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The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(4):504-512; doi:10.1093/qjmam/10.4.504
© 1957 by Oxford University Press
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DETERMINATION OF THE OPTIMUM RESPONSE OF LINEAR SYSTEMS (ZERO DISPLACEMENT ERROR SYSTEMS){dagger}

A. W. BABISTER

( The University Glasgow )

In (1) two response functions L and L1 were defined by the equations


where e is the error at time {tau}. These relations are applied to a linear system having one degree of freedom. By considering the response to a step-function disturbance it is found that systems making L a minimum have a lightly damped oscillatory response. The smaller L1 is, the ‘smoother’ is the response.

Values are obtained for the coefficients of the characteristic equation of any order making L a minimum. An approximate method is given for correcting these coefficients to enable the response to be improved to give equal damping in the least damped modes of oscillation.


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