Positioning Error Analysis and Control of a Piezo-Driven 6-DOF Micro-Positioner

Abstract

This paper presents a positioning error model and a control compensation scheme for a six-degree-of-freedom (6-DOF) micro-positioner based on a compliant mechanism and piezoelectric actuators (PZT). The positioning error model is established by means of the kinematic model of the compliant mechanism and complete differential coefficient theory, which includes the relationships between three typical errors (hysteresis, machining and measuring errors) and the total positioning error. The quantitative analysis of three errors is demonstrated through several experimental studies. Afterwards, an inverse Presiach model-based feedforward compensation of the hysteresis nonlinearity is employed by the control scheme, combined with a proportional-integral-derivative (PID) feedback controller for the compensation of machining and measuring errors. Moreover, a back propagation neural network PID (BP-PID) controller and a cerebellar model articulation controller neural network PID (CMAC-PID) controller are also adopted and compared to obtain optimal control. Taking the translational motion along the X axis as an example, the positioning errors are sharply reduced by the inverse hysteresis model with the maximum error of 12.76% and a root-mean-square error of 4.09%. In combination with the CMAC-PID controller, the errors are decreased to 0.63% and 0.23%, respectively. Hence, simulated and experimental results reveal that the proposed approach can improve the positioning accuracy of 6-DOF for the micro-positioner.

A Compound Control Based on the Piezo-Actuated Stage with Bouc–Wen Model

“…The identified hysteresis will be employed to design the feedforward controller to compensate hysteresis of the piezo-actuated stage. A compound control strategy based an inverse hysteresis model and a proportional-integral-derivative (PID) feedback controller is employed for the compensation of positioning errors [9]. A non-linear feedforward compensation controller based on the Bouc-Wen model describing bias-rate-dependent hysteresis is combined with the displacement PID control to improve the displacement accuracy of the actuator [10].…”

“…the parameters of Equation(9). The identification results are listed as: k1c = 1.86, k3c = −0.75, α c = 1.14, β c = 2.49, γ c = −2.08.A set of asymmetric sinusoidal voltage signals, the piezo-actuated stage.…”

Single-Neuron Adaptive Hysteresis Compensation of Piezoelectric Actuator Based on Hebb Learning Rules

“…The whole control progress proceeds as follows. After getting the desired trajectory and actual trajectory, the state variable x i (t) is calculated using Equation (4). Three state variables correspond to three control outputs produced by the neuron, which are the proportional feedback u 1 (t), first-order differential feedback u 2 (t), and second-order differential feedback u 3 (t), respectively.…”

“…As a sub-nanometer-resolution actuation device, piezoelectric actuators (PEAs) have been widely applied in various applications requiring nanometer-accurate motion [1][2][3][4]. However, the inherent hysteresis nonlinearity of the PEA greatly degrades its positioning accuracy, thus affecting its applicability and performance in precise operation tasks.…”

“…An inversion-free predictive controller was proposed based on a dynamic linearized multilayer feedforward neural network model [27]. A cerebellar model articulation controller neural network PID controller was also proposed [4]. A radial basis function (RBF) network was also used to model and compensate for the PEA's hysteresis [28].…”