# Design and Control of a Pneumatic Muscle Servo Drive Containing Its Own Pneumatic Muscles
## 2 Materials and Methods  
### Test Stand  
In order to verify the assumed thesis, first the static and dynamic characteristics of a single muscle were determined. In this servo drive proportional piezoelectric pressure servo valves Hoerbiger Tecn Plus with output pressure were used to supply the muscle with the working medium \(p\) = 0\(-\)1 MPa and control signal \(u\) = 0\(-\)10 V. A single muscle, along with its associated valve and connecting line, is the object being analyzed. In steady state, this object is characterized by three quantities: valve servicing voltage \(u\) being the input signal for the object and the force generated by the muscle \(F\) and muscle tip position \(x\), which are the output signals of the object. When determining all the characteristics, it was assumed that the position of the muscle tip is the difference between the nominal length of the muscle \(l_{n}\) and its current length \(l\) expressed in millimeters. For the examined muscle, the nominal length was \(l_{n}\) = 350 mm. In steady state hypertension prevailing inside the muscle \(p\) linearly corresponds to the control signal \(u\) by dependence \(p\)(MPa) = 0.1 \(u\)(V). The relationship between the three quantities characterizing the muscle can be represented as three types of static characteristics: isobaric--the dependence of the position on the loading force, with a constant value of the control voltage for several voltage values \(x\) = g(\(F\)); \(u\) = const, isotonic--dependence of the position on the control voltage at constant loading force, for several strength values \(x\) = g(\(u\)); \(F\) = const and isometric--force dependence on the control voltage, with a constant muscle position, for several position values \(F\) = g(\(u\)); \(x\) = const. The scheme for determining these characteristics is presented in Figure 2. However, the behavior of the object over time can be determined by determining two families of dynamic characteristics, one for each of the object's output quantities. The first family of dynamic characteristics presents the relationship of muscle position \(x\) since \(t\) as a response to a step change in the valve control signal \(u\), with constant muscular force \(F\). The second family of characteristics shows the dependence of the force generated by the muscle \(F\) since \(t\) as a response to a step change in the control signal \(u\) with a fixed position of the muscle tip \(x\)[13]. In order to determine the characteristics discussed above, a test stand was designed and constructed, the diagram and real view of which are shown in Figure 3. The stand allows testing of a single muscle (4) and a pair of muscles working in opposite directions connected by a toothed belt gear (3) with a pitch diameter \(d_{p}=63.66\) mm. The station has an absolute optical encoder (2) with a resolution of 16 bits per revolution enabling determination of muscle displacement with accuracy \(\Delta x=0.005\) mm. The stand has also been equipped with Hoerbiger Tecno Plus pressure servo valves (5) for supplying the muscles with a working medium. In addition, the station is equipped with two strain-gauges (6) with a range \(\pm 2\) kN with an analog voltage output \(\pm 10\) V. In order to load muscles with the set force value, the station is equipped with an electric servo drive with a rated power of 400 W and a rated torque of 1.27 Nm with a precise planetary gear ratio \(i=70\) and maximum arc clearance of 9 arcmin (1) driving the toothed belt transmission. This drive allows for the loading of a single muscle with strength \(F_{\mathrm{max}}=2792\) N. In addition, due to the non-linearity of the generated torque in relation to the set electrical current value resulting primarily from the use of planetary gears, an additional control system with a PID type regulator has been implemented to control the muscle loading force. A strain-gauge force sensor was used as the feedback. Figure 3: Model and real view of the test stand.