All sensory units in the device count on the conditioning circuits to convert the measured physical signals into the readable voltage. Since the spatial limit in the head area restricts the adoption of the off-the-shelf products that mostly appear to be too bulky to be installed, the primitive sensors are incorporated in the mechanical parts of the device instead. Therefore, those sensors must undergo a process of calibration for magnitude correctness before put into use.
A. Tilt Measurement Unit Calibration
Calibration of tilt sensors attempts to eliminate the errors in the output, which are derived from three aspects, i.e. the inclination of sensor installing plane, the sensitivity along each axis and the calculation. According to the product manual, the sensitivity that may exhibit difference in two axes due to a mismatch and an offset, results in a carried coefficient involved into the further calculation, as express in Eq. (4-15). Inclination upon the installation of the sensor here refers to the sensing plane (plane XOY referring Figure 4-13) tilt towards the third axis, which could occur during soldering the sensor to circuit board, mounting the board to the device, or wearing the device. So the sensitivity at that power level could be shrunk on both axes due to a tiny angle of the inclination on the plane XOY, leading to the actual rotational angle differing from the calculated one.
ܣை்ሾ݃ሿ ൌ ܣைிி ሺܩܽ݅݊ ൈ ܣ்ሻ (4-15)
Since the installation-plane inclination could hardly be avoided during the wearing for practice, the likely angle will only be rectified through online calculation of the data acquired in operation. The sensitivity on each axis is calibrated in order to re-establish the relationship between the actual tilt angle and the output voltage. Each axis is firstly placed into a +1g and - 1g field to obtain the output voltage of that acceleration, as given in Eq. (4-16); and the sensitivity-related parameters can be calculated in Eq. (4-17) for each axis, which are used to finally calculate the actual sensitivity in Eq. (4-18). By integrating Eq. (4-8), the acceleration at each axis can be expressed in Eq. (4-19) to further calculate the tilt angle in Eq. (4-10).
ቊ ܣାଵሾ݃ሿ ൌ ܣைிி ሺܩܽ݅݊ ൈ ͳ݃ሻ ܣିଵሾ݃ሿ ൌ ܣைிி ൫ܩܽ݅݊ ൈ ሺെͳ݃ሻ൯ (4-16) ൞ܣைிிሾ݃ሿ ൌ ͳ ʹ൫ܣାଵሾ݃ሿ ܣିଵሾ݃ሿ൯ ܩܽ݅݊ ൌͳ ʹ൫ܣାଵሾ݃ሿ െ ܣିଵሾ݃ሿ൯ (4-17) ܣ்ሾ݃ሿ ൌ ሺܣை்െ ܣைிிሻ ܩܽ݅݊Τ (4-18) ܣ்ሺǡሻൌ ൬ܸሺǡሻെ ͳǤ ͳǤ͵ʹ െ ܣைிி൰ ܩܽ݅݊ൗ ሺǡሻ (4-19) Where:
ܣേଵሾ݃ሿ is calculated from the measured voltage ܸାଵ and ܸିଵ based on േభଵǤଷଶିଵǤ respectively.
The third-axis inclination shrinks the sensitivity on both axes in a relationship with the tilt angle ߮, as expressed in Eq. (4-20); the output acceleration at each axis that associates with
the measured voltage is the component of the actual acceleration projected to the XOY plane, which is formulated in Eq.(4-21). By referencing Eq. (4-10), the angular displacement measured by the two-axis sensor is deduced without being affected from the third-axis inclination.
ܣை்ሾ݃ሿ ൌ ܣ்ሾ݃ሿ ή ሺͳ݃ ൈ ߮ሻ ൌ ൜ ߠ ߮ ǡ ߠ ߮ ǡ ܺ െ ܽݔ݅ݏܻ െ ܽݔ݅ݏ (4-20)
ܣ்ሺǡሻ ൌ ܣை்ሺǡሻΤ ߮ൌ ൜ ߠ ߮ ߠ ߮ΤΤ ǡǡ ܺ െ ܽݔ݅ݏܻ െ ܽݔ݅ݏ (4-21)
Where: ߮ is the third-axis inclination angle.
The circuit board is mounted on the larger gear in a two-meshed gear set that rotates around each center, all of which are fixed onto an upright board. The gear teeth ratio is 1:12, which suggests a cycle rotation of the small gear triggers the circuit board rotating by 30°. The calibration is not carried out by incremental rotation, which though is supportive by the setup; only distinctive positions (±1g for both X/Y axes) are chosen to measure the corresponding output voltage.
A NI DAQ card USB-6210 that links the circuit board to PC via USB port is used for calibration to convert the voltage into the readable digital signal flow (setup given in Appendix Figure 8-6). Since the DAQ card supports 16 channels of analog input with 16-bit resolution, higher than the required one to be offered by ADC module, it is able to provide a precise matching relation for all analog converting scenarios through calibration to the electronic system that might be taken advantage to compose of the future control hardware for signal acquisition. Further data processing includes extraction of the data through three modules, i.e. the acquisition, data filter and recording output, which are fulfilled by a program built in the Simulink, as entirely depicted in Figure 4-18 (A). The acquisition module is configured to run in the asynchronous mode and sample the voltage for single-ended input at the rate of 500 Hz, as shown in Figure 4-18 (B). A filter block is affiliated into the program in order to eliminate the noise that may be derived from the interference of multiple channels crossing the ground during the input varying basically via two steps, i.e. a median filter to smooth the signal flow out and then a Butterworth filter to meet the attenuation specifications, as reformatted to output shown in Figure 4-18 (C).
A
B
C
Figure 4-18 Experimental-rig to calibrate the Flexiforce sensor
The voltage at each incremental angle averaged to a single value is sketched out for both axes in Figure 4-19, where the theoretical ones are also illustrated for comparison. The actual sensitivity on the X-axis is deviated from the theoretical about 5%, also accompanied with an offset of 5%, since the zero value can hardly be searched; the offset on the Y-axis is adequately small to be neglected. The clearance along both axes hit the peak smaller than 0.05 V, which may bring about 3° error intrinsically. The output curve in Figure 4-20 approaches closely to the theoretical line, with the error at each incremental step shown in dashed line. The error is approximately between -2° to 2°.
Figure 4-19 The voltage acquired during calibration versus the theoretical one
OutVal Mean Std Stats Scope1 OriVal OutVal Record OriVal DAQ Check Static Range 1 OriVal t U( : ) U( : ) Median Mean butter Filter Clock nidaq Dev1 USB-6210 500 samples/sec HWChannel1 Analog Input |u| Abs1 1 OutVal Switch Submatrix Standard Deviation A B Overwrite Values <= 0.05 Compare To Constant Enable 1 OriVal
Figure 4-20 The tilt angle after calibration
B. Calibration of Flexiforce Sensor
Since Flexiforce sensors that are multiply recruited in the device may exhibit small variance in the resistance; each of them is calibrated upon its own conditioning circuit for operational amplifying. As requested, sensors of two measurement ranges are matched to the two circuit boards in each of identical sorts, totally up to six channels of the corresponding voltage outputs. The USB-6210 DAQ card is recruited again together with the corresponding acquisition block built in Simulink for the data processing.
The sensing area can be treated as a single point according to the manual. For the sensor that never experienced loads before, conditioning is essential to be undertaken on the sensor by placing 110% of the maximum loads to be measured for four times, for the purpose of diminishing the effects of drift; each conditioning usually consumes 20s to 30s till the sensor getting stabilized, and the whole conditioning setup in the loading machine that should be identical with the one for calibration. During calibration, each sensor is placed in the workbench of the machine one by one to bear a string of specified loading that increases gradually with a step size 25g and 500g from zero up to 450g and 10kg for the sensor of force ranging to 1 lb and 25 lb, respectively; the corresponding voltage at each loading condition is recorded in MATLAB.
An approximate linearity is illustrative of the force-voltage correlation according to the plotted data, which generally conforms to the physical characteristics of Flexiforce sensor. With an acquired voltage, the corresponding force on the sensor can be inversely calculated by linear interpolation or extrapolation; and this correlation can hereby be exactly curve-fitted to an expression of Eq. (4-22).
ሺ݅ሻ ൌ ሺ݅ሻ (4-22)
Where:
ሺ݅ሻǡ ሺ݅ሻ represents the loaded force and the mean voltage value of four-time loading, respectively; ǡ are constants to stand for the linearity between voltage and force.
A
B
Figure 4-21 Calibration of the force sensors
The curve-fitting is processed in MATLAB to solve the parameters in each sensor, where the least square method is applied by default. Generally, extrapolation that should be avoided in speculating the outranged force would not be involved in the calculation as the calibrated coverage basically fits the force may occurred herein. Meanwhile, as errors are inevitably accompanied in the practice, the sensors have also been investigated in terms of the precision based on the calibrating data, including characteristics of non-linearity, repeatability, and the hysteresis, apart from the drift prior to the calibration in request; according to the manual where the drift rate is given within 3%/logarithmic time, the precision of further calibration for all current sensors subject to the drift is acceptable.
Figure 4-21 illustrates the conditioning drifts of sensors on the top and one group of the relationship established between the acquired voltage and the incrementally applied force on the bottom via curve fitting. A simple GUI coded in MATLAB for easily recording the acquired voltage values at each step of loading which are further averaged over four times to compose of the calibrating point in the curve.