SILICON-BASED GYROSCOPES AND THEIR SIBLINGS ARE INCREASINGLY PREVALENT IN CONSUMER-ELECTRONICS EQUIPMENT. HOWEVER, INACCURACY IN REPORTED DATA MAY PRODUCE AN END-USER EXPERIENCE THAT’S WORSE THAN NOT HAVING A MEMS-BASED SYSTEM AT ALL. A SIMPLE CALIBRATION FOR MEMS GYROSCOPES

BY MARK LOONEY s ANALOG DEVICES

raditionally, gyroscopes were mechanical devices that measured the angular rate of . One common use of gyroscopes has been in navigation systems to pro- vide heading estimation. Installing these types of gyroscopes into systems typically involved a mechanical design mounted to a bulkhead, providing a mechanical set- screw system for frame-alignment calibration. MEMS (microelectromechanical- system)-gyroscope now provides this function in a variety of packages that enable integration into PCB (printed-circuit-board)-based systems. MEMS gyroscopes employ tiny micromechanical systems on silicon structures, supporting motion-to-electrical transducer functions.

Although MEMS gyroscopes are into valuable bits at the system level. for production-ready processing, it will Tsimpler to integrate into electronic A well-designed calibration takes a speed development cycles and lower systems than their mechanical pre- population of transducer behaviors up-front investment requirements. decessors, many factors still require and produces predictable outputs over consideration, including trade-offs the important conditions for the end MEMS-GYROSCOPE BEHAVIOR among function, performance, and system. Translating MEMS-gyroscope An ideal MEMS gyroscope produces price. For many systems, a key perfor- behaviors into predicable performance a predictable output when you subject mance metric is accuracy. Although at the system level requires you to cul- off-the-shelf products may satisfy some tivate an understanding of the trans- design requirements, a gyroscope that ducer’s performance and behaviors, appears to suit a system design may establish the impact that the sensor’s end up being too inaccurate. Over a behaviors will have on critical system- population of parts, for example, you performance criteria, and develop a can expect sufficient variation in accu- strategy and process for characterizing racy to negatively affect critical system and correcting behaviors that can limit goals. the transducer’s value in the system. Gyroscope calibration offers an For system developers in the ini- option for bridging this gap, enabling tial prototype phase, justifying the the use of an approach that may be investment in accurate motor stages, more favorable due to price, pack- encoders, and stable mechanical struc- Figure 1 A yaw-rate MEMS gyroscope age style, power dissipation, or other tures can be difficult. Although this responds to motion about its predefined attributes. The purpose of calibration approach to calibration will not replace axis of rotation. is to translate transducer behaviors the need to invest in proper equipment

28 EDN EUROPE | JULY 2010 www.edn-europe.com it to a known rate of rotation. It has no noise, perfect linearity, and no offset. Perfection is not typically available on economical manufac- turing processes, however, creating the need for a deeper understanding of MEMS-gyroscope errors. A yaw- rate MEMS gyroscope responds to motion about its predefined axis of rotation (Figure 1). For MEMS gyroscopes, you express the typical unit of measurement for angular rate of rotation in degrees per sec- ond. For analog-output products, scale factors are normally in degrees per second per volt or millivolt. For digital products, scale factors are Figure 2 The root graphs noise impact versus integration time of the normally in degrees per second per ADIS16130 MEMS gyroscope. least-significant bit. The following equation provides a simple behavior model for a MEMS gyroscope: error to the measurement. A common tool for analyzing this impact is the Allan Variance Method, which estab- GYRO=KRATEBIASNOISE lishes the variance for a bias estimate with respect to an 2 3 integration time. For example, the accuracy for a 6-second K2 RATEK3 RATE... integration time is approximately 0.004/sec (Figure 2). Bias, noise, and scale-factor errors, including linearity, Product data sheets typically provide information that have a notable impact on systems that use MEMS gyro- enables estimates for each error term in this equation. scopes for angle-displacement measurements (Figure 3). These estimates enable the second step in this process—to determine the system-level impact and establish perform- ance goals. NEW SYSTEM-LEVEL IMPACT After establishing an understanding of the MEMS gyro- scope’s behaviors and error patterns, you then must deter- mine the impact that they will have on system operation. Setting performance goals that support critical system goals is essential to successful sensor integration. Some systems, such as navigation and platform controls, use the gyroscope full-size outputs to determine relative angle displacement through picture integration. Bias errors add fixed errors to the sensor’s out- put response and can make a device look like it is rotating when it is stationary. The net result is a constant accumula- tion of angle-measurement error that is equal to the prod- uct of the bias error and time accumulation. The following equation shows the mathematical relationship for this drift factor: t1 1 EBIAS=BIASdt=BIASt . 0 Scale-factor errors contribute to displacement-measure- ment errors only when there is motion. The mathematical relationship for the resulting error is as follows:

t1 t1 ESCALE=RATEKdt=RATEKdt. 0 0

Noise that is inversely proportional to the integration time associated with the measurement contributes random www.edn-europe.com Figure 3 MEMS-gyroscope errors in variables such as bias, noise, and scale factors impact systems that use them for angle-displacement measurements.

These errors directly influence head- approach exists. Assuming bias-error mately 90 of rotation motion. ing estimates in navigation systems, correction, the integration of a MEMS 3. Pivot the gyroscope assembly along with the accuracy of a platform- gyroscope provides another mecha- between each stop point to make control system that uses them as a nism for observing scale factor. In this sure that the rotation is clear and feedback-sensing element. case, the scale-factor error is the ratio smooth motion is possible. of the measured angle to the actual 4. Measure the displacement angle SIMPLE CALIBRATION angle displacement. using an independent sensor. One A common goal for calibration is option for this step would be an to narrow the error distribution of a CALIBRATION EXAMPLE accelerometer-based , transducer population and transform Practical steps enable using this such as Analog Devices’ (www.ana- that population into sensor systems approach with a gyroscope. This pro- log.com) ADIS16209, which you that provide a predictable output for cess also works for a system-level fix to the rotating platform. You the measured conditions. This pro- board with a surface-mount MEMS then orient the platform vertically cedure involves characterizing indi- gyroscope. Begin the calibration by and use an inclinometer to measure vidual transducers under known con- considering the physical setup: angular displacement. If the incli- ditions, thereby providing the neces- 1. Select a pivot point and secure it nometer’s accuracy is 0.25 and the sary data for part-specific correction with a -screw assembly. rotation span is 90, the error will formulas. The purpose of this process Experiment with the pivot screw’s be less than 0.3%. is to offer a simple calibration for get- torque to provide for secure attach- Once the setup and angle measure- ting started. A linear-compensation ment that still allows for smooth ments are complete, use the following approach, which addresses first-order rotation on the surface. procedure to measure the gyroscope’s bias and scale-factor errors, will suffice 2. Install mechanical stops for two behaviors: for reaching less-than-1% composite angular positions. One idea would 1. Power the gyroscope on and allow errors. be to attach two M2 spacers using it to reach thermal stability. Many Averaging the MEMS-gyroscope M2 machine screws. Set the screws MEMS gyroscopes provide a tem- output while holding the device in a in positions that provide approxi- perature sensor for this purpose. constant position is a simple method 2. Start measuring the output while for estimating bias errors. The Allan AT A GLANCE holding the gyroscope against the Variance Curve for a gyroscope helps The purpose of MEMS first stop position. Continue sam- in analyzing the trade-off between test (microelectromechanical-system)- pling the output for the following time—that is, length of average—and gyroscope calibration is to translate steps. bias accuracy. You typically character- transducer behaviors into valuable 3. Wait 5 seconds and then turn the ize scale-factor errors using a servo- bits at the system level. gyroscope toward the second stop. motor stage, which employs an opti- You must determine the impact Begin with a smooth motion that cal encoder for precise rate control. of the MEMS gyroscope’s behav- takes 3 to 4 seconds to move the In this approach, MEMS gyroscopes iors and error patterns on system 90 span. rotate at known rates while provid- operation. 4. Wait 5 seconds and then rotate the ing output measurements. Although gyro back to the first stop using a this approach is effective and prob- The Allan Variance Curve helps similar motion. in analyzing the trade-off between ably necessary for later stages of devel- 5. Wait 5 seconds and then stop the test time and bias accuracy. opment and production, a simpler measurements. Save the data.

30 EDN EUROPE | JULY 2010 www.edn-europe.com Using the obtained time record, use Like any other bench- process, sufficient for managing these effects. the following steps to calculate correc- this one requires practice to refine and If not, repeating this process at two tion factors for this MEMS gyroscope improve. Experimentation will help power-supply levels and two tempera- (Figure 4): refine the speed of rotation, but it is tures will help mitigate the first-order 1. Calculate the bias-offset-correction important to make sure that the sen- effects. factor by averaging the first 3 seconds sor does not overrange at any point. This MEMS-gyroscope-calibration of data. The bias correction will be It is also important to make sure that procedure is relatively simple and the opposite polarity of this average. the surface is smooth, so that the requires little investment in equip- In this example, the bias-correction gyro assembly does not jump up and ment. For some systems, this process factor is 8.6/sec. This correction down during the rotation. Another provides the necessary accuracy. For yields an accuracy of greater than area of sensitivity is in approaching other applications, the process simpli- 0.1/sec for the bias estimate. the stop points. If the gyro “bounces” fies the proof-of-concept development 2. Subtract the bias estimate from the off the stop, it may introduce errors. phase, helping to justify the invest- time record. Then integrate output Using adequate transition times eases ment to subsequently either purchase data from the 4-second time stamp the burden of having accurate time or calibrate to the necessary accu- to the 9-second time stamp. In this stamps. The important thing is to racy when the final system goes into case, the measured angle displace- start integrating before the motion production. Managing optimal accu- ment is 95.1. The scale factor from begins and to stop integrating after racy across a wide range of tempera- this step is 90 divided by 95.1, or the motion stops. ture, power supplies, and other envi- 0.946. MEMS gyroscopes are sensitive to ronmental influences will require 3. Using the bias-corrected response acceleration and gravity. Therefore, more investment.EDN from Step 2, integrate output data orientation with respect to gravity is from the 12-second time stamp to worth consideration. In this example, AUTHOR’S BIOGRAPHY the 16-second time stamp. In this gravity has the least effect on the Mark Looney is an applications engi- case, the measured angle displace- gyroscope when you orient the sen- neer with Analog Devices, where his ment is 95.3. The scale factor sor’s axis of rotation to align with responsibilities include developing lit- from this step is 90 divided by 95.3, gravity. In some cases, power-supply erature and application information for or 0.944. and thermal influences may also need advanced inertial-sensing products. Loo- 4. Average the results of steps 2 and 3 management In other cases, repeat- ney obtained a master’s degree in electri- to calculate the scale-factor correc- ing this process immediately before cal engineering from the University of tion, which in this example is 0.945. taking critical measurements will be Nevada, Reno, in 1995.

Figure 4 A time record of the MEMS gyroscope’s output behaviors enables the calcula- tion of correction factors.