Question

The fuel control for an automobile uses a diesel pump that is subject to parameter variations. A unity negative feedback has a loop transfer function $$ G_c(s) G(s)=\frac{K(s+2)}{(s+1)(s+2.5)(s+4)(s+10)} . $$ (a) Sketch the root locus as $K$ varies from 0 to 2000 . (b) Find the roots for $K$ equal to 400,500 , and 600 . (c) Predict how the percent overshoot to a step will vary for the gain $K$, assuming dominant roots. (d) Find the actual time response for a step input for all three gains and compare the actual overshoot with the predicted overshoot.

   The fuel control for an automobile uses a diesel pump that is subject to parameter variations. A unity negative feedback has a loop transfer function
$$
G_c(s) G(s)=\frac{K(s+2)}{(s+1)(s+2.5)(s+4)(s+10)} .
$$
(a) Sketch the root locus as $K$ varies from 0 to 2000 .
(b) Find the roots for $K$ equal to 400,500 , and 600 .
(c) Predict how the percent overshoot to a step will vary for the gain $K$, assuming dominant roots. (d) Find the actual time response for a step input for all three gains and compare the actual overshoot with the predicted overshoot.

Modern Control Systems

Dorf 11th Edition

Chapter 7, Problem 34

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Step 1

To sketch the root locus, we need to find the poles and zeros of the transfer function. The poles are at s=-1, -2.5, -4, and -10, and the zero is at s=-2. As K varies, the root locus will change. At K=0, the root locus will start at the poles, and as K increases, Show more…

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The fuel control for an automobile uses a diesel pump that is subject to parameter variations. A unity negative feedback has a loop transfer function $$ G_c(s) G(s)=\frac{K(s+2)}{(s+1)(s+2.5)(s+4)(s+10)} . $$ (a) Sketch the root locus as $K$ varies from 0 to 2000 . (b) Find the roots for $K$ equal to 400,500 , and 600 . (c) Predict how the percent overshoot to a step will vary for the gain $K$, assuming dominant roots. (d) Find the actual time response for a step input for all three gains and compare the actual overshoot with the predicted overshoot.

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