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The paper proposes a type of symmetrical flexure hinge displacement amplification mechanism, which is based on the differential lever to effectively improve the displacement output stroke of the PZT and reduce the additional displacement. In addition to describes the working principle of the differential displacement amplification, it establishes the semi-model of the micro-displacement amplification mechanism according to the symmetrical structure. The stiffness, displacement loss, and natural frequency of the amplification mechanism are simulated by finite element analysis (FEA). Simultaneously, build the mathematical model of amplification ratio to obtain the optimal driving frequency when the natural frequency is 930.58 Hz. The maximum output displacement of the designed mechanism is 313.05 µm and the amplification ratio is 6.50. Due to the symmetrical structure, the output additional displacement of the whole amplification mechanism is small.It provides a scientific basis for further improving the positioning accuracy of the micro/nano drive control system.

The control performance of a butterfly-shaped linear ultrasonic motor is not good when the target speed is less than 1 mm/s by traditional methods. To improve low-speed controlling characteristics of linear ultrasonic motor, a closed-loop control strategy by using both the step control and the fuzzy PID control was proposed. The controller was constructed with the function of providing a closed-loop control of the speed by adjusting the driving voltage amplitude in stepping driving mode. The corresponding step controlling parameters were determined by experiments. Comprehensive experiments on the developed control strategy were conducted under different target speeds. There was a maximum of 24.5% speed error at the target speed of 10 μm/s, meanwhile, the coefficient of variation and the response time were 16.3% and 0.11 s, respectively. With the triangular or sinusoidal waves speed tracking curves at amplitude of 1 mm/s, the maximum speed tracking error were 0.1 mm/s and 0.15 mm/s respectively. Thus, a good speed tracking performance was obtained. These results support the functional ability and potential of the proposed method as a low-speed precision control method for linear ultrasonic motors. INDEX TERMS linear ultrasonic motor, step control, fuzzy PID control, low speed NOMENCLATURE Coefficient of variation Maximum speed error of the platform Speed error of the platform Change of speed error of the platform Proportional coefficient of the PID controller Initial value of proportional coefficient Change of proportional coefficient Integral coefficient of the PID controller Initial value of integral coefficient Change of integral coefficient Differential coefficient of the PID controller Initial value of differential coefficient Change of differential coefficient Number of driving waves of the driving signal Set speed of the platform Coefficient of determination Driving period of the driving signal Average speed of the platform Actual position of the platform Actual speed of the platform Standard deviation of the platform speed

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