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Homework #2: Universidad Popular Del Cesar

This document provides the details of homework assignment #2 for a control systems course. It includes 4 problems related to closed-loop transfer functions, stability analysis using Routh's criterion, pole-zero cancellation in feedback control systems, and determining steady state error of a robotic arm system. Students are asked to analyze rise time, settling time, percent overshoot for different transfer functions, determine the range of K for stability, obtain the closed-loop transfer function and pole-zero map for a feedback system, and calculate steady state error given motor and gear parameters.

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57 views3 pages

Homework #2: Universidad Popular Del Cesar

This document provides the details of homework assignment #2 for a control systems course. It includes 4 problems related to closed-loop transfer functions, stability analysis using Routh's criterion, pole-zero cancellation in feedback control systems, and determining steady state error of a robotic arm system. Students are asked to analyze rise time, settling time, percent overshoot for different transfer functions, determine the range of K for stability, obtain the closed-loop transfer function and pole-zero map for a feedback system, and calculate steady state error given motor and gear parameters.

Uploaded by

stalin robles
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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UNIVERSIDAD POPULAR DEL CESAR – CONTROL II, GUIDED COURSE

Homework #2

For Everyone (5pts each):

1. Three closed-loop transfer functions are given as follows:

In each case, provide estimates of the rise time, settling time and percent overshoot to a unit-

step input in r.

2. The transfer function of a typical tape-drive system is given by:



Where time is measured in milliseconds. Using Routh’s stability criterium, determine the range

of K for which this system is stable when the characteristic equation is 1+KG(s)=0
UNIVERSIDAD POPULAR DEL CESAR – CONTROL II, GUIDED COURSE

3. Consider the feedback control system in Figure below, where

𝐺1(𝑠) = s+1 and 𝐺2(𝑠) = 1


s+2 s+1

a. Using Matlab, determine the closed-loop transfer function

b. Obtain the pole-zero map. Where are the closed-loop system poles and zeros?

c. Are there any pole-zero cancellations? Why is it important to cancel common poles and

zeros in the transfer function?

4. The shoulder joint of a robotic arm uses a DC motor with armature control and a set of n gears

on the output shaft. The model of the system is shown in Figure with a disturbance torque 𝑇d(𝑠)

which represents the effect of the load.


UNIVERSIDAD POPULAR DEL CESAR – CONTROL II, GUIDED COURSE

a. Determine the steady state error when the desired angle input is a set so that 𝜃d(𝑠) = A/s,

𝐺c(𝑠) = 𝐾 and the disturbance input is 0.

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