The aim of this paper is to investigate the control problem for a two-link rigid–flexible manipulator with input quantization. Abundant studies of the quantized control problem are based on the lumped parameter system, which is expressed using ordinary differential equations. In this paper, the dynamic model for a two-link rigid–flexible manipulator is represented using partial differential equations. The controller design and analysis with input quantization are based on the partial differential equation model. By means of an auxiliary system, tracking errors and boundary vibrations can be eliminated. Simulations are given to verify the effectiveness of the proposed controller with quantized input.
CaoFLiuJ (2017) An adaptive iterative learning algorithm for boundary control of a coupled ODE–PDE two-link rigid–flexible manipulator. Journal of the Franklin Institute354(1): 277–297.
2.
CaoFLiuJ (2018a) Adaptive actuator fault compensation control for a rigid-flexible manipulator with ODEs-PDEs model. International Journal of Systems Science49(8): 1748–1759.
3.
CaoFLiuJ (2018b) Boundary control for a constrained two-link rigid-flexible manipulator with prescribed performance. International Journal of Control91(5): 1091–1103.
4.
FuMXieL (2005) The sector bound approach to quantized feedback control. IEEE Transactions on Automatic Control50(11): 1698–1711.
5.
GaoSLiuJ (2018) Adaptive fault-tolerant vibration control of a wind turbine blade with actuator stuck. International Journal of Control. Epub ahead of print 16 Oct 2017. DOI: 10.1080/00207179.2018.1484572.
6.
HeWZhangS (2017) Control design for nonlinear flexible wings of a robotic aircraft. IEEE Transactions on Control Systems Technology25(1): 351–357.
7.
HeWHeXZouM, et al. (2019) PDE model based boundary control design for a flexible robotic manipulator with input backlash. IEEE Transactions on Control Systems Technology27(2): 790–797.
8.
HeWMengTHeX, et al. (2018a) Iterative learning control for a flapping wing micro aerial vehicle under distributed disturbances. IEEE Transactions on Cybernetics49(4): 1524–1535.
9.
HeWMengTHeX, et al. (2018b) Unified iterative learning control for flexible structures with input constraints. Automatica86: 326–336.
10.
HeWMengTHuangD, et al. (2018c) Adaptive boundary iterative learning control for an Euler–Bernoulli beam system with input constraint. IEEE Transactions on Neural Networks and Learning Systems29(5): 1539–1549.
11.
HeidariHKorayemMHHaghpanahiM, et al. (2013) Optimal trajectory planning for flexible link manipulators with large deflection using a new displacements approach. Journal of Intelligent and Robotic Systems72(3–4): 287–300.
12.
HeidariHKorayemMHHaghpanahiM (2017) Optimal trajectory planning for increased stability of mobile flexible manipulators undergoing large deflection. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture231(1): 85–95.
13.
JiangTLiuJHeW (2015) A robust observer design for a flexible manipulator based on a PDE model. Journal of Vibration & Control23(6): 871–882.
14.
LiGLinY (2017) Adaptive output feedback control for a class of nonlinear systems with quantised input and output. International Journal of Control90(2): 239–248.
15.
LiberzonD (2003) Hybrid feedback stabilization of systems with quantized signals. Automatica39(9): 1543–1554.
16.
LiuTJiangZHillD (2012) Small-gain based output-feedback controller design for a class of nonlinear systems with actuator dynamic quantization. IEEE Transactions on Automatic Control57(5): 1326–1332.
17.
LiuZLiuJHeW (2017) Modeling and vibration control of a flexible aerial refueling hose with variable lengths and input constraint. Automatica77: 302–310.
18.
LiuZZhaoZAhnCK (2019) Boundary constrained control of flexible string systems subject to disturbances. IEEE Transactions on Circuits and Systems II. Epub ahead of print 25 February 2019. DOI: 10.1109/TCSII.2019.2901283.
19.
LochanKRoyBSubudhiB (2017) Robust tip trajectory synchronisation between assumed modes modelled two-link flexible manipulators using second-order PID terminal SMC. Robotics and Autonomous Systems97: 108–124.
20.
Mahamood R and Pedro JO (2011) Hybrid PD/PID controller design for two-link flexible manipulators. In: 8th Asian control conference, Kaohsiung, Taiwan, 15–18 May 2011, pp. 1358–1363. Piscataway, NJ: IEEE.
21.
MengTRenZWenG (2018) Boundary adaptive robust control of a flexible riser system with input nonlinearities. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 49: 1971–1980.
22.
TianEYueDZhaoX (2007) Quantised control design for networked control systems. IET Control Theory & Applications1(6): 1693–1699. .
23.
XiaYYanJShiP, et al. (2013) Stability analysis of discrete-time systems with quantized feedback and measurements. IEEE Transactions on Industrial Informatics9(1): 313–324.
24.
Xin X (2011) Swing-up control for a two-link underactuated robot with a flexible elbow joint: New results beyond the passive elbow joint. In: 50th IEEE conference on decision and control and European control conference, Orlando, FL, USA, 12–15 December 2011, pp. 2481–2486. Piscataway, NJ: IEEE.
25.
XingXLiuJ (2017) LMI-based boundary and distributed control design for flexible string subject to disturbance. International Journal of Control92(8): 1959–1969.
26.
YunSChoiYParkP (2010) Dynamic output-feedback guaranteed cost control for linear systems with uniform input quantization. Nonlinear Dynamics62(1–2): 95–104.
27.
Zhang L and Liu J (2012) Optimal trajectory control of flexible two-link manipulator based on PDE model. IEEE 51st annual conference on decision and control (CDC), Maui, HI, USA, 10–13 December 2012. Piscataway, NJ: IEEE.
28.
ZhaoZHeXRenZ, et al. (2018) Output feedback stabilization for an axially moving system. IEEE Transactions on Systems, Man, and Cybernetics: Systems89(4): 2431–2440.
29.
ZhaoZLinSZhuD, et al. (2019) Vibration control of a riser-vessel system subject to input backlash and extraneous disturbances. IEEE Transactions on Circuits and Systems II. Epub ahead of print 30 April 2019. DOI: 10.1109/TCSII.2019.2914061.
30.
ZhouJWenCYangG (2014) Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal. IEEE Transactions on Automatic Control59(2): 460–464.
