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

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

Problem 03
For the Adams-Schlumberger predictor,

(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

For the Adams-Schlumberger corrector, determine
(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.