This paper proposes a robust observer for a flexible single-link manipulator based on the partial differential equation (PDE) dynamic model. Unlike observers for the PDE model introduced by previous researchers, this observer is designed to estimate the distributed spatiotemporally varying states with unknown boundary disturbance and spatially distributed disturbance. The asymptotic stability of the proposed observer is proved by theoretical analysis and demonstrated by simulation results.
Atashzar SF, Talebi HA, Towhidkhah F, et al. (2010) Tracking control of flexible-link manipulators based on environmental force disturbance observer, 49th IEEE Conference on Decision and Control, Atlanta, GA, IEEE, 15–17 December, pp.3584–3589.
2.
ChenCS (2011) Supervisory adaptive tracking control of robot manipulators using interval type-2 TSK fuzzy logic system. IET Control Theory Applications5(15): 1796–1807.
3.
HashemiSMAbbasHSWernerH (2012) Low-complexity linear parameter-varying modeling and control of a robotic manipulator. Control Engineering Practice20(3): 248–257.
4.
HeWGeSSChooYS (2011) Robust adaptive boundary control of a flexible marine riser with vessel dynamics. Automatica47(4): 722–732.
5.
HeWHowBVEGeSS (2014) Dynamics and Control of Mechanical Systems in Offshore Engineering, London, UK: Springer Verlag.
6.
IoannouPASunJ (1996) Robust Adaptive Control, Upper Saddle River, NJ: Prentice-Hall, pp. 75–76.
7.
LeeHHPrevostJ (2005) A coupled sliding-surface approach for the trajectory control of a flexible- link robot based on a distributed dynamic model. International Journal of Control78(9): 629–637.
8.
MeirovitchL (2001) Fundamentals of Vibrations, New York, NY: McGraw-Hill.
9.
MonjeCARamosFFeliuV (2007) Tip position control of a lightweight flexible manipulator using a fractional order controller. IET Control Theory Applications1(5): 1451–1460.
10.
MustafaDOmerM (2012) Boundary control of a rotating shear beam with observer feedback. Journal of Vibration and Control18(4): 2257–2265.
11.
NabilGCNassimK (2014) Integrated controller–observer system for marine surface vessels. Journal of Vibration and Control20(3): 381–394.
12.
Nguyen TD and Egeland O (2005a) Observer design for a flexible robot arm with a tip Load, Proceedings of American Control Conference, Portland, OR, IEEE, 8–10 June, pp.1389–1394.
13.
Nguyen TD and Egeland O (2005b) 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.
14.
RahnCD (2001) Mechatronic Control of Distributed Noise and Vibration, New York, NY: Springer.
15.
VossoughiGRKarimzadehA (2006) Impedance control of a two degree-of-freedom planar flexible link manipulator using singular perturbation theory. Robotica24(2): 221–228.
16.
WaiRJHuangYCYangZW (2010) Adaptive fuzzy-neural network velocity sensorless control for robot manipulator position tracking. IET Control Theory Applications4(6): 1079–1093.
17.
YooSJParkJBChoiYH (2008) Output feedback dynamic surface control of flexible-joint robots. International Journal of Control, Automation and Systems6(2): 23–233.
18.
Zhang L and Liu JK (2012a) Optimal trajectory control of flexible two-link manipulator based on PDE model, 51st IEEE Conference on Decision and Control, Maui, Hawaii, IEEE, 10–13 December, pp.4406–4411.
19.
ZhangLLiuJK (2012b) Observer-based partial differential equation boundary control for a flexible two-link manipulator in task space. IET Control Theory & Application6(13): 2120–2133.
20.
Zhang L and Liu J (2012c) Nonlinear PDE observer design for a flexible two-link manipulator, American Control Conference, Fairmont Queen Elizabeth, Montréal, Canada, IEEE, 27–29 June, pp.5336–5341.
21.
ZhangLLiuJK (2013) Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model. IET Control Theory & Applications7(1): 43–51.
22.
ZhangHShiYWangJ (2013) Observer-based tracking controller design for networked predictive control systems with uncertain Markov delays. International Journal of Control86(10): 1824–1836.
23.
ZhouYSohYCShenJX (2014) High-gain observer with higher order sliding mode for state and unknown disturbance estimations. International Journal of Robust and Nonlinear Control24(15): 2136–2151.