Institute for Systems Research Technical Reports

Our approach to this problem is based on plant diagonalization.To do this, we search for basis transformations for the vector of outputs coming from the sensors and the vector of inputs applied to the actuators so that, in the new bases, the MIMOsystem becomes a collection of decoupled SISO systems.This formulation provides a number of advantages for the synthesis and implementation of a feedback control law,particularly for systems where the number of inputs and outputs is large.

Of course, in order for this idea to be feasible,the required basis transformations must have properties which allow them to be implemented on a distributed control network. Namely, they must be computed in a distributed manner which respects the spatial distribution of the data(to reduce communication overhead) and takes advantage of the massive parallel processing capability of the network (to reduce computation time).

In this thesis, we present some tools which can be used to find suitable transforms which achieve "approximate"plant diagonalization. We begin by showing how to search the large collection of orthogonal transforms which are contained in the wavelet packet to find the one which most nearly, or approximately, diagonalizes a given real valued matrix.Wavelet packet transforms admit a natural distributed implementation,making them suitable for use on a control network.We then introduce a class of linear operators called recursive orthogonal transforms (ROTs) which we have developed specifically for the purpose of signal processing on distributed control networks.

We show how to use ROTs to approximately diagonalize fixed real and complex matricesas well as transfer function matrices which exhibit a spatial invariance property. Numerical examples of allproposed diagonalization methods are presented and discussed.

We offer a method for computing a workingapproximation to the controllability energy function, one of the mainobjects involved in the method. Moreover, we show that for a class ofsecond-order mechanical systems with dissipation, under certain conditionsrelated to the dissipation, an exact formula for the controllabilityfunction can be derived. We then present an algorithm for a numericalimplementation of the Morse-Palais lemma, which produces a local coordinatetransformation under which a real-valued function with a non-degeneratecritical point is quadratic on a neighborhood of the critical point.

Application of the algorithm to the controllabilty function plays a key rolein computing the balanced representation. We then apply our methods andalgorithms to derive balanced realizations for nonlinear state-space modelsof two example mechanical systems: a simple pendulum and a double pendulum.

The second part (Chapter 5) deals with modeling of rapid thermal chemicalvapor deposition (RTCVD) for growth of silicon thin films, viafirst-principles and empirical analysis. We develop detailedprocess-equipment models and study the factors that influence depositionuniformity, such as temperature, pressure, and precursor gas flow rates,through analysis of experimental and simulation results. We demonstratethat temperature uniformity does not guarantee deposition thicknessuniformity in a particular commercial RTCVD reactor of interest.

In thethird part (Chapter 6) we continue the modeling effort, specializing to acontrol system for RTCVD heat transfer. We then develop and apply ad-hocversions of prominent model reduction approaches to derive reduced modelsand perform a comparative study.

In this work we report on experimentalresults obtained with a deformable tactile sensor whose properties arewell-suited to manipulation. The results presented here show that thesensor described provides a rich set of tactile data.

The overallobjective is to improve manufacturing effectiveness for epitaxial growth ofsilicon and silicon-germanium (Si-Ge) thin films on a silicon wafer. Growthtakes place in the ASM Epsilon-1 chemical vapor deposition (CVD) reactor, aproduction tool currently in use at ESSS. Phase II project results includedevelopment of a new comprehensive process-equipment model capable ofpredicting gas flow, heat transfer, species transport, and chemical mechanismsin the reactor under a variety of process conditions and equipment settings.

Applications of the model include prediction and control of deposition rate andthickness uniformity; studying sensitivity of deposition rate to processsettings such as temperature, pressure, and flow rates; and reducing the use ofconsumables via purge flow optimization. The implications of varioussimulation results are discussed in terms of how they can be used to reducecosts and improve product quality, e.g., thickness uniformity of thin films. We demonstrate that achieving deposition uniformity requires some degree oftemperature non-uniformity to compensate for the effects of other phenomenasuch as reactant depletion, gas heating and gas phase reactions, thermaldiffusion of species, and flow patterns.

(This work to appear in Proc. 1999 American Control Conference.)

The DHOBE algorithm, for eachrecursion, returns an outer bounding ellipsoid of the estimated parameters. If the center of the ellipsoid each time istaken as the model coefficients, the explicit model update isimplemented which leads to a model-reference method. If we choose theworst-case point which maximizes the cost function in the set, then wecan apply the set-valued worst case approach. These two methods were compared with two other main RtRcontrol schemes: the Exponentially Weighted Moving Average (EWMA) methodand the Optimizing Adaptive Quality Controller (OAQC) method. Simulation results showed the superior performance of the RtRcontrollers based on the DHOBE algorithm. Furthermore this paper showedthat it is necessary to applynonlinear models to compensate for severe nonlinear processes.