**3.5 Error analysis**

According to the possible error sources, the measurement error sources of the C-tube torsion pendulum are divided into the error introduced by the optical lever structure, the error introduced by the PDS sensor, and the error introduced by the acquisition card and the calibration error. The optical lever is used to measure the mechanical response of the C-tube torsion pendulum, and its structure affects the resolution of the C-tube torsion pendulum. PDS is a part of the optical lever and a sensor sensitive to the change of light spot displacement. Its resolution and optical path of the optical lever together determine the resolution of the C-tube torsion pendulum. The acquisition ability of the data acquisition card determines the system's ability to capture signals, and the acquisition accuracy of signals also affects the accuracy of the system's measurement results. Calibration is the basis for accurate measurement of C-tube torsion pendulum, and the calibration error introduced by calibration will be directly introduced into the measurement results. Other factors that may cause the measurement error of the system include the mechanical vibration of the system, the imperfection of the measuring circuit, and some undetected influencing factors. The mechanical vibration of the system will cause the vibration of the

**Figure 8.** *Test device.*

### *Propulsion Systems – Recent Advances, New Perspectives and Applications*


### **Table 1.**

*Measuring results of thrusts.*


### **Table 2.** *Measuring results of impulses.*

C-tube, plane mirror, laser light source, and other structures of the system. The vibration of these structures will cause the vibration of the measuring optical path and cause low-frequency vibration interference to the measuring signal. The preliminary measurement circuit is not optimized, and the circuit itself may affect the quality of the measured signal, resulting in the reading error of the signal.

At the same time, the measuring range of the C-tube torsion pendulum is related to the machining accuracy and assembly accuracy when machining structural parts. For example, the beam and C-shaped tube, in order to ensure that the torsion pendulum has sufficient accuracy and resolution, the beam should have sufficient strength, and the processing should have good symmetry. When cutting an ordinary tube into a C-shaped tube, it should ensure sufficient cutting accuracy; otherwise, it will affect the mechanical properties of the C-shaped tube. During assembly, the structural dimension shall be measured before assembly. In the optical lever structure, the biggest influence on the measurement is the angle between PDS and incident light.

*Impulse Measurement Methods for Space Micro-Propulsion Systems DOI: http://dx.doi.org/10.5772/intechopen.110865*

When the pendulum is still, PDS and incident light should be perpendicular, so the measurement model can be approximated as a linear model. Although this introduces method error, the relative error introduced by this approximation is very small. When the pendulum swing angle is 1 degree (actually far less than 1 degree), the relative error introduced by the approximation is about 0.1%. The relative position of the parallel plane mirror will affect the size of the system error. The larger the included angle of the plane mirror, the greater the system error caused, and of course, the greater the impact on the measurement results. Therefore, one of the mirrors can be installed on an adjustable platform, and the platform can be used to adjust the two mirrors close to the parallel state. The installation accuracy of the circular reflector does not need to be particularly high, but the connection between the circular reflector and the C-tube must be ensured to be tight enough.
