## 4 Frequency Response of Cam Angular Control  
To investigate the response of the servo valve, we controlled the angle of the cam. The zero point was adjusted, the tube was set to an appropriate closing amount, and the experiment was then performed by applying a supply pressure of 500 kPaG, which is a value that is normally used in our pneumatic servo applications, satisfying the required driving force with the maximum working pressure  
Figure 11: Flow characteristics of developed pinch-type valve. range. The frequency response was measured as a sine wave signal with amplitudes corresponding to 20 and 40 degrees for the target value of the angle. The target value of the angle corresponded to 25% and 50% with respect to the maximum rotation angle of 80 degrees. Figure 12 shows the block diagram of the angular control, and Table 1 shows the control gains. The angular control was performed by adding the feedforward of spring force compensation to the PD control. In the figure, \(\theta\) corresponds to the value read by the encoder. The output torque of the motor was proportional to input voltage \(u\) of the motor controller, and the proportionality constant corresponded to 34.8 mNmN/V. Figure 13 shows the Bode diagram in which it is confirmed that the band width is approximately 60 Hz when the angular amplitude corresponds to 20 degrees and 40-50 Hz when it corresponds to 40 degrees. However, the phase lag significantly exceeds 90 degrees, therefore the maximum frequency that the motor can track the target value is 30-40 Hz. Responsiveness depends on the dynamic characteristics of the servo motor. Thus, it was necessary to select a motor with a higher response to improve responsiveness. the pressures \(P_{1}\) and \(P_{2}\) of the respective chambers of the pneumatic cylinder and the pressurized areas \(A_{1}\) and \(A_{2}\). The driving force \(F\) was fed back. Additionally, friction compensation was added to the target value \(F_{\text{ref}}\) of the driving force as feedforward. We conducted experiments with sinusoidal waves of 0.1 and 1 Hz as the position target values to check whether smooth motion was achieved without a stick-slip. Figure 15 shows the experimental results. With respect to the position of the pneumatic cylinder, driving force, and motor angle, the blue line indicates the measured values, and the red line indicates the target values. With respect to the pressure, the blue line denotes \(P_{2}\), and the red line denotes \(P_{1}\). The driving force of the pneumatic cylinder is well controlled with only 40 ms of delay, even though approximately 3 degrees of motor angle error is seen in Figure 15. The position tracking performance achieved with the gain of \(-0.14\) dB and the phase delay of 2.5 degrees in 0.1 Hz without a stick-slip phenomenon. When the target value is 1 Hz, the gain is 0.14 dB and the phase delay is 5.3 degrees. Moreover, the results of position control in the same condition using a conventional spool-type servo valve (FESTO, MPYE-5-M5-010-B) is shown in Figure 16. The voltage in the figure represents the opening rate that corresponds to motor angle of the developed pinch-type servo valve. When 5 V is applied, the spool is positioned at the neutral position where the valve is supposed to be closed. The position tracking performance using the developed valve shown in Figure 15 is almost equal or greater when compared to those using the conventional spool valve in Figure 16. We calculated the tracking error for the result of 0.1 and 1 Hz, respectively. The tracking errors of the developed valve are 2.5% at 0.1 Hz and 1.7% at 1 Hz while those of spool-type valve are 4.2% at 0.1 Hz and 4.0% at 1 Hz. From this, we confirmed that the developed pinch valve works as well as the conventional servo valve to control pneumatic actuator.