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 Vp=kpx=(kp/k)mgsin, and the final output after a gain kv amplifier is: Vo=(kpkv/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 kp 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 Tn= (k/m). Reducing k to obtain a sizeable sensitivity results in a reduction of the response speed.