Christopher P. Lewis

A novel micromachined accelerometer capacitive interface

In this paper a feasibility study of a novel interface concept is described for the design of a closed-loop accelerometer based upon a micromachined capacitive sensing element. The approach combines the advantages of the simple signal pick-off arrangement typically used for analogue accelerometers with those of accelerometers based upon an oversampling technique or sigma-delta modulation, which include direct digital output signal, an inherent self-test feature and improved system stability. The interface circuitry is low in component count, which makes it particularly suitable for prototype evaluation, yet has the potential for a high-performance device.

Mathematical model for a micromachined accelerometer

A mathematical model is developed for both open- and closed-loop accelerometers having capacitive sensing and electrostatic feedback. Test results on actual micromachined devices are compared with simulation employing the mathematical model.

A low cost analogue current transducer

The development and construction of a low cost current transducer is described. A simplified mathematical model is derived by filtering the limit cycle with a low pass filter. The test results were made with a variety of ferrite cores. As no Hall effect device is required, there are considerable manufacturing advantages and the device is not temperature sensitive.

Stability of nonlinear systems and the effects of time delay control

The study of dynamical systems is of significant practical importance. We investigate here the concept of the safe basin and the use of the amplitude/frequency of forcing parameters plane which can be applied to a wide range of dynamical systems including control applications. A computer aided study of the performance of such systems using Matlab/Simulink with a Watcom C/C++ compiler is illustrated. The technique is easy to use and is only limited by the properties of the Matlab/Simulink programme in which the system is simulated. The behaviour of a pressure transducer is used as a simple example; as a further example the stab ility and robustness of a practical control strategy, designed to control chaotic behaviour, has also been investigated.

Digital pressure transducer

A closed-loop digital pressure transducer is described which employs a quartz sensor embedded into a sigma delta modulator. Limit cycle analysis and test results are included for this nonlinear discrete-data system.

Chaos in sigma-delta modulator-based transducers

Work based upon the application of computer techniques for the study of safe basins of stability and Poincare sections for such devices has been extended to investigate the performance of high order models and also the relation to their forced performance. This paper combines a standard approach with methods based on ideas stimulated by chaotic solution. The effects of integrator leak, saturation, and nonlinear compensation techniques are also investigated with a view to chaotic behavior. Work previously due to Feely & Chua has also been extended to include higher order models.

Dynamic Behaviour of Fröhlich's Brain-Wave Model

Abstract Motivated by the empirical finding that the EEG corresponding to varying degrees of consciousness exhibit deterministic chaos to a corresponding degree, Frohlich’s Brain-Wave model is analysed for the first time in its full generality (3 degrees of freedom). Some new results are presented concerning the response of the system to external stimuli - both ac and dc . In contrast to an earlier claim that a restricted version of the model (containing only 2 degrees of freedom) exhibits a chaos only when the external stimulus contains both ac and dc components, we find that ac component alone is sufficient. Readmitting the 3rd degree of freedom can result in much more complex bifurcation scenarii, as is readily seen from consideration and comparison of the control space basins.

Control System Design Study for a Micromachined Accelerometer

Abstract In this paper an analogue, closed loop accelerometer based upon a bulk-micromachined, capacitive sensing element is described. The sensing element is embedded in a closed loop control system using electrostatic forces as a reset mechanism. A mathematical model is derived which allows to employ conventional linear control theory. The validity of the model is discussed. Particular attention is paid to the controller design; here a PID controller is used. The simulated results are compared to measurements on the actual hardware prototype.

Computer aided study of the dynamic behaviour of nonlinear systems

Abstract A design aid developed in a Matlab/Simulink environment is presented which may be used given to examine the dynamic behaviour of nonlinear systems. The degree of stability of a system is determined by the control space basin. In the case of a disturbance the transient motion of the system is observed from a range of initial conditions. The technique is extended to enable the investigation of the accuracy and sensitivity of closed loop analogue and digital transducers.

Dynamic Behaviour of Nonlinear Measurement Systems

Abstract A computer based technique has been developed to test the performance of complex nonlinear systems, using Matlab/Simulink™ and C/C++. In this approach a dynamic system, represented by its mathematical model, is stimulated by a sequence of sinusoidal signals and the system stability is observed by a stability diagram. Furthermore the technique is developed to test the degree of accuracy and sensitivity of transducers. Such devices are complicated nonlinear, closed-loop, systems in their own right. In this paper the long term stability of a typical pressure transducer model with hard and soft spring effects is examined. The range of use is determined by a shaded stability diagram. In addition performance of a micromachined, silicon, accelerometer is examined. Important properties of the accelerometer such as the degree of accuracy and sensitivity are considered