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Adaptive Control of Nonlinear Systems With Applications to the Control of Flexible Robot Arms

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Final rept. 15 Jun 1988-14 Jun 1991

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On this grant we made major progress in three areas Adaptive Control of Nonlinear Systems In this work, we extended our previous work on direct adaptive control of Single Input Single Output nonlinear systems to schemes for adaptive identification, indirect adaptive control and also adaptive model matching of Multi Input Multi Output nonlinear systems. We also studied adaptive versions of the nonlinear regulator. Approximate Linearization by state feedback of nonlinear systems While the full set of conditions for input- output linearization of a nonlinear system by state feedback have been given in the literature, the question of how to proceed when the conditions follow slightly short of being met have not been answered. For example, input-output linearization hinges on a certain set of regularity conditions existence of relative degree in the SISO case and minimum phase conditions being met by the plant. If the plant is not regular and is slightly nonminimum phase the techniques of input-output linearization need to be modified. We discussed these techniques in the context of flight control and also other examples, for instance, the ball and beam system. This in turn led to a deeper understanding of the structure of the zero dynamics of a nonlinear system and their structure under perturbation. CAD tools for nonlinear controller design We have developed a set of CAD tools for linearization and approximate linearization of nonlinear systems using spline software which operates in real time and is capable of accepting nonlinear system description in numeric, tabular or functional form. A user interface is being written and it is being tried out on several examples.

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  • Operations Research

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