Control of nano-manipulating systems: key technology supporting ultrahigh precision motions

Nano-manipulating systems are playing a more and more important role in ultrahigh precision servo tasks, with successful applications in various emerging areas, such as atomic force microscope (AFM), nano-assembly and manufacturing, and semiconductor instruments.

Note that piezoelectric actuators and flexure-based mechanisms have been recognized as the important components of a nano-manipulating system due to their advantages of high displacement resolution, high bandwidth, compact size, and friction-free motion. However, the control of such nano-manipulating systems is challenging due to the ultrahigh precision requirements and model complications such as the hysteresis nonlinearities of piezoelectric actuators, high-order dynamics of the flexure-based mechanisms, and the existence of model uncertainties.

To address the above problems, existing methods follow the methodology of hysteresis compensation combined with closed-loop control strategies based on the modeling of both hysteresis nonlinearities and dynamic characteristics of the nano-manipulating system. Note that most of the reported works were concerned with the stability and robustness problems of the closed-loop system. However, the results on quantitative analysis of the motion errors caused by the model uncertainties, high-order unmodeled dynamics, and the compensation error are very rare, which limits their applications to tracking/scanning based servo tasks.


Fig 1. Experimental setup of a nano-manipulating system

To improve both the motion accuracy and the transient performance, Professor Peng Yan’s team from the School of Automation Science and Electrical Engineering proposed a sliding mode disturbance observer-based adaptive integral backstepping control method with hysteresis compensation for the nano-manipulating system (as shown in Fig 1), where an improved rate-dependent Prandtl-Ishlinskii (PI) model was constructed. The proposed method can improve the robustness of the nano-manipulating system, and better deal with the model uncertainties, various disturbances, and compensation errors.


Fig 2. Comparisons of the hysteresis loops between experimental results and the model outputs

By establishing an accurate mathematical model, including the hysteresis of the piezoelectric actuators and the dynamics of the electromechanical characteristics of the system, we derive the feedback controller combined with the forward compensator to achieve robust tracking capability and optimized transient behavior so that the overall system can deliver nano-precision motions when tracking reference trajectories.


Fig 3. Circular contour tracking and tracking error


Fig 4. Nano-manipulator based high precision SPM scanning

 The proposed control framework is applied to a nano-manipulating test platform (see Fig 1), where real time embedded algorithms are developed based on the control methodology. The comparisons of the hysteresis loops between the experimental result and the rate-dependent PI model simulation result in both X-axis and Y-axis are depicted in Fig 2, where good modeling accuracy is demonstrated. Meanwhile, the circular contour tracking is also performed when X-axis and Y-axis sinusoidal tracking experiments are simultaneously actuated. The circular contour tracking results are given in Fig 3, where excellent tracking performance with two-dimensional contouring error less than 30nm is validated in the experiments.

It is worth pointing out that the developed high precision control technique has better tracking capability and transient responses, compared to existing results on nano-positioning methods. Therefore, the proposed technique can be considered as a better option supporting high precision scanning of AFM or SPM (scanning probe microscope) where trajectory tracking/scanning performance is critical for such systems, which can be illustrated in Fig 4.



Peng Yan, professor, school of automation science and electrical engineering, Beihang University, E-mail:



[1]Y. Zhang and P. Yan*, Sliding mode disturbance observer-based adaptive integral backstepping control of a piezoelectric nano-manipulator, Smart Materials and Structures, vol.25, no.12, pp. 125011-1-125011-12, 2016.

[2]Y. Zhang, P. Yan*, and Z. Zhang, Robust adaptive backstepping control for piezoelectric nano-manipulating systems, Mechanical Systems and Signal Processing, vol.83, pp.130-148, 2017.