Background: As a high-performance functional material, stacked piezoelectric actuator
can produce a displacement under the effect of changing voltage. Its advantages of fast response and
easy operation make it to be widely applied in the precision structure field. However, its small displacement
stroke and hysteresis nonlinearity affect the accuracy of the output.
Methods: In order to enlarge the displacement of piezoelectric actuator and reduce the influence of
hysteresis, this study designs a diamond-shaped amplifying mechanism to amplify the output of the
piezoelectric actuator, and then develops a self-tuning fuzzy fractional-order PIλDμ controller for the
high precision displacement control of the proposed amplifying mechanism. After analyzing the
working principle and modeling the amplifying mechanism, the fractional-order PIλDμ control model
of the proposed mechanism was built and discretized according to the theoretical base of the fractional
calculus in the time domain. Moreover, the fuzzy control algorithm was also introduced to
achieve self-turning of parameters. Besides, the amplifying mechanism was also adopted for a microdroplet
jetting dispenser to verify the practicability of the mechanism and control strategy.
In the next step, some experiments were undertaken based on the constructed platform.
Results: Experiments show that the displacement overshoots, the times of reaching a steady state of
the traditional integer-order controller and the fractional-order controller are 5.08%, 1.17% and 17.25
s, 12.00 s, respectively. However, the fuzzy PIλDμ controller lowers the overshoot and the time of
reaching a steady state to 0.95% and 9.00 s, respectively. The control algorithm can not only improve
the follow-ability of the output displacement of the proposed mechanism, but also maintain the deviation
within the range of 0.4% after the displacement stroke is stable and reduce the entering time of
the mechanism up to 47.8%. In actual application, the droplet volume of micro-droplet jetting dispenser
under fuzzy fractional-order PID control method is more stable, and its repeatability accuracy
can reach up to 1.6475%.
Conclusion: Experimental results indicate that the self-tuning fuzzy fractional-order PIλDμ controller
can significantly improve the tracking performances of the PID and the integer-order PID with regard
to the amplifying mechanism with the advantages of good dynamic character and regulation
precision. Furthermore, the diamond-shaped amplification mechanism and control strategy can be
applied for some micro-droplet jetting dispensers used in microelectronic packaging, life science and
3D printing fields.