UPDATED: 12/00/99

BY: Chris Holand?

Its assumed that the ADXL202 will work for this sensor application. The maximum acceleration that the ADXL202 will read is 2g. It is possible that this might be exceeded by the helicopter vibration. Consequently, all readings should be checked for over range values. If they occur, the ADXL202 can be replaced with the ADXL210 which reads a maximum acceleration of 10g.

When implementing the ADXL202 data into the control system,
a compromise must be made in determining a value to use for calculation of the
tilt angle. Referring to the data sheet,
you will see that the sensitivity of the ADXL202 changes with the tilt
angle. For angles less than ±30°, the
change is very small and average value could be used with out introducing a
large error. For the rate damping part
of the control system, the primary concern is not necessarily with the exact
angle of tilt, but with the change in tilt.

A 0.1µF capacitor is required for power supply decoupling with 100Ω in supply line for additional decoupling.

Equation for -3dB bandwidth:

_{} =_{}

Where C is the value of the capacitance used on both analog
outputs. From table 1 in the data sheet, a value of 0.47µF gives a -3dB of
10Hz. **For MicroCART, the low bandwidth will filter out any vibrations that
have a frequency higher than 10Hz**.
This takes care of a lot of problems that could occur due to
vibration. The bandwidth of the ADXL202
is 0.01Hz to 5 kHz. If 10Hz bandwidth doesn’t eliminate vibration, then the
bandwidth of the ADXL202 can be lowered to near DC levels.

Even for analog operation, the DCM period must be set by R_{set}
resistor. Any value between 500kΩ and 2MΩ will work. For this
project a 1.3MΩ resistor will be used.

It should be noted that the device itself has noise with characteristics of white Gaussian noise that contributes equally to all frequencies. The noise is proportional to the square root of the bandwidth of the accelerometer and is described by the following equation:

_{}

It should be noted from this equation that the noise decreases as the bandwidth decreases. For more detailed information about noise, consult the data sheets.

Figure 1 shows the schematic for tilt sensing. The diagram does not give the orientation the
accelerometer must be in for two axis tilt sensing. This can be determined from the data sheet
easily. Capacitor C_{DC} and
resistor R_{f} is for power supply decoupling and R_{SET} is
used to set the DCM period which isn't used, but must have a value. Table 2 has
a list of the values used in the schematic.

Figure 1. Schematic for ADXL202.

** Component Value**

C_{Yfilt}=C_{Xfilt} 0.47µF

C_{DC} 0.1µF

R_{SET} 1.3MΩ

R_{f} 100Ω

Table 2. List of component values for figure 1.

The sensitivity of the ADXL202 relative to the supply voltage is given by the following equation:

_{}

At a power supply of +5V, V_{dd}, results in 300mV/g. For future reference in the document, the
sensitivity will be as:

_{}

The zero g offset is found from the following equation:

_{}

Again at the power supply voltage of +5V, V_{dd}, the zero g offset is +2.5 V.

From figure 14 of the ADXL202/ADXL210 spec sheets, you can see that the output varies slightly due to different orientations. A valid assumption is that the ADXL202 will not have to measure angles more than ±30°. This makes the variation negligible. For the following calculations, it’ll be assumed that the ADXL202 will measure angles of ±45°. This will represent the extreme for determining the sensitivity of the output relative to a degree change in tilt. Again from figure 14, the output will change by 12.2 mg/degree tilt. This will result in a change of:

_{}

If the instrumentation amplifiers have an offset voltage on the order of 100µV, they will not introduce any significant error.

With a sensitivity of 300mV/g, the ADXL202 will have an output that varies from 2.5±300mV. Hence, the instrumentation amplifiers will need gain. Using the extreme of ±45° again, the output of the ADXL202 will vary ±0.707g. This results in a variance of:

_{}

Using an amplification of 5 V/V:

_{}

Therefore the range of measuring voltages will be:

_{}

The MicroGyros will read a maximum angular velocity of ±150 deg/sec. The sensitivity is 1.11mV/deg/sec. The analog output is defined as:

_{}

where V_{ref} is 1.225 V and V_{g1,g2} is an
output that changes according to applied rotation. Since no movement implies a zero output, V_{g1},V_{g2}
equals V_{ref} in this condition.
Over the full range of the sensor:

_{}

According to the data sheet, single ended measurement cannot
be made of V_{g1} or V_{g2} outputs. The measurement of output has to be take as
the difference as stated before. Hence,
the difference will result in an net output of:

_{}

Using an amplification of 5 V/V:

_{}

Figure 2 shows the schematic for the MicroGyro. The following is a listing of the pin number
and the corresponding name for the pin.
The capacitor C_{BC} is for decoupling the power supply.

1.
V_{ref1}

2.
V_{g1}

3.
G_{nd}

4.
V_{dd}

5.
V_{ref2}

6.
V_{g2}

7. Wake

8. Temp

9. NC - No Connection

Figure 2. Schematic for MicroGryo.

Note that the wake pin needs to be high in order for the device to function. The optional temperature sensor pin is not used in this diagram.

__AD623__

The basic circuit for use with the AD623 instrumentation
amplifier is shown in figure 3. Its
possible for op amps to rectify RF signals which shows up as a DC offset. This design is taken from the data sheets and
has the specific benefit of attenuating any RF interference. Table 2 has a list of the components of the
corresponding value. The resistor R_{G} sets the gain at 5 V.

__Component Value__

C_{1}=C_{2} 1000pF

C_{3} 0.047µF

C_{S1} 0.033µF

C_{S2} 0.01µF

R_{G} 24.9kΩ

R_{1}=R_{2} 4.02kΩ

Table 2. List of component values for figure 3.

All resistors should be 1% or __better __metal film
units. All the capacitors __need __to
be 5% or __better.__ These components
need to be precise as possible otherwise the benefits of using this circuit
design and precision instrumentation amplifier are wasted.

Figure 3. Schematic for the instrumentation amplifier AD623.

V_{ss} is connect to Gnd for connection to the
ADXL202, but the MicroGyros require V_{ss} to be connection to a
negative power supply in order to allow the output to swing negative. This in amp is rail to rail on operation of a
single supply only, hence leave room between the maximum negative voltage
needed for output and the negative power supply.

Here is some general information that needs to be considered when choosing the A/D converter. The sensitivity of the ADXL202 was determined to be 300 µV/g and the MicroGyro is 1.11mV/deg/sec. In both cases a gain of 5 V/V was used. This results in new sensitivity of 1.5 mV/mg and 5.55 mV/deg/sec for the ADXL202 and the MicroGyro respectively. In the worst case, the ADXL202 changes 12.2mg/degree, hence the output will change:

_{}

This is the worst case for sensitivity of the ADXL202. Therefore, the MicroGyro is the limiting factor in choosing the resolution of the A/D converter. Use of a 10 bit A/D converter over 0 to 5 V would result in the following resolution:

_{}

Since 4.88 mV < 5.55mV for the MicroGyro, 10 bits of resolution is sufficient for the A/D converter.

All sensors and amplifiers need to be decoupled from the power supply. If possible, a separate supply and ground should be used for the analog devices. This help minimize the digital noise. Both the ADXL202 and the MicroGyro have an offset voltage that needs to be determined and compensated for. Data sheets for both devices have information for how to go about doing this. Temperature compensation is something that can be considered for the MicroGyro.

Data sheets are available from the Analog Devices web site for the ADXL202 and the AD623 (http://www.analog.com). Information for the MicroGyros is also available at their web site (http://www.gyration.com). I have also found the following references useful about helicopter flight, control systems, and general information:

·
__The Helicopter__ by John Fay, ISU call
number TL 716 F35 1976 C.2, this was an easy read about helicopters, but had
good general information

·
__Foundations of Helicopter Flight, __by
Newman, ISU call number TL716 N39 1994b

·
__Helicopter Performance, Stability, and
Control,__ ISU call number TL716.P725 1986

·
__The Art and Science of Helicopter Flight,__
I don't have the call number, but I think this was the best book overall. It does a very good job of explaining
Automatic Flight Control Systems (AFCS)

·
__Automatic Flight Control__, ISU call number
TL 589.4 P34 1993