A Continuous Charge Estimation for Gravitational Wave Detections

Ladies and gentleman. It‘s an honor to have the opportunity to address such a distinguished audience. I come from the Center for Gravitational Experiments of Huazhong University of Science and Technology in China, my name is Lihonggang. The title of my report is A Continuous Charge Estimation for Gravitational Wave Detections Space inertial sensor is widely applied in Gravity measurement satellite and Gravitational wave detection satellite, because it has the advantage of small size, high precision. And it can detect Six degrees of freedom at the same time. The core subject of inertial senor is called test mass, it is a cube coated with gold, and surrounded by electrodes and housing. Normally, the TM is freely suspended, the capacitance change between the electrodes and TM is used for science measurement. In order to seek higher measurement accuracy, the test mass is required low disturbance. However, Due to the existence of solar energetic particles and galactic cosmic rays in the universe, these charged particles with energy higher than 100million electron volt will penetrate the outer shell of the spacecraft to reach the test mass and gradually accumulate charge on the surface of the test mass. Studies have shown that the acceleration noise caused by the charge of the test mass will exceed Ten to the minus sixteen meters per second‘s square per root Hertz. In Gravitational Wave Exploration Program, the acceleration noise caused by the test mass charge is required to be less than Ten to the minus sixteen meters per second‘s square per root Hertz. So charge management is an essential part of gravitational wave detection. Now, we use the photoelectric effect to control the charge on the TM, This method keep the TM isolated, so it will not introduce more disturbance. Also, UV discharge has been successfully applied in GP-B and LISA Pathfinder. When the charge value is negative, we turn on the Light1, and when the charge value is positive, we turn on the Light2. With the help of the electric field, we can make sure the charge is below the required value. While, before we control the charge, we must have to know its value. The Current methods of charge measurement is to apply active voltages on the four electrodes to produce a torque and make the TM rotate, and then measure the angle and calculate the charge. Obviously, this method will introduce a strong disturbance, so the science measurement has to be interrupted. So we’d like to study a method of measuring charge while making scientific measurement. In order to avoid the coupling effect between the degrees of freedom of TM, the control system uses an AC control scheme. AC voltages are applied to the sensing electrodes. Take a two-degree-of-freedom model as an example,. As you can see, By combining the plate voltage, the motion of each degree of freedom can be controlled. It is the Expression of the electrostatic force between a single electrode and TM This is the torque expression based on AC control scheme. UTM is the potential of TM, which is equal to the charge divided by the value of the total capacitance. We can see that the influence of charge is modulated to a certain frequency, so a well-designed filter can help us extract it. Divide it by the moment of inertia integrate it twice we can obtain the angle. At this time, the inertial sensor can measure this angle. And then demodulate the angle with the Sine and cosine control voltage across the plate at the same frequency. We can obtain the charge after multiplying by the gain. No interference is generated in this method; the science measurement does not have to be interrupted because of the charge measurement. So we call this method as continuous charge estimation. Based on above theory, we build a simulation model on Simulink, the left is acceleration input and charge input, the following is the TM dynamics model, and the final is the charge estimation. On account of the bandwidth of controller in AC control scheme is about 250Hz, we set four different frequency acceleration input, and each acceleration input is given three different charge input. Here are the simulation results, in four pictures, the first row is the displacement of TM, the second row is the rotation of TM, and the last row is the result of charge estimation. The given charge inputs for the three columns are 0, five multiplied by ten to the power of minus thirteen coulomb and five multiplied by ten to the power of minus twelve coulomb. As we can see, the rotation is more sensitive than the displacement. In the first picture, with none acceleration input, the charge estimation accuracy can reach Ten to the minus eighteen coulomb. Finally, this is the conclusion. This paper demonstrate that the continuous charge measurement method is available in theory, so it needs further validation in practice.