A thrust stand for evaluating high frequency variation

Objectives

Thrusters, small rocket engines, are boarded in satellites for attitude control and station keeping. Because some thrusters have heavier weight than their thrust, their thrust was measured using a pendulum-type thrust measurement device (thrust balance, or thrust stand). From the view point of mechanics, thrust stand is equivalent to a torsional/ballistic pendulum where displacement is proportional to external force. Hence, pendulum displacement was measured in thrust evaluation.

On the other hand, pendulums, which always have their own natural frequency (resonant frequency), do not yield displacement that is proportional to thrust in the case that thrust variation frequency is beyond one-third or one-tenth of the resonant frequency. Accordingly, conventional thrust stand can evaluate thrust accurately below 10 Hz. In this study, we proposed to apply an active control and a disturbance observer to the thrust stand in order to evaluate thrust with high frequency variation beyond the resonant frequency.

Proposed method

Figure 1 Schematic of proposed thrust stand

Figure 1 shows a schematic diagram of the proposed thrust stand. The proposed thrust stand has a solenoid actuator for keeping the pendulum at a target point, and accelerometer on the pendulum. Displacement that is measured with a displacement sensor is transferred to a PC-based controller. The controller adjusts actuator driving current on the basis of pendulum displacement. Accordingly, the pendulum motion is suppressed by the controller. Spontaneously, the disturbance observer determines thrust based on angular acceleration of the pendulum and solenoid-actuator-driving current.

Principles

The equation of motion for the thrust stand is described as

where I_m is the moment of inertia, c is damping coefficient and k is spring constant，l_t is the length between the hinge and thruster，l_a is the length between the hinge and solenoid actuator, F₀ is thrust to driving current ratio for actuator, and i is solenoid actuator driving current. When the set-point control for the pendulum is successful, we can make an approximation:

Then, thrust is expressed using angular acceleration and solenoid-driving current,

The equation shows that thrust can be evaluated using pendulum acceleration and solenoid-actuator driving current.

Experimental results

Control systems of prototype

A calibration solenoid actuator gives time-varying reference thrust with offset to the prototype thrust stand. Linux with RTAI (Real Time Application Interface) is installed in the controller (a desktop computer). The controller determined pendulum velocity, displacement and its time integral by use of discrete Kalman filter.

Time history of evaluated and reference thrusts

Figure 2 Time history of evaluated and reference thrust for 7-Hz reference thrust.

Figure 2 illustrates time histories of thrust evaluated by the proposed method (red line), that evaluated by conventional method (yellow line), and reference thrust (green line), which was provided with a calibrator. At 3 Hz, both proposed and conventional methods can evaluate thrust variation correctly. Nevertheless, enhancing thrust variation frequency induces evaluation error in thrust.

Figure 3 Time history of evaluated and reference thrust for 10-Hz reference thrust.

Figure 3 presents time histories at 10 Hz. As you see, the conventional method (yellow line) exhibits error in thrust evaluation although the proposed method agrees with the reference thrust.

Figure 4 Time history of evaluated and reference thrust for 30-Hz reference thrust.

At 30 Hz, the conventional method exhibits overestimation by a factor of 9.1. The resonant frequency of the prototyped thrust stand seems near 30 Hz. In contrast, the proposed method evaluated thrust with an error of 28%. Currently, improvement in thrust stand rigidity allows more accurate thrust evaluation.

Figure 5 Time history of evaluated and reference thrust for 75-Hz reference thrust.

Figure 5 presents time histories of evaluated and reference thrusts at 75 Hz. Thrust is not correctly evaluated by he conventional method with a phase delay and reduced amplitude. In contrast, the proposed method correctly determined thrust variation.

Dynamic properties

Figure 6 Dependence of thrust amplitude ratio of evaluated thrusts on thrust variation frequency.

Figure 6 shows the dependence of thrust amplitude ratio of evaluated thrusts on thrust variation frequency. Red and yellow points represent the results for the proposed method, and the conventional method, respectively. Light-blue points, showing the thrust evaluated on the basis of acceleration, yield no physical thrust, but shows how the proposed method compensate the conventional method.

The ideal value of thrust amplitude is 1, which shows no discrepancy between the reference and evaluated thrusts. As shown in Fig. 6, the conventional method overestimated thrust amplitude at a resonant frequency of 30 Hz by a factor of 9.1. On the other hand, the proposed method yielded an error of 10 % by compensating the conventional method using pendulum acceleration.

Above 30 Hz, the conventional method yields thrust amplitude ratio of approx. 1.0, but shows a significant phase delay as shown in Fig. 5. The proposed method can determine thrust variation in high frequency range beyond 30 Hz with an error of 20%. From these results, the proposed method can evaluated thrust with high frequency variation by use of disturbance observer and active control.

Journal papers and conference proceedings

Akira Kakami, Kenji Kashihara, Shota Takeshida, and Yasuyuki Yano, "A new thrust measurement method for evaluating higher frequency variation by applying acceleration measurement to null-balance method," International Electric Propulsion Conference 2015, IEPC-2015-256/ISTS-2015-b-256, 2015/7/9, July 4-10 2015, Kobe, Japan.
Akira Kakami and Takeshi Tachibana, "Thrust Evaluation in Wide Frequency Range using Active Control and Disturbance Observer,” Journal of Propulsion and Power, Vol. 29, Issue 6, pp. 1274-1281, DOI: 10.2514/1.B34849, November 2013.
Akira Kakami and Takeshi Tachibana, “Measurement of Thrust with Wide-Frequency Range Variation by Applying Active Control and Disturbance Observer”，Journal of the Japan Society for Aeronautical and Space Sciences，Vol. 60, No. 5, pp. 203-211, October 2012．(In Japanese)
Akira Kakami，and Takeshi Tachibana，A thrust stand using acceleration measurement and setpoint control for high-frequency thrust variation, Space Transportation Symposium, STCP-2011-027，January 19-20 2012，Sagamihara, Japan. (In Japanese)
Akira Kakami, Ryoma Hiyamizu, Shinichiro Masaki and Takeshi Tachibana, “A Preliminary Study on an Active-controlled Thrust Stand for Thrust Variation Measurement,” Selected paper of 25th International Symposium on Space Technology and Science, ISTS2006-b-19, pp. 212-217, June 2006.

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