Download Designing smart transducers using feedforward neural networks

Developing smart micromachined transducers using feed-forward neural networks: a
system identification and control perspective
E.I. Gaura, R.J. Rider, N. Steele
Coventry University, Priory Street, Coventry, CV1 5FB, UK
tel: +44-(0)2476-888825, fax: +44-(0)2476-888949
e-mail: [email protected]
I. Introduction
Despite the relatively short period during which artificial neural networks have been used in system
identification and control, there is already a rich history and a vast amount of literature describing successful
applications [1,2]. Most reported achievements are in the areas of process control, robotics and manufacturing.
There is no doubt that the use of such networks as been a major development in the field of control of nonlinear
systems [2]. A newer area of applications for neural networks is that of instrumentation systems, more specifically,
the development of intelligent transducers. As instrumentation equipment and measurement procedures become
more automated, the need for sophisticated sensors and a control approach increases [3]. This is particularly true
when developing acceleration measurement systems [4].
Since their inception, the acceleration sensors have generally been complex electromechanical devices,
consisting of relatively large proof masses, hinges and servos [5]. Recent advances in micro-electro-mechanical
system (MEMS) technologies have made possible silicon acceleration sensors of very small size and with low power
consumption [5]. Such features permit a wide range of possible applications where motion/movement-controlled
systems are used [6].
However, in spite of the advances in micromachining, no sensor is perfect in its manufacture and the capacitive
sensors considered here are no exception [3,4]. These devices not only exhibit non-idealities such as offset, drift,
non-linearity and noise, but also the magnitude of these non-idealities can vary. Moreover, fundamental
characteristics of the sensor, e.g. sensitivity, may be subject to manufacturing tolerances, varying material properties
and ambient effects [6]. Compensation of time-variant ambient effects requires continuous monitoring of these
effects and on-line correction of the sensor behaviour [3]. On the other hand, time-invariant departures from ideal
behaviour can be corrected using single-shot calibration procedures. Both correction procedures may require
additional hardware and software and must therefore be considered during the design phase of the sensor system [5].
In this paper, the issues of identification and control of such sensors are approached with the aim of developing
improved performance transducers. Several neural network based smart transducer designs are discussed, and their
performance compared to that of open-loop, off-the-shelf capacitive acceleration sensors.
II. The micromachined acceleration sensor identification problem
Amongst sensors, accelerometers are of special significance since by integrating their output signal,
accelerometers can additionally provide a measure of velocity and position. The class of acceleration sensors
considered here, are those with a capacitive type of pick-off [6]. The sensing element typically comprises a seismic
mass, which can move freely between two fixed electrodes, each forming a capacitor with the seismic mass, which
acts as a common central electrode. The differential change in capacitance between the capacitors is proportional to
the deflection of the seismic mass from the mid-position. A capacitive half-bridge technique is used for the
measurement of the differential change in capacitance. The pick-off method has the advantages of high output
levels, very low sensitivity to temperature drift, and, most importantly, can be readily used in force-balancing
configurations (closed-loop operation) [6]. Self-test can be implemented by applying voltages to the outer electrodes
to emulate the inertial force on the seismic mass.
The sensing element is basically a second-order system with a proof mass, a spring and a form of nonlinear
damping caused by the motion of this mass in a gaseous medium. The input to the system is the acceleration force
acting on the mass, causing it to deflect from the rest position. The output signal is a measure of the position of the
mass. The pick-off circuit can be modelled as a proportional gain factor, which converts the displacement of the
proof mass into a voltage [6].
It has been shown both by mathematical analysis and measurements that the micromachined devices described
above are dynamical nonlinear systems [6,7]. Enhancing the measurement performance of these devices implies
applying a form of control [7]. If a model-based control approach is chosen, the development of an accurate sensor
model is of paramount importance [1]. The most natural strategy would be to use a detailed mechanistic model of
the sensor as the basis of the controller [6]. Accurate mechanistic models, which would include manufacturing
tolerances and faults (in particular offset of the seismic mass), are difficult to generate for micromachined devices
[6]. Alternatively, the use of a generic non-linear process modelling technique could be considered, for example,
artificial neural networks [1].
The problem of identification consists of setting up a suitably parameterised identification model and adjusting
the parameters of the model to optimise a performance function based on the error between the real system and the
identification model outputs. Depending on the application area of the smart transducer to be developed, the sensor
identification can refer to:
 the static characteristic of the micromachined sensor – if the transducer is to be used in static-low frequency
applications, or
 the dynamic behaviour of the sensor – if the transducer is to be used over its entire frequency working range.
Both identification procedures are discussed here, and open-/closed-loop transducer designs based on the models
obtained are presented.
III. Sensor forward and inverse identification for static, low frequency applications.
A vital step in attempting to produce improved measurement performance when using acceleration sensors, is to
select a suitable control strategy to be applied to the sensing element. A large number of control strategies based on
neural networks have been proposed and used [1,2]. One of the simplest options, which could be used in static/low
frequency transducer applications, is open-loop, direct inverse control, which utilises an inverse system model. If the
model of the sensor is invertable, then the inverse of the sensor model can be approximated. This model is then used
as the controller. The inverse model is simply cascaded with the controlled system in order that the aggregated
system results in an identity mapping between the desired response (i.e. the network output) and the controlled
system input. Thus, the network acts directly as a controller in such configurations [1].
The transducer design proposed here (based on the above technique), addresses some of the manufacturing
problems associated with micromachined sensors having a capacitive type of pick-off. It has been shown, both by
mathematical modelling and by measurements that these devices are inherently nonlinear [6,8,9], two typical
nonlinear effects to be addressed being the offset of the seismic mass from the central position between the plates
and the squeeze film damping. The latter results in a dynamic nonlinearity. Compensating for these nonlinear effects
implies characterising the behaviour of the micromachined sensing element with a view of producing accurate direct
and inverse models of the sensor [8].
The identification procedure adopted here was based on static measurements, undertaken by mounting a sensing
element on a dividing head and rotating it in the gravitational field. In this way, accelerations of between 1g could
be applied to the sensing element. Several sensing elements have been tested using this experimental set-up. It has
been found that over the acceleration range of 1g, the sensor characteristics exhibited both offset and hysteresis.
Due to the presence of hysteresis, a dynamic type of neural network was needed for modelling both the inverse
and forward characteristics of the sensor. As only the static behaviour of the sensor was being considered, the wellestablished method of using tap-delayed-lines (TDL) dynamic networks was not suitable, as this method would
involve modelling the dynamic behaviour of the sensor and its inverse. The aim here is a fast design procedure and
simple hardware implementation of the smart transducer, with the possibility of network re-training on line, without
the use of sophisticated measuring equipment. A simple approach is proposed to design the type of network able to
compensate history dependent nonlinearities such as those exhibited by the sensor. The networks, for both the direct
and inverse models, are of a multilayer perceptron type, with two inputs, a single output and two layers of hidden
neurons. The novelty of the proposed network type consists in using a ‘flag’ in order to account for the one-stepback history of the signal to be processed by the network, as opposed to the tap-delayed approach found in the
literature [1]. Hence, one network input is the current value of the input signal, whilst the other is the ‘flag’ whose
value depends on the evolution of the input signal. The ‘flag’ takes arbitrarily chosen values of 0.99 if the current
input is greater than or equal to its previous value and -0.99 if it is less. Figure 1 shows the block diagrams of the
training schemes used for the forward and inverse neural models.
The training sets were based on input-output measurements taken from the sensor rotating in the gravitational
field. The static characteristic of the particular sensing element considered here is represented by the dotted line in
Figure 2. The sensor exhibits an average offset error of 203% and a hysteresis error of 16%. The sensitivity of the
device was calculated as 1.4V/g. A dynamic error-back-propagation training algorithm was designed which included
both a variable learning rate and momentum term [10].
Once trained, the inverse and forward networks were subsequently connected (cascaded) together to perform an
identity mapping, aiming at a 1V/g sensitivity for the calibrated sensor system. Tests undertaken by exciting the
simulated system with an array of sine wave signals, showed that the measurement system functionality has been
significantly improved.
Figure 1a: ANN training for forward modelling
Figure 1b: ANN training for inverse modelling
Output voltage [V]
1
0
-1
-2
-3
-4
-5
-1
-0.5
0
0.5
1
Input acceleration [g]
Figure 2: Measured static characteristic of a micromachined sensing element (dotted line); Effects of direct inverse
control on sensor behaviour (full line)
The success of this procedure encouraged the implementation of the smart transducer as an embedded system
with the neural processing being supported by an Intel 486 microprocessor. A block diagram of the smart transducer
hardware implementation is presented in Figure 3. A computer program was developed to read the input from the
ADC, filter and ‘flag’ the data and perform the neural processing. The calibration curve of the smart sensor obtained
using this novel approach is presented in Figure 2 (the full line). It can be observed that the offset was completely
compensated while the hysteresis error was reduced to 5%.
Figure 3: Block diagram of the smart transducer hardware implementation
The direct inverse control procedure implemented with ‘flag’ networks has been successful and uncomplicated
for this particular problem. For applications where accuracy and linearity is needed over a larger dynamic range and
at higher frequencies, the procedure may not, however, be straight-forward. Also, it may be noted that the system is
not robust to the incidence of extraneous disturbances, due to the open-loop nature of the control system. Moreover,
exposure to accelerations greater than a threshold value causes irreversible latch-up of the seismic mass to one or
other of the outer electrodes. One way of increasing the system robustness and stability is to apply some form of
feedback. This approach has been considered at simulation level and is presented next.
IV. Dynamic sensor identification
Based on the mechanical structure of the sensor [1], a good approximation of the sensor behaviour is given by:
ma  m
d 2 x A 
1
1  dx

  x (1)
2 
3 
2  (d 0  x) (d 0  x) 3  dt
dt
where: a is the input acceleration; m is the mass of the proof mass; x is the movement of the proof mass relative
to casing; A is the area of the proof mass; d 0 is the distance between the seismic mass and either of the outer plates
at rest; K is the spring constant and µ is the viscosity of air. By discretizing equation (1), it can be seen that the
output of the sensor is fully nonlinear in the input as well as the output signal history.
A series-parallel model procedure was adopted for the sensor identification, as shown in Figure 4. ‘TDL’ in
Figure 4 denotes a tapped delay line whose output vector has as its elements the delayed values of the input signal.
The identification neural network (INN) has three inputs (the sensor input at instant (k-1) and the sensor outputs at
the instants (k-1) and (k-2)) and one output (the sensor output at instant k).
xs k 
a k 
Scaled output voltage
1
Accelerometer
TDL
TDL
xs k  1
INN
a k  1
TDL
xs k  2
0.5

ek  1


0
-0.5
xˆ s k 
-1
-1
-0.5
0
0.5
1
Scaled input acceleration
Figure 4.: Series-parallel identification structure
Figure. 5: Scaled input-output sensor characteristic
A common choice in building the network training set for the purpose of identification is to perturb the
system/sensor with uniformly distributed white noise covering the whole dynamic range of the system. The working
range of the sensor has been identified as 5g in the amplitude domain and [0.5 - 80 Hz] in the frequency domain.
The scaled input-output sensor characteristic for white noise is presented in Figure 5.
A TDL-MLP 3-9-5-1 architecture has been trained up to a training error of 0.057/850 samples, in 50000 epochs.
The neural model obtained identified the sensor with a maximum error of 2%, over its entire working range. Thus,
the NN identification had a resolution of 0.1g for the whole range. In spite of all later attempts, it has been
impossible to obtain a more accurate global sensor model. Instead, several local models have been generated, and,
for example, a resolution of 0.05g was achieved for the range [15 - 80 Hz]. Such models could now be used as the
basis for both open- and closed-loop transducer designs, for a variety of applications in terms of imposed
measurement ranges.
Although designing an open-loop transducer based on the direct inverse control procedure is possible (by
adopting a similar procedure to that presented in Section III and replacing the “flag” networks by TDL-MLPs) and
would be beneficial in terms of performance enhancement, such a design would not eliminate the main drawback of
capacitive acceleration sensors, namely, the latch up condition for large input accelerations. Eliminating such
condition involves applying some form of feedback to the sensing element.
The small size of the sensing element allows electrostatic actuation to be used as a form of feedback [6]. Thus,
an opposing electrostatic force balances the inertial force acting on the proof mass. The nonlinear mapping
capabilities of neural networks could be used for controlling the sensing element and linearising the electrostatic
forces. A block diagram representation of the proposed system is given in Figure 6.
Prior to the neural network design approach, simple linear PI control has been attempted [6] but this fails to solve
latch-up problem. Nevertheless, the PI approach has been used in many devices described in the literature [6] since
it does improve the sensor performance compared to open-loop operation.
Fig.6: Block diagram of closed-loop neural transducer
In the block diagram of Figure 6, the feedback neural network (FNN) has two functions. Firstly, it calculates the
square root of the output voltage, providing a linear feedback relationship between the system output and the
electrostatic forces acting on the electrodes. Secondly, the network demodulates the output signal in order to apply
the feedback to only one electrode at a time: the bottom electrode will be activated if the proof mass has moved
towards the top electrode and vice-versa [7].
Two options were investigated for the design of the Controller Neural Network (CNN). The first one involved
simply replacing the PI controller by a static neural network, which provides a soft-limiting nonlinear gain control.
The second was based on a Model Reference (MR) control procedure. Both transducer designs combine the
advantages of linear feedback electrostatic forces and time domain separation of feedback signals. Upon completing
the design process, the functionality of the systems was studied by subjecting the transducers to a wide variety of
stimuli and establishing both their advantages and limitations.
A. Static neural network for closed loop sensor control
A simple MLP with one input, six hidden neurons and one output was trained to perform the sensor control task in
closed loop. Upon completion of training, the network was incorporated within the transducer structure. The system
obtained exhibits a maximum departure from linearity of 3.8% over the range 6g (as opposed to linearity over the
1g range for the “off-the-shelf” sensing element), maximum hysteresis of 5% between 6g and 8g, followed by
saturation for acceleration magnitudes in excess of 8|g|. This performance compares with a departure from linearity
of 8% for the conventional PI transducer, over its entire dynamic range of 4g. Shocks in acceleration of up to 25g
can be withstood by the transducer, without irreversible latch-up.
According to the application requirements for the acceleration sensor, the design can be easily altered. Improved
linearity can be obtained for a restricted range (precision applications), or the whole dynamic range extended, by
reducing accuracy in linearity.
B. Dynamic neural network for closed loop sensor control
In an attempt to exploit the dynamic mapping abilities on neural networks, a Model Reference control structure was
used for designing the CNN (Figure 7). In this case, the desired performance of the closed-loop system is specified
through a stable, linear reference model (Ideal Sensor Model in Figure 7). The control system attempts to make the
system output match the reference model output asymptotically. The error “e” is used to train the network acting as
the controller (CNN). This approach is related to the training of inverse system models: when the reference model is
the identity mapping (which is the case here), the two approaches coincide.
The neural controller trained was of a tap delayed lines multilayer perceptron type, with 3 inputs (the system
outputs at instants k, (k-1), (k-2)), two hidden layers and one output (the input acceleration at instant k). White noise
was used for network training, covering the magnitude range of ±10g. Upon completion of the training process, and
inclusion of the CNN in the closed loop structure, the transducer exhibited a sensitivity of 1V/g and a measurement
error of maximum 5% over the ±7g, [0,80Hz] ranges. Shocks in acceleration up to 50g can be whistood by the
transducer, the latch up condition being virtually eliminated.
Compared to the static CNN, the dynamic controller was more difficult to train and no significant improvement
on the above figures could be obtained by varying either the network architecture, training set or length of training.
Model Reference
(Ideal Sensor model)
1[g/V]
Model Reference
output
error
Input
acceleration
+10g
+

–
Micromachined
Acceleration Sensor
(Mathematical Model)
White
noise
NN
controller
NN
NN
output
+  –
Training
–10g
Feedback
Electrostatic
forces
Square root
NN
Figure 7. Model Reference, closed-loop training scheme for the CNN with white noise acceleration input
V.
Conclusions
The paper describes some possible applications of feed-forward neural networks in the sensorial field. The
subject of the research was a micromachined acceleration sensor, with a capacitive type of pick-off. Static sensor
identification (based on measurement results) and dynamic identification (based on the mechanical model of the
sensor) was performed with a view to develop, neural, open- and closed-loop transducers with improved
performance characteristics. Measurement results are presented for the open loop, neural transducer, which was
implemented in hardware. Two closed-loop structures were proposed which used static and/or dynamic networks.
The performance of these transducers was assessed based on simulation results. All neural network controlled
transducers showed an extended measurement range compared to the “off-the-shelf” sensors and, in the closed loop
designs, the latch-up condition was eliminated.
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