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Analog computer techniques for plotting Bode and Nyquist diagrams

Authors:

G. A. Bekey,

L. W. NeustadtAuthors Info & Claims

IRE-AIEE-ACM '60 (Western): Papers presented at the May 3-5, 1960, western joint IRE-AIEE-ACM computer conference

Pages 165 - 172

https://doi.org/10.1145/1460361.1460384

Published: 03 May 1960 Publication History

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Abstract

Two methods of plotting Bode and Nyquist diagrams with an analog computer are presented. Both methods have the advantage of being able to give the open loop response from a closed loop simulation on the computer, which makes them applicable to systems with open loop poles in the right hand plane. Neither method requires any adjustment by the operator, other than to change the frequency of the input signal.

The first method makes use of some trigonometric identities, which yield functions which identically equal the real and imaginary parts of points in the Nyquist diagram. It makes rather extensive use of multiplying equipment, but no other non-linear equipment is required.

The second method makes use of diode and relay switching techniques to measure phase, and peak value readers to measure amplitude. One divider and no multipliers are used, but diodes and relays are necessary.

Nyquist and Bode plots are presented, as computed by both methods.

References

[1]

Fuchs, A. M. "Control System Test Equipment, Part II: Complete Test and Evaluation Systems", Control Engineering, v. 6, pp. 125--132 (May 1959)

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[2]

V. L. Larrowe, M. M. Spencer, S. R. Lampert, University of Michigan, "Application of a Gas Turbine Engine Performance Computer to a Twin Spool Engine", Report IP - 250, (Nov. '57)

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[3]

The circuit is also described in "The Simulation Council Newsletter", Instruments and Automation, v. 31, pp. 1691--1696, (Oct. 1958)

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[4]

Cowley, Percy, "The Application of an Analog Computer to the Measurement of Process Dynamics", ASME Paper No. 56 - IRD - 20 (1956)

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[5]

Goldberg, E. A. "An Analog Computer Nyquist Plotter", IRE Convention Record (1960)

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IRE-AIEE-ACM '60 (Western): Papers presented at the May 3-5, 1960, western joint IRE-AIEE-ACM computer conference

May 1960

391 pages

ISBN:9781450378697

DOI:10.1145/1460361

Conference Chair:
R. M. Bennett
IBM Corp., San Jose, California

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 03 May 1960

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Nyquist Meets Bode on the z-Plane

Sphere decoder with box optimisation for faster‐than‐Nyquist non‐orthogonal frequency division multiplexing

Multistream faster than Nyquist signaling

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