Determine a discrete-time transfer function

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Problem 01

Any linear multistep method can be used as an associative operational substitution method. Use operational substitution to determine a discrete-time transfer function that approximates G(8) using the Adams-Schlumberger predictor as an operational substitution method. You may use a computer algebra package to help with the resulting algebra.

Problem 02

(A) the order of accuracy,
(B) the error constant, and
(C) the open loop z-plane poles and zeroes of the integrator.

Problem 03

(A) sketch the closed-loop z-plane trajectories when the Adams-Schlumberger is applied to the first-order test system with pole at A < 0;
(B) on the trajectory map, identify the principal and spurious roots; and
(C) Determine the two maximum values of T, one that guarantees accuracy and the other that guarantees stability- of the simulation.

Problem 04

Plot the stability region for the Adams-Schlumberger predictor. Discuss "good" and -bad" regions with regard to tuning, relative stability, and absolute stability.

Problem 05

Plot a step response for the system whose transfer function is G(s) using the Adams-Schlumberger predictor method. Use as large a time step T as possible while retaining stability and accuracy of the simulation.

Problem 06

(A) the order of accuracy,
(B) the error constant, and
(C) the open loop z-plane poles and zeroes of the integrator.

Problem 07
Plot the stability region for the Adams-Schlumberger corrector. Discuss good" and "bad" regions with regard to tuning, relative stability, and absolute stability.

Problem 08
Simulate the system whose transfer function is G(s) using the Adams-Schlumberger predictor-corrector pair. You may correct as many times as you like. Estimate the size of the predictor corrector stability region. You may Plot the stability region, but this is not required.

Verified Expert

Solution is about modeling the control system using Adams – Schlumberger predictor and Adams – Schlumberger corrector. the tasks are to find Order of accuracy, Error constant, Open loop poles and zeros. Next is the stability analysis done using step response plot from MATLAB.Good Region are estimated to be Region in green and Bad Region are estimated to be Region in red. finally Large T for stability is founded and analyzed.

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Reviews

len1449748

4/3/2017 8:36:27 AM

any simulation needed should be done in matlab. detailed solution with explanation and reasoning is required. Estimate the size of the predictor corrector stability region. You may Plot the stability region, but this is not required.