### Browsing by Author "Frankpitt, Bernard A."

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Item A Computational Method for Hontroller Design in the Frequency Domain(1994) Frankpitt, Bernard A.; Berenstein, Carlos A.; Baras, John S.; ISRA new approach to frequency domain design of robust controllers for distributed parameter systems is presented. The central idea is to use techniques that were developed for the solution of the Corona Problem, for the solution of both the Bezout equation and an auxiliary equation that arises form the Nehari interpolation problem. An algebraic reformulation of these equations allows the solution to be computed from the solution of an inhomogeneous Cauchy Riemann equation with a Carleson measure as the inhomogeneous term. The theory is applied to a single input single output system with delay to yield the transfer function of a stabilizing controller with guaranteed Hstability margin. Finally the framework is extended to handle multi-input multi- output systemsItem Estimation of Hidden Markov Models for Partially Observed Risk Sensitive Control Problems(1997) Frankpitt, Bernard A.; Baras, John S.; ISRWe look at the problem of estimation for partially observed, risk-sensitive control problems with finite state, input and output sets, and receding horizon. We describe architectures for risk sensitive controllers, and estimation, and we state conditions under which both the estimated model converges to the true model, and the control policy will converge to the optimal risk sensitive policy.Item A Frequency Domain Design for the Control of a Distributed Parameter System(1993) Frankpitt, Bernard A.; Baras, J.S.; Berenstein, C.A.; ISRThis thesis presents a new approach to frequency domain design of robust controllers for distributed parameter systems. The central idea is to use techniques from complex analysis, that were developed for the solution of the Corona Problem, for the solution to the Bezout equation that arises in the parameterization of stable feedback controllers. An algebraic reformulation of the Bezout equation allows the solution to be computed from the solution of an auxiliary equation with a Carleson measure as the inhomogeneous term.We first show how the Bezout equation arises in the problem of feedback controller design, then we present techniques that are used for its solution. An example is given in which the solution to a Bezout equation derived from an unstable plant with a delay is calculated. Finally this example is extended to show how the techniques developed for the Bezout equation may be used to calculate a sub-optimal solution to the Nehari Problem for a single-input single output system.

Item A Model of the Dynamics of a Lathe Toolpost that Incorporates Active Vibration Suppression(1995) Frankpitt, Bernard A.; ISRA simple, linear, system model is presented for a lathe with a toolpost that incorporates active vibration suppression. The toolpost model is built from linear dynamic models of the component parts of the toolpost design: the actuator and drive circuitry, and the mechanical toolpost. The toolpost model is then combined with linear models for the lathe dynamics and cutting process to produce a model of the entire mechanical system. This model is used as the basis for a controller design that uses a measurement of the actuator current for a sensor signal, and the voltage applied to the actuator by the power amplifier as a control signal.The controller design uses the Hdesign methodology. The performance criteria for the toolpost design are interpreted as measures on transfer functions associated with the system model, and predictions of the performance of the design are made on the basis of these measures. The conclusion drawn from this work is that with careful design, the active control of vibration in turning processes is a promising application for stack piezo-ceramic actuators.