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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 ek 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. References Irwin, G.W., Warwick, K., Hunt, K.J., “Neural networks applications in control”, IEE Control Engineering Series 53, Short Run Press Ltd., UK, 1995 2. Steele, N., Gaura, E., Godjevac, J., "Neural Networks in Control", The 3rd European IEEE Workshop on Computer-Intensive Methods in Control and Data Processing, Proceedings, pp.187-199, Prague, Czech Republic, Sept. 1998 3. Lang, W., “Reflections on the future of microsystems”, J. Sensors and Actuators 72 (1999), pp. 1-15 4. Bao, M., Wang, W., “Future of microelectromechanical systems (MEMS)”, J. Sensors and Actuators A 56 (1996), pp. 135-141 5. Hosticka, B. J., “CMOS sensor systems”, J. Sensors and Actuators A 66 (1998), pp. 335-341 6. Kraft, M. : "Closed-loop accelerometer employing oversampling conversion", PhD Thesis, Coventry University, 1997 7. Gaura, E., Steele, N., Rider, R.J., "A Neural Networks approach for the design of micromachined accelerometers", International Conference in Computational Intelligence for Modelling, Control and Automation, Proceedings, pp.117-121, Feb. 1999, Vienna, Austria 8. Gaura, E., Steele, N., Rider, R.J., "A Neural Network Approach for the Identification of Micromachined Accelerometers", Second International Conference on Modelling and Simulation of Microsystems, MSM’99, Proceedings, pp.245-248, April 1999 San Juan, Puerto Rico, USA 9. Steele, N., Gaura, E., Rider, R.J., "Direct Inverse Control Of Sensors By Neural Networks For Static/Low Frequency" ICANNGA’99, Proceedings, Portoroz, Slovenia, April 1999 10. Gaura E., Burian A., "A dedicated medium for the synthesis of BKP networks", Romanian J. of Biophysics, Vol. 5, No. 15, 1995, Bucharest, Romania. 1.