Method for parameter extraction of sensitive probe and degree-of-freedom coupling calculation of capacitive displacement sensor

A method for parameter extraction of a sensitive probe and degree-of-freedom coupling calculation of a capacitive displacement sensor, comprising:

• step 1:
• performing translational or rotational displacements with different directions on the TM in the sensitive probe with a multi-conductor structure, setting N(N+1)/2 groups of conductor excitation charges, and then calculating the three-dimensional electrostatic field distribution under each group of excitation charges to compute the electrostatic field energy, thereby obtaining the full capacitance matrix for different translational or rotational displacements, where N is the number of conductors in the sensitive probe;
• step 2:
• obtaining capacitances among the conductors in the sensitive probe based on the full capacitance matrix extracted in step 1 to calculate the N-port indefinite admittance matrix YN×N of the sensitive probe;
• step 3:
• based on the full capacitance matrix extracted in step 1, establishing the equivalent circuit model in combination with a specific connection of the sensitive probe to each capacitive displacement sensing channel, directly writing an equation I=YV satisfied by the voltages and the currents of the N nodes according to the indefinite admittance matrix, and then substituting V−I characteristics satisfied by external termination components of the N nodes into the above equation to obtain the voltage and the current at each node, thereby finally obtaining the output complex voltage of each capacitive displacement sensing channel;
• step 4:
• based on the full capacitance matrix for different translational or rotational displacements extracted in step 1, performing interpolation fitting on the variation value sequence of each distributed capacitance with displacement to obtain the continuous variation curve of each distributed capacitance versus displacement;
• step 5:
• arbitrarily specifying a time-varying manner of displacement of the TM in the sensitive probe, and obtaining a value of each distributed capacitance at each displacement moment according to the variation curve of each distributed capacitance versus displacement obtained in step 4, which is then applied to compute the output complex voltage of each capacitive displacement sensing channel in step 3;
• and
• step 6:
• combining the time sequence of the output complex voltage of each capacitive displacement sensing channel with displacement degrees of freedom, and then performing Fourier transform to obtain the spectrum of the output signal of each displacement degree of freedom, thereby calculating the couplings among the multi-degree-of-freedom displacements caused by the sensitive probe.