Closed-Loop Input Shaping with Quantitative Feedback Controller Applied to Slewed Two-Staged Pendulum



In this paper, 2 practical techniques for control of dynamic systems are integrated. An input shaper is placed outside of a closed-loop system to reduce vibrations induced by the reference input. A quantitative feedback controller handles the vibrations induced by disturbances and noise while ensuring good tracking and stability. They are practical because designing an input shaper only requires knowledge of natural frequencies and damping ratios of the system whereas a quantitative feedback controller lets the designer quantitatively evaluate tradeoffs among tracking, disturbances and noise rejections, and stability among others. Various frequency-domain specifications are combined for the controller to meet requirements for all plants in an uncertain plant set. The proposed control system is applied to a 2-staged pendulum to suppress residual vibration from point-to-point movement.


Closed loop, input shaping, quantitative feedback, vibration reduction, two-staged pendulum

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NC Singer and WC Seering. Preshaping command inputs to reduce system vibration. J. Dyn. Syst. Meas. Contr. 1990; 112, 76-82.

OJM Smith. Posicast control of damped oscillatory systems. Proc. IRE 1957; 45, 1249-55.

GH Tallman and OJM Smith. Analog study of dead-beat posicast control. IRE T. Automat. Contr. 1958; 4, 14-21.

W Singhose. Command shaping for flexible systems: A review of the first 50 years. Int. J. Precis. Eng. Manuf. 2009; 10, 153-68.

JR Huey and W Singhose. Trends in the stability properties of CLSS controllers: A root-locus analysis. IEEE Trans. Contr. Syst. Tech. 2010; 18, 1044-56.

J Stergiopoulos and A Tzes. Hinf closed-loop control for uncertain discrete input-shaped systems. J. Dyn. Syst. Meas. Contr. 2010; 132, 1-8.

V Kapila, A Tzes and Q Yan. Closed-loop input shaping for flexible structures using time-delay control. J. Dyn. Syst. Meas. Contr. 2000; 122, 454-60.

U Staehlin and T Singh. Design of closed-loop input shaping controllers. In: Proceeding of the American Control Conference, Denver, Colorado, 2003, p. 5167-72.

K Zuo and D Wang. Closed loop shaped-input control of a class of manipulators with a single flexible link. In: Proceeding of the IEEE International Conference on Robotics and Automation, Nice, France, 1992, p. 782-7.

A Zolfagharian, A Noshadi, MZM Zain and ARA Bakar. Practical multi-objective controller for preventing noise and vibration in an automobile wiper system. Swarm Evol. Comput. 2013; 8, 54-68.

FM Aldebrez, MS Alam and MO Tokhi. Input-shaping with GA-tuned PID for target tracking and vibration reduction. In: Proceeding of the Mediterranean Conference on Control and Automation, Limassol, Cyprus, 2005, p. 485-490.

MC Pai. Robust input shaping control for multi-mode flexible structures using neuro-sliding mode output feedback control. J. Frankl. Inst. 2012; 349, 1283-303.

Q Hu, XZ Gao and G Ma. Reference model variable structure output feedback for attitude maneuvers control of flexible spacecrafts. Intell. Autom. Soft Comput. 2009; 15, 53-62.

JR Huey and W Singhose. Design of proportional-derivative feedback and input shaping for control of inertia plants. IET Control Theory A 2012; 6, 357-64.

M Kenison and W Singhose. Concurrent design of input shaping and proportional plus derivative feedback control. J. Dyn. Syst. Meas. Contr. 2002; 124, 398-405.

AG Dharne and S Jayasuriya. Increasing the robustness of the input-shaping method using adaptive control. In: Proceeding of the American Control Conference, Denver, Colorado, 2003, p. 1578-83.

JR Huey, KL Sorensen and WE Singhose. Useful applications of closed-loop signal shaping controllers. Contr. Eng. Pract. 2008; 16, 836-46.

S Skogestad and I Postlethwaite. Multivariable Feedback Control. John Wiley and Sons, New York, 2005.

O Yaniv. Quantitative Feedback Design of Linear and Nonlinear Control Systems. Springer, New York, 1999.


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Last updated: 17 May 2019