# Design and Control of a Pneumatic Muscle Servo Drive Containing Its Own Pneumatic Muscles
## 3 Results
### Synthesis of Regulation System  
The servo drive presented in this section is used to work out a given moment of force for a single arm of a parallel manipulator. The locations of all its components are shown in Figure 20.  
The servo drive consists of two pneumatic muscles (4). In each of them, one end was immobilized by connecting it to the fixed base (7) through a strain gauge force sensor (6) with a range of \(\pm 2\) kN. The free ends of the muscles are connected together by the toothed belt (2) driving the toothed wheel with a pitch diameter of \(d_{p}=63.66\) mm, thus creating a toothed belt transmission, by means of which the push-pull movement of the muscles is converted into a rotational movement of the arm. The pitch diameter of the pulley and the length of the muscles allow the servo drive to move in the range \(-\frac{\pi}{3}\) rad to \(\frac{\pi}{3}\) rad, and the maximum force generated by a single muscle allows you to work out a torque of \(M=25.46\) Nm. The servo drive is also equipped with two pneumatic pressure servo valves (5) controlling the work of the muscles and an absolute angular position sensor (1) with a resolution of 16 bits per revolution, allowing for measuring the angular position with \(\Delta\theta\ =\ 9.58\cdot 10^{-5}\) rad accuracy. The diagram also shows an electric servo drive (3), which was used on the test stand to load the muscle servo drive with a given moment of force. The control system for the torque servo drive has been synthesized. In Figure 21 a diagram of the control system for the entire servo drive is shown, where: \(\theta\)--current value of the angular position of the servo drive, \(x_{a,1}\)--current value of the linear position of the first  
Figure 20: Diagram of a servo drive structure. 1—absolute angular position sensor, 2—toothed belt, 3—electric servo drive, 4—pneumatic muscle, 5—pneumatic pressure servo valves, 6—force sensor, 7—base. muscle, \(x_{a,2}\)--current value of the linear position of the second muscle, \(M\)--current value of the moment of force generated by the servo drive, \(F_{a,1}\)--current value of the force generated by the first muscle, \(F_{a,2}\)--current value of the force generated by the second muscle, \(M_{zad}\)--set value of the moment of force that the servo drive is to generate, \(F_{a,1:2 ad}\)--set value of the first muscle strength, \(F_{a,2:2 ad}\)--set value of the second muscle strength, \(F_{1}\)--adjustment error for the first muscle regulator, \(F_{2}\)--adjustment error for the second muscle regulator, \(u_{a,11}\)--component of the signal controlling the first muscle valve generated by the inverse model, \(u_{a,12}\)--signal component controlling the first muscle valve generated by the PIDn controller, \(u_{a,1}\)--signal controlling the first muscle valve, \(u_{a,21}\)--signal component controlling the second muscle valve generated by the inverse model, \(u_{a,22}\)--the component of the signal controlling the second muscle valve generated by the PIDn controller, \(u_{a,2}\)--signal controlling the second muscle valve. The servo drive control system consists of two independently operating regulating systems, one for each muscle, in which the controlled quantities are the forces generated by the muscles. The signal about the set point value of the servo drive force is converted into the set value of the first muscle force and is entered into the inverse model of the first muscle. In addition, the signal about the current value of the servo drive torque is converted to the current value of the force generated by the first muscle and is introduced into its inverse model. Furthermore, the signal with the current value of the angular position of the servo drive is converted to the current value of the linear position of the first muscle and is entered into its inverse model. Then, the inverse model of the first muscle generates a control signal.