Application Cases

Experiment Name: Modeling and Control of Dielectric High-Strain Polymer Bimorph Bending Actuators

Experiment Purpose: To establish a dynamic model of the bending actuator's large deformation process using the Hamilton principle and assumed mode method, and to develop a corresponding adaptive control method based on this dynamic model to compensate for uncertainties and nonlinearities in the driving process. The experimental results demonstrate the performance of the control strategy in the dynamic bending process.

Testing Equipment: High-voltage amplifier, laser displacement sensor, control board, etc.

Experiment Process:

Figure 1: Schematic Diagram of the Experimental Setup for Bimorph Bending Actuator

The experimental setup is shown in Figure 1. A complete control process is as follows: The laser displacement sensor measures the vertical displacement of the current bending actuator and sends real-time data to the control board. The control board samples the displacement signal and processes the sampled signal using interpolation to eliminate the effect of the actuator's horizontal displacement. The velocity signal is obtained by differentiating adjacent displacement measurements, and the acceleration signal is similarly obtained. After calculating the control quantity based on the feedback signal, the control board sends the analog control signal to the high-voltage amplifier. The high-voltage amplifier amplifies the received control signal into the voltage output on the actuator. Additionally, a general-purpose computer serves as the host machine to communicate with the control board for control parameter adjustment and data recording. The control frequency of this system is set at 1kHz.

Figure 2: Parameter Identification Experimental Results, Displacement-Time Curve under Sine Excitation

Some dynamic parameters in the control law need to be identified. The initial values of the parameters can be obtained through formulas, and then further adjusted by fitting simulation results with experimental data in Simulink software. The final identification results are shown in Figure 2. The figure shows the parameter identification results for an input voltage signal with a peak-to-peak value of 700V and a frequency of 1Hz. The simulation results (black curve) match the experimental results (red curve) well. The identified parameter estimates will be dynamically changed through the adaptive law in the actual control process.

Next, the performance of the proposed controller is verified. To prove the effectiveness of the adaptive law, the following experiments compare the performance of a controller without parameter adaptation (C1) and a controller with parameter adaptation (C2).

Figures 3, 4, and 5 show the control experimental results for tracking sine reference trajectories with frequencies of 1Hz, 1.5Hz, and 2Hz, respectively. It can be seen that at 1Hz, the displacement generated by both controllers can track the reference trajectory well, but C2 has higher tracking accuracy than C1. As the frequency of the reference trajectory increases, the performance gap between C2 and C1 becomes larger. Even though the feedback gain 𝑘𝑘𝑎𝑎 of C1 is larger than that of C2, C2 still outperforms C1 in terms of error, overshoot, and phase lag.

Figure 3: Experimental Results of Bimorph Bending Actuator Tracking a 1Hz Sine Trajectory

Figure 4: Experimental Results of Bimorph Bending Actuator Tracking a 1.5Hz Sine Trajectory

Figure 5: Experimental Results of Bimorph Bending Actuator Tracking a 2Hz Sine Trajectory

Experimental Results:

Dielectric elastomer (DE) films with anisotropy were prepared by stretching and orienting SBAS triblock copolymer materials, and further used to fabricate dielectric bimorph bending actuators. The bending actuator was dynamically modeled, and an adaptive controller based on the model was designed for the actuator. The main conclusions are as follows:

(1) Isotropic SBAS films, after uniaxial stretching and thermal relaxation treatment, exhibit material orientation.

(2) Anisotropy facilitates the deformation tendency of SBAS films under an electric field, eliminating the need for pre-stretching and oriented fibers in the fabrication of actuators. Traditional DE actuators often require driving voltages in the kilovolt range, while the bimorph bending actuators prepared in this chapter have driving voltages in the hundreds of volts.

(3) A dynamic model of the DE bending actuator was established using the Hamilton principle and assumed mode method, considering the axial nonlinear coupling displacement caused by large lateral bending deformation.

(4) An adaptive controller for the DE bending actuator was designed based on the simplified dynamic model to compensate for uncertainties and nonlinearities in the driving process. Experimental results demonstrate that this controller has better control performance compared to traditional PID control methods.

High-Voltage Amplifier Recommendation: ATA-7025

Figure: Specification Parameters of the ATA-7025 High-Voltage Amplifier

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