# Design and Control of a Pneumatic Muscle Servo Drive Applied to a 6-DoF Parallel Manipulator
## 3 Results
### Synthesis of Angular Position Control System
Figure 21: Control system diagram for angular position servo drive: _theta_—current angular position of the servo drive, \(x_{a,1}\)—current linear position of the first muscle, \(x_{a,2}\)—current linear position of the second muscle, \(theta_{zad}\)—desired angular position of the servo drive, \(x_{a,1,2 ad}\)—desired linear position of the first muscle, \(x_{a,2,2 ad}\)—desired linear position of the second muscle, \(M\)—current force moment generated by the servo drive, \(F_{a,1}\)—current value of force generated by the first muscle, \(F_{a,2}\)—current value of force generated by the second muscle, \(x_{1}\)—regulation error for the first muscle regulator, \(x_{2}\)—regulation error for the second muscle regulator, \(u_{a,11}\)—component of the control signal for the first muscle valve generated by the inverse model, \(u_{a,12}\)—component of the control signal for the first muscle valve generated by the PID regulator, \(u_{a,1}\)—control signal for the first muscle valve, \(u_{a,21}\)—component of the control signal for the second muscle valve generated by the inverse model, \(u_{a,22}\)—component of the control signal for the second muscle valve generated by the PID regulator, and \(u_{a,2}\)—control signal for the second muscle valve. Table 6 presents the results of the evaluation of the performance of the developed servo drive. For all four sinusoidal waveforms and one square waveform, the average absolute error and the maximum absolute error were calculated. All parameters were calculated over a time interval covering two complete cycles of the reference signal, starting from the second complete cycle. Analyzing the results of the tests conducted on the developed angular position servo drive, it was observed that in the case of sinusoidal signals, the largest error occurs when changing the direction of motion of the drive. This is likely due to the presence of friction forces between the muscle bundle fibers and between the fibers and the rubber bladder. The influence of friction forces on positioning accuracy is most significant at muscle velocities close to zero. It was also noticed that for low-frequency signals, apart from the moment of changing the direction of the drive, the error value changes slightly and is not dependent on the current drive position. However, a strong correlation between the external load \begin{table}
\begin{tabular}{l c c} \hline \hline  & \(\mathbf{e_{mean}}\) **(rad)** & \(\mathbf{e_{max}}\) **(rad)** \\ \hline \(theta_{2 ad}=\frac{2 pi}{9}sin(t)\) rad & 0.0051 & 0.013 \\ \(M=0\) Nm & & \\ \(theta_{2 ad}=\frac{2 pi}{9}sin(3t)\) rad & & \\ \(M=0\) Nm & & \\ \(theta_{2 ad}=\frac{2 pi}{9}sin(t)\) rad & 0.005 & 0.013 \\ \(theta_{2 ad}=\frac{2 pi}{9}sin(3t)\) rad & & \\ \(M=5\) Nm & & \\ \(theta_{2 ad}=step\) rad \(M=0\) Nm & 0.028 & 1.047 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of angular position servo drive operation. Figure 25: Results of angular position servo drive operation for a reference signal described by \(theta_{2 ad}=\frac{2 pi}{9}sin(3t)\) rad with a constant load torque \(M=5\) Nm: servo drive behavior (on the left side) and servo drive error (on the right side). Figure 26: Results of angular position servo drive operation for a square wave reference signal with an amplitude of \(A=\frac{pi}{6}\) rad and a period of \(T=6\) s and with a constant load torque \(M=0\): servo drive behavior (on the left side) and servo drive error (on the right side). and the positioning accuracy of the servo drive was not observed. This is evidenced by the fact that the average absolute error values, as presented in Table 6, for signals with the same pulsations are close to each other. Similarly, the average absolute error values for signals with the same pulsations do not differ significantly from each other. Analyzing the test results, it was observed that the maximum average absolute error value for sinusoidal signals is 0.028 radians, which translates to a muscle positioning error of 0.89 mm considering the pitch diameter of the belt drive.