The Research On The Measurement Of Gravitational Constant G With Angular Acceleration Method And Related Control Problems

The newton gravitational constant G is a fundamental constant in physics. Up to now, the truth-value of G cannot be obtained through any theory. The value which is widely used in the scientific research and engineering comes from the measurement experiments. The newest recommended value of G in CODATA-2010(Committee on Data for Science and Technology) is6.67384(80)x10-11m3kg-1s-2with uncertainty of120ppm. Compared with the value of G which was measured by Cavendish in two hundred years ago, the improvement of the accuracy is less than two orders of magnitude. Therefore, the measurement of G with high precision is necessary. Further more; the adopted G values in the report of CODATA-2010are disagreement in their claimed uncertainties. The largest difference between the four values with uncertainty less than30ppm yields300ppm. The disagreement is caused by the unknown systematic errors in different measurement experiments. An effective way to study those systematic errors is carrying out two different measurement experiments in the same place. Our laboratory is working on the measurement of G with the time-of-swing method in the past twenty years. Three results, HUST-99, HUST-05and HUST-09, are adopted by the CODATA. For exploring the unknown systematic errors in different methods, we start a new experiment with the angular acceleration method.The measurement of G with the angular acceleration method is a complex scientific experiment. The research in this paper is focused on the modeling of the experiment and the feedback control related issues. They are listed as follows.This paper analyzes the principle of the measurement of gravitational constant G with the angular acceleration method. According to the motion equation of the torsion balance in a rotating coordinate sytem and the caclculated gravitational torques in a gravitational field, we build the model of the experiment for the discussion of the requirements of the two feedback control loops. The first is minimizing the twist angle of the torsion balance to about zero by changing the turntable’s angular speed. The second is adjusting the angular speed of the source masses turntable to ensure a constant value for the speed difference. Based on the goal of this experiment (uncertainty25ppm), the requireed uncertainty of each part are allocated. We also discuss the anelastic effect of the torsion fiber which contriutes a system error to the value of G.This paper descirbes the process of building the apparatus, expecially the feedback control system. This system contorls the process of the experiment, records the data, and provides the feedback control of the two turntables. The controller for this experiment is an embedded computer. The sensors are two high resolution angle encoders and an autocollimator. The actuators are two turntables (RT600V and Huber440). During the process of building the appratus, the characteristics of each module are tested by the modulating experiment. The noise levels of each module are also measured.This paper also describes the design of the two PID controllers. The classic PID control algorithm is used in the initial experiments. There are periodicity errors in the angle of torsion balance. Then, the blending PID control algorithm is used as an improvment. Based on the modeling of the feedback control system, the range of the parameters are finding with the limits of the gain in closeloop and the stability of the control system. After that, the proper parameters for the controller are searched by the simulation. With the preliminary tests, the performances of the two controllers meet the requirements.Finally, this paper analyzes the results of the primary experiment. With this feedback control system, the repeatability of the angular acceleration is100ppm in8group results which contributes a100ppm uncertainty to the G value. Expecially, the residual angle of the torsion balance is7.3x10-7rad/(?)Hz at the signal frequency of2mHz, which contributes a0.4ppm uncertainty to the G value. It not only meets the2ppm requirements of the design and also is the highest level of the world.