic response of a 120 mm smoothbore tank barrel during horizontal and inclined firing positions," Latin American Journal of Solids and Structures, vol. 12, pp. 1462–1486, Aug. 2015. DOI: https://doi.org/10.1590/1679-78251576

I. Esen, "Dynamic response of a functionally graded Timoshenko beam on two-parameter elastic foundations due to a variable velocity moving mass," International Journal of Mechanical Sciences, vol. 153–154, pp. 21–35, Apr. 2019. DOI: https://doi.org/10.1016/j.ijmecsci.2019.01.033

I. Esen, "Dynamic response of functional graded Timoshenko beams in a thermal environment subjected to an accelerating load," European Journal of Mechanics - A/Solids, vol. 78, Nov. 2019, Art. no. 103841. DOI: https://doi.org/10.1016/j.euromechsol.2019.103841

M. Balas, "Feedback control of flexible systems," IEEE Transactions on Automatic Control, vol. 23, no. 4, pp. 673–679, Aug. 1978. DOI: https://doi.org/10.1109/TAC.1978.1101798

D. Antic, Z. Jovanovic, S. Peric, S. Nikolic, M. Milojkovic, and M. Milosevic, "Anti-Swing Fuzzy Controller Applied in a 3D Crane System," Engineering, Technology & Applied Science Research, vol. 2, no. 2, pp. 196–200, Apr. 2012. DOI: https://doi.org/10.48084/etasr.146

C. T. Kiang, A. Spowage, and C. K. Yoong, "Review of Control and Sensor System of Flexible Manipulator," Journal of Intelligent & Robotic Systems, vol. 77, no. 1, pp. 187–213, Jan. 2015. DOI: https://doi.org/10.1007/s10846-014-0071-4

K. G. Aktas and I. Esen, "State-Space Modeling and Active Vibration Control of Smart Flexible Cantilever Beam with the Use of Finite Element Method," Engineering, Technology & Applied Science Research, vol. 10, no. 6, pp. 6549–6556, Dec. 2020. DOI: https://doi.org/10.48084/etasr.3949

L. Cui, H. Wang, and W. Chen, "Trajectory planning of a spatial flexible manipulator for vibration suppression," Robotics and Autonomous Systems, vol. 123, Jan. 2020, Art. no. 103316. DOI: https://doi.org/10.1016/j.robot.2019.103316

D. Lee and C.-W. Ha, "Optimization Process for Polynomial Motion Profiles to Achieve Fast Movement With Low Vibration," IEEE Transactions on Control Systems Technology, vol. 28, no. 5, pp. 1892–1901, Sep. 2020. DOI: https://doi.org/10.1109/TCST.2020.2998094

H. Karagülle, L. Malgaca, M. Dirilmiş, M. Akdağ, and Ş. Yavuz, "Vibration control of a two-link flexible manipulator," Journal of Vibration and Control, vol. 23, no. 12, pp. 2023–2034, Jul. 2017. DOI: https://doi.org/10.1177/1077546315607694

H. J. Yoon, S. Y. Chung, H. S. Kang, and M. J. Hwang, "Trapezoidal Motion Profile to Suppress Residual Vibration of Flexible Object Moved by Robot," Electronics, vol. 8, no. 1, Jan. 2019, Art. nol. 30. DOI: https://doi.org/10.3390/electronics8010030

B. Spruogis, A. Jakstas, V. Gican, V. Turla, and V. Moksin, "Further Research on an Anti-Swing Control System for Overhead Cranes," Engineering, Technology & Applied Science Research, vol. 8, no. 1, pp. 2598–2603, Feb. 2018. DOI: https://doi.org/10.48084/etasr.1774

N. C. Singer and W. P. Seering, "Preshaping Command Inputs to Reduce System Vibration," Journal of Dynamic Systems, Measurement, and Control, vol. 112, no. 1, pp. 76–82, Mar. 1990. DOI: https://doi.org/10.1115/1.2894142

W. Singhose, "Command shaping for flexible systems: A review of the first 50 years," International Journal of Precision Engineering and Manufacturing, vol. 10, no. 4, pp. 153–168, Oct. 2009. DOI: https://doi.org/10.1007/s12541-009-0084-2

C.-G. Kang, "Impulse Vectors for Input-Shaping Control: A Mathematical Tool to Design and Analyze Input Shapers," IEEE Control Systems Magazine, vol. 39, no. 4, pp. 40–55, Dec. 2019. DOI: https://doi.org/10.1109/MCS.2019.2913610

M. Kenison and W. Singhose, "Concurrent Design of Input Shaping and Proportional Plus Derivative Feedback Control," Journal of Dynamic Systems, Measurement, and Control, vol. 124, no. 3, pp. 398–405, Jul. 2002. DOI: https://doi.org/10.1115/1.1486009

J. R. Huey, "The Intelligent Combination of Input Shaping and PID Feedback Control," Ph.D. dissertation, Georgia Institute of Technology, Atlanta, GA, USA, 2006.

J. R. Huey and W. Singhose, "Design of proportional–derivative feedback and input shaping for control of inertia plants," IET Control Theory & Applications, vol. 6, no. 3, pp. 357–364, Feb. 2012. DOI: https://doi.org/10.1049/iet-cta.2010.0456

M. Muenchhof and T. Singh, "Concurrent Feed-forward/Feed-back Design for Flexible Structures," in AIAA Guidance, Navigation, and Control Conference and Exhibit, Monterey, CA, USA, Aug. 2002. DOI: https://doi.org/10.2514/6.2002-4941

R. Mar, A. Goyal, V. Nguyen, T. Yang, and W. Singhose, "Combined input shaping and feedback control for double-pendulum systems," Mechanical Systems and Signal Processing, vol. 85, pp. 267–277, Feb. 2017. DOI: https://doi.org/10.1016/j.ymssp.2016.08.012

D. Newman and J. Vaughan, "Concurrent Design of Linear Control with Input Shaping for a Two-Link Flexible Manipulator Arm," IFAC-PapersOnLine, vol. 51, no. 14, pp. 66–71, Jan. 2018. DOI: https://doi.org/10.1016/j.ifacol.2018.07.200

M.-C. Pai, "Closed-loop input shaping control of vibration in flexible structures using discrete-time sliding mode," International Journal of Robust and Nonlinear Control, vol. 21, no. 7, pp. 725–737, 2011. DOI: https://doi.org/10.1002/rnc.1618

M.-C. Pai, "Closed-Loop Input Shaping Control of Vibration in Flexible Structures via Adaptive Sliding Mode Control," Shock and Vibration, vol. 19, no. 2, pp. 221–233, 2012. DOI: https://doi.org/10.1155/2012/803479

J. Oliveira, P. M. Oliveira, T. M. Pinho, and J. B. Cunha, "PID Posicast Control for Uncertain Oscillatory Systems: A Practical Experiment," IFAC-PapersOnLine, vol. 51, no. 4, pp. 416–421, Jan. 2018. DOI: https://doi.org/10.1016/j.ifacol.2018.06.130

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, "On the LambertW function," Advances in Computational Mathematics, vol. 5, no. 1, pp. 329–359, Dec. 1996. DOI: https://doi.org/10.1007/BF02124750

D. Qian and J. Yi, Hierarchical Sliding Mode Control for Under-actuated Cranes. Berlin, Heidelberg: Springer, 2015. DOI: https://doi.org/10.1007/978-3-662-48417-3

Downloads

How to Cite

[1]
M. D. Duong, Q. T. Dao, and T. H. Do, “Settling Time Optimization of a Critically Damped System with Input Shaping for Vibration Suppression Control”, Eng. Technol. Appl. Sci. Res., vol. 12, no. 5, pp. 9388–9394, Oct. 2022.

Metrics

Abstract Views: 716
PDF Downloads: 443

Metrics Information