This paper presents the design and testing of a novel continuous third-order integral terminal sliding mode control (3-ITSMC) strategy dedicated to motion tracking control of a piezoelectric-driven nanopositioning system. In comparison with the available sliding mode controllers, the significant improvement of the proposed controller lies in the fact that it completely eliminates the chattering effect, achieves a finite-time convergence, and produces a higher sliding mode precision. The model uncertainty involving the hysteresis effect is estimated by the perturbation estimation technique. Higher order derivatives of the position are generated by using a robust exact differentiator. Based on an integral terminal type of sliding surface, a third-order sliding mode precision is obtained by resorting to the third-order supertwisting algorithm. The convergence and stability have been proved in theory. The performance improvement of the developed controller versus the conventional second-order and third-order sliding mode controllers is validated by carrying out both simulation and experimental studies. Results demonstrate that the proposed 3-ITSMC controller provides quicker transient response speed and smaller steady-state error for the piezoelectric nanopositioning system along with a better robustness against model uncertainty and external disturbance.

Continuous Integral Terminal Third-Order Sliding Mode Motion Control for Piezoelectric Nanopositioning System

This paper presents the design, implementation and control of a new piezoelectrically actuated compliant micromanipulator dedicated to multiscale, precision and reliable operations. To begin with, the manipulator is devised to obtain multi degrees of freedom and large workspace ranges. Two-stage amplification mechanisms (consists of the leverage and the rocker mechanisms) and composite parallelogram mechanisms are combined to construct the lower microstage. Meanwhile, the structure design of the upper dual-driven microgripper is based on the bridge-type mechanism and the unilateral parallelogram mechanism. Through finite-element analysis, the structural parameters of the micromanipulator are optimized and the structural interaction performances are examined. Moreover, a cooperative control strategy is proposed to achieve the synchronous control of the motion trajectory, the gripper position and the contact force. Precision motion control in terms of the hysteresis phenomenon and system disturbances is ensured by using an adaptive sliding mode control (SMC). In particular, an improved nonsymmetrical Bouc–Wen model and a fuzzy regulator are proposed in the SMC. Several experimental investigations are conducted to validate the effectiveness of the developed micromanipulator by performing transferring operations of a micro-object. Experimental results demonstrate that the micromanipulator presents good characteristics, and precision and robust operation can be acquired using the cooperative controller.

Design and control of a multi-DOF micromanipulator dedicated to multiscale micromanipulation

Nanopositioning systems are very popular and playing an increasingly vital role in micro and nano-scale positioning industry due to their unique ability to achieve high-precision and high-speed operation. However, hysteresis, commonly existing in piezoelectric actuators, degrades the precision seriously. Uncertain dynamics and sensor noises also greatly affect the accuracy. To address those challenges, a variable bandwidth active disturbance rejection control (VBADRC) is proposed and realized on a nanopositioning stage. All undesired issues are estimated by a time-varying extended state observer (TESO), and cancelled out by a variable bandwidth controller. Convergence of the TESO, advantages of a TESO over a linear extended state observer (LESO), and the closed-loop stability of the VBADRC are proven theoretically. Improvements of the VBADRC versus the linear active disturbance rejection control (LADRC) are validated by simulations and experiments. Both numerical and experimental results demonstrate that the VBADRC is not only able to provide the same disturbance estimation ability as the LADRC, but also more powerful in noise attenuation and reference tracking.

/pdf/on-the-disturbance-rejection-of-a-piezoelectric-driven-2x0omhyyuc.pdf

On the Disturbance Rejection of a Piezoelectric Driven Nanopositioning System

Accurate modeling and identification of piezoelectric actuators are increasingly demanded for intelligent micro–nano manufacturing to improve the accuracy of positioning and scanning. In this article, one coupled fractional-order creep and hysteresis model is established using only five parameters. Then, the properties of the coupled fractional-order creep and hysteresis are investigated under sinusoidal and step inputs. The identification approaches are thus proposed by leveraging the special characteristics of the proposed fractional-order model. Simulation and experimental studies are carried out to validate the effectiveness of the proposed fractional-order creep and Bouc–Wen hysteresis model. Additionally, model-based inversion feedforward is implemented to validate the parameter identification. The experimental results demonstrate the effectiveness of the modeling and parameter identification approaches.

Fractional Order Based Modeling and Identification of Coupled Creep and Hysteresis Effects in Piezoelectric Actuators

In this article, a closed-loop control framework for dual-stage nanopositioning systems is presented that allows the user to allocate control efforts to the individual actuators based on their range capabilities. Recent work by the authors has focused on range-based control of dual-stage actuators implemented as a prefilter, which assumes that each individual actuator has sensor feedback enabling them to be controlled separately. This article seeks to address the problem of range-based control of dual-stage systems when sensor measurements are only available from the total output of the system, a commonly encountered design. This is a significant departure from previous work since the range-based filter is included in the dual-stage system feedback loop and stability becomes a concern. In this article, the controller is presented, stability conditions are determined, and imaging experiments are performed on an atomic force microscope. Tracking results show that the root-mean-square tracking error for various triangular reference trajectories is improved with the presented range-based control structure by up to 50% compared to frequency-based methods.

Closed-Loop Range-Based Control of Dual-Stage Nanopositioning Systems

A dual-stage piezoelectric stack is presented. It consists of three parts, which are used for high-speed actuation, vibration isolation, and long-range actuation. This dual-stage piezoelectric stack is a modified piezoelectric stack and appears as a single stack. The first resonance frequency of the original piezoelectric stack is 40 kHz. The 1-dB cutoff frequency of the original piezoelectric stack is approximately 12 kHz, and the travel range is 16 μm. The 1-dB cutoff frequency of the dual-stage piezoelectric stack is approximately 85 kHz, and the travel range varies approximately from 1.2 to 12.8 μm. The main contribution of this paper is the use of a vibration isolation actuator to prevent coupling between high-speed and long-range actuators.

Yong Liu

Papers

A Dual-Stage Piezoelectric Stack for High-Speed and Long-Range Actuation