In this paper, a boundary controller for a flexible manipulator is proposed based on a partial differential equation (PDE) robust observer. In the previous work we have proposed a PDE robust observer to estimate the infinite dimensional states of the flexible manipulator with unknown boundary disturbance and spatially distributed disturbance. On the basis of the proposed robust state observer, a boundary controller is designed to achieve the stability control, regulate the joint position and suppress elastic vibration in this paper. The stabilities of the proposed observer and the boundary controller are validated by theoretical analysis. Numerical simulations are provided to demonstrate the effectiveness of the closed-loop system.
ArteagaMASicilianoB (2000) On tracking control of flexible robot arms. IEEE Trans. Autom. Control45: 520–527.
2.
Atashzar SF, Talebi HA, Towhidkhah F and Shahbazi M (2010) Tracking Control of Flexible-Link Manipulators Based on Environmental Force Disturbance Observer. IEEE Conf. Decision and Control. Atlanta, GA, USA, IEEE, 15-17 December, pp. 3584-3589.
3.
BecedasJPayoIFeliuV (2010) Generalised proportional integral torque control for single-link flexible manipulators. IET Control Theory & Applications4: 773–783.
4.
DwivedySKEberhardP (2006) Dynamic analysis of flexible manipulators, a literature review. Mechanism and Machine Theory41: 749–777.
5.
GeSSHeWHowBVEet al. (2010) Boundary control of a coupled nonlinear flexible marine riser. IEEE Transactions on Control Systems Technology18: 1080–1091.
6.
GeSSLeeTHGongJQ (1998) Dynamic Modeling of a Smart Materials Robot. American Institute of Aeronautics and Astronautics36: 1466–1478.
7.
HardyGHLittlewoodJEPolyaG (1959) Inequalities, Cambridge: Cambridge University Press.
8.
HeWGeSSZhangS (2011b) Adaptive boundary control of a flexible marine installation system. Automatica47: 2728–2734.
9.
HeWGeSSHowBChooYS (2014) Dynamics and Control of Mechanical Systems in Offshore Engineering, Verlag London: Springer.
10.
HeWGeSSHowBVEet al. (2011a) Robust adaptive boundary control of a flexible marine riser with vessel dynamics. Automatica47: 722–732.
11.
IoannouPASunJ (1996) Robust Adaptive Control, Upper Saddle River, NJ: Prentice-Hall, pp. 75–76.
12.
JiangTLiuJHeW (2015) A robust observer design for a flexible manipulator based on a PDE model. Journal of Vibration and Control. Epub ahead of print. DOI: 10.1177/1077546315587443.
13.
MeirovitchL (2001) Fundamentals of Vibrations, New York: Waveland Press.
14.
MirshekaranMPiltanFEsmaeiliZet al. (2013) Design sliding mode modified fuzzy linear controller with application to flexible robot manipulator. International Journal of Modern Education & Computer Science5: 53–63.
15.
MirzaeeEEghtesadMFazelzadehSA (2010) Maneuver control and active vibration suppression for a two-link flexible arm using a hybrid variable structure/Lyapunov control design. Acta Astronautica67: 1218–1232.
16.
MohammadiATavakoliMMarquezHJHashemzadehF (2013) Nonlinear disturbance observer design for robotic manipulators. Control Engineering Practice21: 253–267.
17.
MonjeCARamosFFeliuVVinagreBM (2007) Tip position control of a lightweight flexible manipulator using a fractional order controller. IET Control Theory & Applications1: 1451–1460.
18.
Nguyen TD and Egeland O (2005a) Output tracking control of a flexible robot arm. Proceedings of the 44th IEEE conference on Decision and Control, and the European Control Conference, Seville, Spain, IEEE, 12-15 December, pp. 5269-5274.
19.
Nguyen TD and Egeland O (2005b) Observer design for a flexible robot arm with a tip load. Proceedings of American Control Conference, Portland, OR, USA, IEEE, 8-10 June, pp. 1389-1394.
20.
RahnCD (2001) Mechatronic Control of Distributed Noise and Vibration, New York: Springer.
21.
VakilMFotouhiRNikiforukPN (2012) A new method for dynamic modeling of flexible-link flexible-joint manipulators. Journal of Vibration and Acoustics134: 014503.
22.
YooSJParkJBChoiYH (2008) Output Feedback Dynamic Surface Control of Flexible-Joint Robots. International Journal of Control Automation and Systems6: 223–233.
23.
ZhangLLiuJ (2012a) Observer-based partial differential equation boundary control for a flexible two-link manipulator in task space. IET Control Theory & Application134: 2120–2133.
24.
Zhang L and Liu, J (2012b) Optimal Trajectory Control of Flexible Two-Link Manipulator Based on PDE Model. 51st IEEE Conference on Decision and Control. Maui, Hawaii, USA, IEEE, 10-13 December, pp. 4406-4411.
25.
ZhangLLiuJ (2013) Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model. IET Control Theory & Applications7: 43–51.
26.
ZhangXXuWNairSSet al. (2005) PDE modeling and control of a flexible two-link manipulator. IEEE Trans. Control Syst. Technol13: 301–312.
27.
Zuyev A and Sawodny O (2006) Observer design for a flexible manipulator model with a payload. Proceedings of the 45th IEEE Conference on Decision & Control, San Diego, CA, USA, IEEE, 13-15 December, pp. 4490-4495.
