Summary. In spite of the success of traditional sampled-data theory in computer control it has some disadvantages particularly for distributed, asynchronous, and multi-rate system. Event based sampling is an alternative which is explored in this paper. A simple example illustrates the differences between periodic and event based sampling. The architecture of a general structure for event based control is presented. The key elements are an event detector, an observer, and a control signal generator, which can be regarded as a generalized data-hold. Relations to nonlinear systems are discussed. Design of an event based controller is illustrated for a simple model of a micro-mechanical accelerometer.

Event Based Control

Optimal dynamic quantizers for discrete-valued input control

This paper presents an optimal dynamic quantizer synthesis method for controlling linear time-invariant systems with discrete-valued input. The quantizers considered here include dynamic feedback mechanism, for which we find quantizer parameters such that the system composed of a given linear plant and the quantizer is an optimal approximation of the linear plant in terms of the input-output relation. First, the performance of an arbitrarily given dynamic quantizer is analyzed, where we derive a closed form expression of the performance. Based on this result, it is shown that the quantizer design is reduced to a nonconvex optimization problem for which it is hard to obtain a solution in a direct way. We obtain a globally optimal solution, however, by taking advantage of a special structure of the problem which allows us to relax the original nonconvex problem. The resulting problem is easy to solve, so we provide a design method based on linear programming and derive an optimal structure of the dynamic quantizers. Finally, the validity of the proposed method is demonstrated by numerical examples.

Synthesis of Optimal Dynamic Quantizers for Discrete-Valued Input Control

An important aspect of analog-to-digital conversion is the impact of quantization errors. This paper outlines how finite horizon constrained optimization methods can be utilized to design converters which minimize a weighted measure of the quantization distortion. We propose a novel converter, which can be implemented as a feedback loop. It embeds /spl Sigma//spl Delta/ conversion in a more general setting and typically provides better performance. We also examine the role played by the associated design parameters in ensuring error convergence.

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Multistep optimal analog-to-digital conversion

Sigma-delta modulation is the most popular form of analog-to-digital conversion used in audio applica- tions. It is also commonly used in D/A converters, sample-rate converters, and digital power amplifiers. In this tutorial the theory behind the operation of sigma-delta modulation is introduced and explained. We explain how performance is assessed and resolve some discrepancies between theoretical and experi- mental results. We discuss the issues of usage, such as limit cycles, idle tones, harmonic distortion, noise modulation, dead zones, and stability. We characterize the current state of knowledge concerning these issues and look at what are the most significant problems that still need to be resolved. Finally, practical examples are given to illustrate the concepts presented.

Understanding Sigma-Delta Modulation: The Solved and Unsolved Issues

Analog-to-Digital Conversion DS Modulators - Architectures Single-Bit Single-Stage DS Modulators, Modeling and Design Implementation of DS Modulators Practical Limitations of DS Modulators Stabilization and Suppression of Tones for the Higher-Order Single-Stage DS Modulators Decimation, Interpolation and Converters Applications

Delta-SIGMA Modulators: Modeling, Design and Applications

Wave active filters with reduced numbers of operational amplifiers are studied with regard to their sensitivity and the operation at high frequencies. An effective method of compensation for the effect of the finite gain/bandwidth product of the operational amplifiers is suggested and applied successfully. Finally, a ‘lossy’ and a ‘lossless’ WAF realising the same 6th-order bandpass function are compared with respect to their sensitivity and suitability for high-frequency operation.

Sensitivity and high-frequency performance of new wave active filters

The design of reliable single-bit sigma-delta (/spl Sigma//spl Delta/) modulators is considered. Observations on the behavior of various /spl Sigma//spl Delta/ modulators impose constraints on their noise transfer function (NTF) known as stability criteria. These constraints can be used to design /spl Sigma//spl Delta/ modulators with optimum performance. The optimality of the resulting /spl Sigma//spl Delta/ modulators can be shown by comparing the performance of the latter with the performance of modulators derived using other designing methods.

Optimal NTFs for single-bit /spl Sigma//spl Delta/ modulators

Existing models for the quantizer of /spl Sigma//spl Delta/ modulators make assumptions on the probability density function (pdf) of the quantization error, or some other convenient signal of the modulator. In this paper, a method for the determination of this pdf for single-bit /spl Sigma//spl Delta/ modulators is presented. First, a numerical method is proposed in order to solve the simplified equation for the quantization error pdf for first-order systems considering noiseless and noisy dc input signals. Then, it is shown how most practical high-order (>2)/spl Sigma//spl Delta/ modulators, resulting from well-established design methods, can be modeled as first-order systems plus an additive noise source at the input. Hence, their quantization error pdf is analyzed using the proposed method. Simulation results are shown to be in considerable agreement with those of the proposed method.

Numerical method for determining the quantization error PDF of single-bit /spl Sigma//spl Delta/ Modulators

The issue of stability of higher-order, single-stage Sigma-Delta (ΣΔ) modulators is addressed using a method from nonlinear system theory. As a result, theoretical bounds for the quantizer input of the modulators are derived. A new method for stabilizing the ΣΔ modulators is then presented. It uses the quantizer input bound for possible instability detection. Upon detection of such a state, the highest-order integrator is cut off, effectively reducing the order of the modulator, and thus resulting in a stable system. The method is easily implemented and results in a very good signal-to-noise ratio (SNR) and fast return to normal operation compared to other stabilization methods.

Theodore L Deliyannis

Papers

Delta-SIGMA Modulators: Modeling, Design and Applications

Sensitivity and high-frequency performance of new wave active filters

Optimal NTFs for single-bit /spl Sigma//spl Delta/ modulators

Numerical method for determining the quantization error PDF of single-bit /spl Sigma//spl Delta/ Modulators

Stabilization of third-order, single-stage Sigma-Delta modulators