In this paper, a new composite controller (feedforward + feedback) is proposed for the trajectory tracking control of a piezo-driven bridge displacement amplifier. A hysteresis model considering dynamic effects is established based on the modified Bouc–Wen (MBW) model, which can describe the asymmetry and frequency-dependence behaviors. The effectiveness of the modified model is verified by the experimental comparison. A feedforward controller is designed to compensate for hysteresis nonlinearity based on the inverse multiplicative structure of the modified model. A feedback controller with the Kalman observer is designed based on a modified model predictive control (MMPC). The proportional term and integral term of feedback error are introduced into the MPC control law to improve the response speed and reduce the steady-state error. The proposed MBW + MMPC is compared with MBW + proportional–integral–derivative (PID), and MBW + MPC. The experimental tracking results of continuously differentiable signals and non-differentiable signals verify MBW + MMPC feasibility and show that it can improve tracking performance.
Al JanaidehMRakotondrabeMAljanaidehO (2016) Further results on hysteresis compensation of smart micropositioning systems with the inverse Prandtl–Ishlinskii compensator. IEEE Transactions on Control Systems Technology24(2): 428–439.
2.
AridoganUShanYLeangKK (2009) Design and analysis of discrete-time repetitive control for scanning probe microscopes. Journal of Dynamic Systems, Measurement, and Control: Transactions of the ASME131(6): 061103.
3.
BashashSJaliliN (2007) Robust multiple frequency trajectory tracking control of piezoelectrically driven micro/nanopositioning systems. IEEE Transactions on Control Systems Technology15(5): 867–878.
4.
BashashSJaliliN (2008) A polynomial-based linear mapping strategy for feedforward compensation of hysteresis in piezoelectric actuators. Journal of Dynamic Systems, Measurement, and Control: Transactions of the ASME130(3): 031008.
5.
CaoYChengLChenXB, et al. (2013) An inversion-based model predictive control with an integral-of-error state variable for piezoelectric actuators. IEEE/ASME Transactions on Mechatronics18(3): 895–904.
6.
ChenYQiuJPalaciosJ, et al. (2012) Tracking control of piezoelectric stack actuator using modified Prandtl–Ishlinskii model. Journal of Intelligent Material Systems and Structures24(6): 753–760.
7.
FengZLingJMingM, et al. (2017) High-bandwidth and flexible tracking control for precision motion with application to a piezo nanopositioner. Review of Scientific Instruments88(8): 085107.
8.
GanJZhangX (2018) An enhanced Bouc-Wen model for characterizing rate-dependent hysteresis of piezoelectric actuators. Review of Scientific Instruments89(11): 115002.
9.
GuG-YZhuL-MSuC-Y, et al. (2016) Modeling and control of piezo-actuated nanopositioning stages: A survey. IEEE Transactions on Automation Science and Engineering13(1): 313–332.
10.
HaJLKungYSFungRF, et al. (2006) A comparison of fitness functions for the identification of a piezoelectric hysteretic actuator based on the real-coded genetic algorithm. Sensors and Actuators A: Physical132(2): 643–650.
11.
HassaniVTjahjowidodoTDoTN (2014) A survey on hysteresis modeling, identification and control. Mechanical Systems and Signal Processing49(1–2): 209–233.
12.
IkhouaneFHurtadoJERodellarJ (2007) Variation of the hysteresis loop with the Bouc–Wen model parameters. Nonlinear Dynamics48(4): 361–380.
13.
IsmailMIkhouaneFRodellarJ (2009) The hysteresis Bouc-Wen model, a survey. Archives of Computational Methods in Engineering16(2): 161–188.
14.
JilesDCAthertonDL (1986) Theory of ferromagnetic hysteresis. Journal of Magnetism and Magnetic Materials61(1–2): 48–60.
15.
KangSWuHLiY, et al. (2021) A fractional-order normalized Bouc–Wen model for piezoelectric hysteresis nonlinearity. IEEE/ASME Transactions on Mechatronics27: 126–136.
16.
KangSWuHYangX, et al. (2022) Discrete-time predictive sliding mode control for a constrained parallel micropositioning piezostage. IEEE Transactions on Systems, Man, and Cybernetics: Systems52(5): 3025–3036.
17.
LiCXLiLLGuGY, et al. (2016) Modeling of rate-dependent hysteresis in piezoelectric actuators using a Hammerstein-like structure with a modified Bouc-Wen model. In: Proceedings of the international conference on intelligent robotics and applications, Tokyo, Japan, 22–24 August, pp. 672–684. Cham: Springer.
18.
LinCJYangSR (2006) Precise positioning of piezo-actuated stages using hysteresis-observer based control. Mechatronics16(7): 417–426.
19.
LinhNMMinhMTVChenX (2015) Precise tracking control for piezo-actuated stage using inverse compensation and model predictive control. In: Proceedings of the 2015 international conference on advanced mechatronic systems (ICAMechS), Beijing, China, 22–24 August, pp. 467–472. New York: IEEE.
20.
LiuWChengLHouZG, et al. (2015) An inversion-free predictive controller for piezoelectric actuators based on a dynamic linearized neural network model. IEEE/ASME Transactions on Mechatronics21(1): 214–226.
21.
LiuYShanJGabbertU, et al. (2013) Hysteresis and creep modeling and compensation for a piezoelectric actuator using a fractional-order Maxwell resistive capacitor approach. Smart Materials and Structures22(11): 115020.
22.
QiaoZGanZWangC (2014) Sliding mode control using linear extended state observer (LESO) and hysteresis compensator based on Bouc-Wen model in sinusoidal position control of a piezoelectric actuator. In: Proceedings of the 33rd Chinese control conference, Nanjing, China, 28–30 July, pp. 3840–3845. New York: IEEE.
23.
RakotondrabeM (2011) Bouc–Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators. IEEE Transactions on Automation Science and Engineering8(2): 428–431.
24.
RanaMSPotaHRPetersenIR (2015) Nonlinearity effects reduction of an AFM piezoelectric tube scanner using MIMO MPC. IEEE/ASME Transactions on Mechatronics20(3): 1458–1469.
25.
SchitterGThurnerPJHansmaPK (2008) Design and input-shaping control of a novel scanner for high-speed atomic force microscopy. Mechatronics18(5–6): 282–288.
26.
TangHLiY (2015) Feedforward nonlinear PID control of a novel micromanipulator using Preisach hysteresis compensator. Robotics and Computer: Integrated Manufacturing34: 124–132.
27.
TangWQCaiYL (2013) High-order sliding mode control design based on adaptive terminal sliding mode. International Journal of Robust and Nonlinear Control23(2): 149–166.
28.
WangGChenGBaiF (2015) Modeling and identification of asymmetric Bouc–Wen hysteresis for piezoelectric actuator via a novel differential evolution algorithm. Sensors and Actuators A: Physical235: 105–118.
29.
WangL (2009) Model Predictive Control System Design and Implementation Using MATLAB. London: Springer Science+Business Media.
30.
XuQ (2017) Continuous integral terminal third-order sliding mode motion control for piezoelectric nanopositioning system. IEEE/ASME Transactions on Mechatronics22(4): 1828–1838.
31.
YangXWuHLiY, et al. (2020) Dynamics and isotropic control of parallel mechanisms for vibration isolation. IEEE/ASME Transactions on Mechatronics25(4): 2027–2034.
32.
YuSXieMWuH, et al. (2022) Composite Proportional-Integral sliding mode control with feedforward control for cell puncture mechanism with piezoelectric actuation. ISA Transactions124: 427–435.
33.
ZareinejadMRezaeiSMAbdullahA, et al. (2009) Development of a piezo-actuated micro-teleoperation system for cell manipulation. International Journal of Medical Robotics and Computer Assisted Surgery5(1): 66–76.
34.
ZhuWRuiXT (2016) Hysteresis modeling and displacement control of piezoelectric actuators with the frequency-dependent behavior using a generalized Bouc–Wen model. Precision Engineering43: 299–307.
35.
ZhuWWangDH (2012) Non-symmetrical Bouc–Wen model for piezoelectric ceramic actuators. Sensors and Actuators A: Physical181: 51–60.
