Sensors - September 2003 - A Novel Auto-Zero Servo-Inclinometer

A next-generation servo-inclinometer exhibits accuracy of a few arc-seconds, has virtually banished the zero drift problem (even under harsh conditions), and can go without recalibration for extended periods of time.

Federico Singer, Instruments & Control Inc.
Yuval Singer, Singer Instruments & Control Ltd.

Force-balance inclinometers overcome the limitations of spring-and-mass sensors by replacing the mechanical spring with an electromagnetic balancing force. The residual errors are mostly negligible or can be compensated—with the exception of the random zero drift. A new auto-zero servo-inclinometer solves the zero-drift problems through geometry and computation.

Inertial-type inclinometers measure tilt by sensing the component of the Earth gravity vector along their sensitive axis.

Figure 1. In an open-loop inclinometer, the gravity force on the mass m will extend the spring to which it is attached. Since the force depends on the amount of tilt, the corresponding displacement as measured by a position sensor is also a function of the tilt.

As illustrated 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:

Figure 2. A block diagram of the open-loop inclinometer shows that the final result of the measurement V_o is the product of the force input and the transfer functions of all the components. Any error of those components from any source will directly affect the accuracy of the measurement.

Each element 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, resulting in nonlinearity and repeatability errors. The amplifier contributes other errors of an electrical character. Another limitation of an open-loop sensor is the tradeoff between sensitivity and response speed, a measure of which is the natural frequency

_n = (k/m). Reducing k to obtain a sizeable sensitivity results in a reduction of the response speed.

The Force-Balance Inclinometer
The force-balance closed-loop configuration overcomes most of the open-loop mass-and-spring inclinometer errors, as well as the speed limitation. In the force-balance inclinometer shown in Figure 3, force F = mgsin

is again acting on the mass m, causing a deflection, x, that results in a pickoff output, V_p, going into an amplifier of gain k_v.

Figure 3. In a force-balance inclinometer, the gravity-induced force on the mass is balanced by an electromagnetic force proportional to the displacement of the mass, making it an “electromagnetic spring.” It is much stiffer than the mechanical spring attached to the mass, which is designed only to guide it on a linear path. As a first approximation, the mechanical force can be neglected.

Here, the similarity with the open-loop ends—the output voltage V_o is now fed to an actuator made of a coil moving inside the magnetic field of a permanent magnet. The coil drives the mass m with a force:

B	=	magnetic field density
I	=	current through the coil
l	=	coil wire length

Because the spring’s only function is to suspend and guide the mass, it is designed to be as weak as possible, and its restoring force is replaced by an electromagnetic balancing force. As the mass begins to move under the gravitational force, the coil applies an opposing force, F_e, proportional to V_o, which tracks the deflection x (negative feedback); the mass movement will stop as the forces balance each other.

The electromagnetic spring action results from the restoring force F_e’s being proportional to the deflection x as follows: the current through the coil is:

where the expression inside the brackets is the electromagnetic stiffness coefficient.

Figure 4. As shown in this block diagram of the closed-loop inclinometer as a classic servo-system with negative feedback, the forward path G is driven by the difference between the input force F and the feedback force F_e. Increasing the gain of G reduces the difference (error), and the output-to-input ratio becomes dependent solely on the transfer function of the feedback path H, virtually eliminating the effect of the forward-path (open-loop) elements on the output.

Using conventional servo-loop methods, the transfer function of the forward path is:

while that of the feedback path is H = Bl. The transfer function of the closed loop is:

From (9), the total stiffness K = k_e + k of the closed-loop spring is the sum of the electromagnetic and mechanical stiffness coefficients.

The condition for an effective force-balance sensor is for the electrical stiffness coefficient to be much higher than the mechanical one, k_e>>k. However, the effect of the elastic suspension cannot be neglected in one regard: the stability of the inclinometer bias (residual output for zero input).

The elastic suspension of the mass suffers from all the stability problems characteristic of elastic elements—residual stress and stress relief over time; dimensional changes due to temperature, shock and vibration; and so forth. Since any force on the mass resulting from those changes will be interpreted as an input and result in a change in the coil current to restore balance, an effect of bias instability will appear. This effect is the most difficult error source to compensate due to its mostly random or unpredictable character. It is most troubling when the inclinometer is used as a leveling device, or in very low range tilt sensors.

The Auto-Zero Force-Balance Inclinometer
The inclinometer described here is designed to correct bias and misalignment drift from all sources. The basic idea is to apply a generations-old method used by carpenters and builders to check bubble levels—turning the tool 180° on the measured surface. If the bubble shows the same result, it is working correctly; if not, it indicates an error of alignment equal to half the peak-to-peak difference between the positions of the bubble. In this implementation, the servo-inclinometer sits on a rotary disc with its input axis IA parallel to the disc surface, which is turned 180° between two diametrically opposed positions for the bias correction operation (see Figure 5).

Figure 5. The zero errors of the servo-inclinometer (bias and misalignment) are independent of the sensor position. Therefore, the output of the sensor attached to a horizontal rotary disc will not change when turned to two different positions.

The output of the inclinometer for zero input (the inclinometer base is on a perfectly horizontal surface) has two components:

If the rotating base in Figure 5 turns in a perfectly horizontal plane, it is evident that both the bias output V_B and the misalignment output

of the inclinometer remain the same in both positions: V₀ = V_B + .

Now suppose that the rotating base is tilted by an angle

around the Y axis, and we repeat the same procedure (see Figure 6).

Figure 6. Turning the sensor in two diametrically opposed positions produces two readings of equal magnitude and opposite polarity, plus two identical bias readings. Subtracting the two position outputs results in elimination of the bias, leaving only twice the value of the tilt angle.

It becomes evident that by rotating the sensor as shown, the magnitude of

remains the same in both positions, while the direction of the input axis is inverted, thus inverting the polarity of the voltage output

. The voltage outputs in positions 1 and 2 can then be found by superposition to be:

Finally, subtracting the outputs of positions 1 and 2 (V₁– V₂= 2 ) leads to the desired result,

In words, the bias and misalignment errors can be completely eliminated from the equation, leaving only the real tilt result. In effect, this an auto-zero feature.

To put the described principle into practice, some basic requirements need to be fulfilled:

This principle has been implemented in several ways. The preferred one uses a servo-inclinometer mounted on an accurately machined disc, which in turn is seated on high-accuracy bearing balls sandwiched between it and a second plate, in a thrust-bearing configuration. A motor drives the disc between two stops at 180° from each other. At each of the stops a reading is taken and converted using an A/D converter of sufficient resolution, accuracy, and speed; the data are stored in memory; and the final result is computed with a microprocessor. The digital output is serially transmitted in RS-232 or other format (see Figure 7).

Figure 7. A practical auto-zero tilt sensor consists of a servo-inclinometer mounted on a high-accuracy thrust bearing. The microprocessor-controlled motor drives the rotor to two test positions defined by the stops. The outputs are digitized, stored, and computed to provide a high-resolution linearized serial output.

After the auto-zero operation, the inclinometer is turned back to its initial position, where it continues measuring tilt as a conventional tilt sensor starting from a bias-corrected output. The auto-zero operation can be repeated as needed, or periodically at preselected time intervals.

Figure 8. The technology described here has been realized as a single-axis auto-zero inclinometer with RS-232 output (A) and a dual-axis auto-zero inclinometer used for antenna horizontal reference (B).

A second implementation is a dual-axis device, in which two inclinometers are mounted on the rotary base to measure and bias-correct in two perpendicular directions. In both the single- and dual-axis devices, a third accelerometer can be used to detect any movement or vibration appearing during the auto-zero operation, which could produce a false result. In that case, a signal is sent to the microprocessor to repeat the operation. Both the single- and dual-axis devices are shown in Figure 8.

A third embodiment of the invention uses a simpler bearing that drives a low-cost mass-produced inclinometer. This arrangement makes it possible to use inexpensive inclinometers in cost-sensitive leveling applications by vastly improving the accuracy of small-angle readings.

Applications
The single-axis version has been used in tank fire-control systems, in which it demonstrated accuracy down to a few arc-seconds under repeated shocks of thousands of g’s, vibration, and temperature extremes. It is currently being considered for leveling the transporters used by NASA to carry spacecraft to the launching pad.

The dual-axis model is being used as a horizontal reference for the radar antenna of the Arrow anti-missile systems, where a 0.0028° accuracy over the full temperature range and over a period of years is required.

Low-range MEMS accelerometers could be used for less demanding leveling and low-range tilt measurement, if the bias stability is improved. One application used a MEMS accelerometer mounted on a simple rotary device to level diamond-polishing tables, achieving an order of magnitude accuracy improvement.

The inclinometers could also find applications in laboratories and other test setups that require accuracy and repeatability of single-digit arc-seconds over long periods of time. Another scenario is installations in which the device is hard or impossible to reach for calibration purposes, such as under water, under ground, high altitudes, or remote locations. Finally, the sensor could be used on equipment working under extreme environmental conditions (e.g., variable temperatures, high-level shock and vibration), as long as some stable periods are available for the bias correction operation.

Test Results
The results of a typical temperature test of auto-zeroing operation in a single-axis device are given in Figure 9.

Figure 9. A typical temperature test shows superb stability of the servo-inclinometer itself, ~7 mV for a 90ºC change. Still, the bias correction improved that to <1 mV.

V₀ and V₁₈₀ are direct readings from the internal servo-inclinometer at the two measurement positions for bias correction, while V_out is the computed result for bias correction. In this case, the internal sensor shows very low temperature sensitivity, ~0.007 V max. change over a 90°C range, which comes to 0.07% full-range total for a ±5 V range (1 V/°), or 0.0008% F.R./°C. Still, after bias correction the change is reduced to <1 mV or 3 arc-seconds over the temperature range, well within the error range of the measurement equipment.

Summary
Servo-inclinometers achieve high accuracy due to the closed-loop principle and predictable errors compensation, but because their random zero drift cannot be compensated, they do not work well for low-range tilt and leveling. The sensor described here virtually cancels zero drift, even under harsh environmental conditions. Calibration is not required over even extended periods of time, and consistent leveling accuracy of a few arc-seconds is possible.

Yuval Singer is President, Singer Instruments & Control Ltd., Tirat Carmel, Israel; 972-4-8578880, yuval@singer-instruments.com.