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Sampled data design by log gain diagrams

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2 Author(s)
Pastel, M. ; U.S. Naval Postgraduate School, Monterey, CA, USA ; Thaler, G.J.

The bilinear transformationz = (1+w)/(1-w)converts az-transform functionG(z)of a sampled-data system into a new functionG(w), called thew-transform function, which is a rational function in variablew. This bilinear transformation maps the unit circle on thez- plane onto the imaginary axis of thew-plane. Consequently, it is now possible to readily draw log magnitude and phase diagrams against a frequency scale of the open-loopw-transform function of a sampled-data system by use of asymptotic techniques. Then, by use of a Nichols chart and correlation information available from continuous systems, it is possible to predict the approximate time domain performance. Design by modification of the open-loop transfer function can be made on the diagram in the same manner as employed for continuous systems on the Bode diagram. The resultingw-transform can be converted to its equivalent Laplace transform. The ratio of this transform function and the original Laplace transform function of the system's equipment gives the required compensator. Remote s-plane poles may have to be added to have the compensator physically realizable. Restricting the modifyingw-plane poles to lie between (0) and (-1) permits the compensator to be realizable as an RC network.

Published in:

Automatic Control, IRE Transactions on  (Volume:4 ,  Issue: 2 )

Date of Publication:

Nov 1959

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