The Open-Loop Inclinometer

Inertial type inclinometers measure tilt by sensing the component of the earth gravity vector along their sensitive axis, as shown in the open loop sensor in figure 1.

FIGURE 1 An open-loop mass/spring inclinometer

In figure 1, a tilt angle  results in a gravity induced force F=mgsin on the mass m, and a deflection x of the suspension spring x=F/k=(mg/k)sin, where k is spring stiffness. A pickoff converts the deflection x into an output value V_p=k_px=(k_p/k)mgsin, and the final output after a gain k_v amplifier is: V_o=(k_pk_v/k) mgsin (figure 2).

FIGURE 2 Block diagram of the open-loop inclinometer

Each of the elements in the open loop sensor contributes to the total measurement error. Both the spring coefficient k and the pickoff scale factor k_p change with deflection, temperature and time producing non-linearity and repeatability errors, and the amplifier contributes other errors of electrical character.

Another limitation of an open loop sensor is the trade-off between sensitivity and response speed, a measure of which is the natural frequency T_n= (k/m). Reducing k to obtain a sizeable sensitivity results in a reduction of the response speed.

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