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The Quarterly Journal of Mechanics and Applied Mathematics 1958 11(1):119-128; doi:10.1093/qjmam/11.1.119
© 1958 by Oxford University Press
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DETERMINATION OF THE OPTIMUM RESPONSE OF LINEAR SYSTEMS

(ZERO-VELOCITY-ERROR AND ZERO-ACCELERATION-ERROR SYSTEMS){dagger}

A. W. BABISTER

( The University Glasgow )

In (1) two response functions L and L1were defined by the equations

where e is the error at time T. In (2) it was shown how these response functions could be used to obtain the optimum response for zero-displacement-error systems. The analysis is here applied to zero-velocity-error and zero-acceleration-error systems. The systems having the optimum response in velocity or in acceleration have a nonzero displacement lag. It is shown how the method can be extended to allow for the requirement of a zero-displacement-error in the final steady state.


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