Improving actuation stability with sigma-delta noise shaping technique for space gravitational reference system

Abstract Electrostatic actuation of the gravitational reference system is critical for TianQin. This actuation must function effectively in both wide range and high resolution modes. However, amplitude fluctuations of the AC control voltage on non-sensitive axes can adversely affect the sensitivity of the sensitive axis, imposing stringent requirements on the amplitude stability of AC actuation. Traditional open-loop actuation, constrained by the limitations of the high-voltage amplifier (HVA), has difficulty meeting this demand. To address this, we developed an AC actuation prototype based on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Σ</mml:mi> </mml:mrow> <mml:mo>−</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> </mml:mrow> </mml:mrow> </mml:math> noise shaping technique to suppress the HVA gain instability. Furthermore, we built an evaluation platform with a measurement resolution of 0.05 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>ppm</mml:mtext> <mml:mstyle scriptlevel="0"/> <mml:msup> <mml:mtext>Hz</mml:mtext> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> at 1 mHz to assess AC amplitude stability. Experimental results demonstrate that the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Σ</mml:mi> </mml:mrow> <mml:mo>−</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> </mml:mrow> </mml:mrow> </mml:math> actuation improves AC amplitude stability from 8 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>ppm</mml:mtext> <mml:mstyle scriptlevel="0"/> <mml:msup> <mml:mtext>Hz</mml:mtext> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> in the open loop design to 1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>ppm</mml:mtext> <mml:mstyle scriptlevel="0"/> <mml:msup> <mml:mtext>Hz</mml:mtext> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> at 1 mHz. Further analysis indicates that the ADC’s voltage reference is the primary factor limiting amplitude stability, providing a clear pathway for future optimization.