ECE 421, Spring 2006 Solutions to HW Assignment #8
Problem B-6-1 K (s + 1) , H (s) = 1, K0 (1) s2 On the real axis, the root locus lies to the left of s = 1. There are two poles (n = 2) and one zero (m = 1), so there is only n m = 1 asymptote. The angle a
ECE 421, Spring 2006, HW Assignment #1 Signals and Systems Review Problems Due Tuesday, January 31 1. Determine the Laplace transform for the following time-domain signal. Express the answer in the normal transfer function format, that is, as a ratio of p
ECE 421, Spring 2006 Solutions to Textbook Problems for HW Assignment #10
The solutions to the additional problems appear after in a separate le. For these HW problems, if there is a choice of the desired dominant closed-loop pole s1 , it can be done base
ECE 421, Spring 2006 Solutions to HW Assignment #11
Problem #B-8-5 The Bode magnitude and phase plots are shown in Fig. 1. The transfer function has one poles at the origin (N = 1), so at low frequencies the magnitude plot has a slope of 20 db/decade and
ECE 421, Spring 2006 Solutions to HW Assignment #12
Problem #B-8-26 The forward transfer function is as + 1 (1) s2 The two poles at s = 0 provide 180 phase shift at all frequencies. The requirement on phase margin of P M = 45 means that at the gain crosso
1
ECE 421, Spring 2006 Solutions to HW Assignment #13 Bode Compensator Design Problems
1) The rst thing to check is the steady-state error requirement. For the given plant Kv = 2, so with the specication that the steady-state error for a unit ramp input m
324. Consider industrial automatic controllers whose
control actions are proportional, integral, proportional-plus-
integrai, proporonal-plus-derivative, and proportional-plus-
integralplusderivative. The transfer functions of these
controllers can be giv
ECE 421, Spring 2006 Solutions to Additional Problems for HW Assignment #10
The solutions to the textbook problems B-7-11, B-7-12, B-7-13, B-7-15, and B-7-16 appear after in a separate le. None of the problems has a unique solutioneach of the problems has
ECE 421, Spring 2006 Solutions to HW Assignment #9
Problem #B-7-9 Gp (s) =
5 10 = s (0.5s + 1) s (s + 2)
(1)
The phase shift of Gp (s1 ) is 210 = +150 , so the compensators phase shift at s1 must be 6 Gc (s1 ) = 30 . Since this angle is positive, a lead c
ECE 421, Spring 2006, HW Assignment #4 Due Thursday, February 16, 2006
Problems from the text: B-5-9, B-5-10, B-5-11, B-5-27 1. The forward transfer function for a unity-feedback closed-loop system is given by G(s) = K s (s + p) (1)
Specications imposed o
ECE 421, Spring 2006, HW Assignment #5 Stability Analysis with the Routh Array Due Thursday, March 2 1. Textbook problems B-5-23, B-5-24, B-5-25, B-5-26, B-5-28. 2. A linear model for the steering dynamics of an ocean-going tanker ship is given by the fol
ECE 421, Spring 2006, HW Assignment #6 Due Tuesday, March 7, 2006
1. Textbook problems B-5-30 and B-5-32 2. For each of the following systems, determine the closed-loop steady-state errors for unit step, unit ramp, and unit parabolic reference input signa
ECE 421, Spring 2006, HW Assignment #7 Due Thursday, March 9, 2006
1. In the .zip le there are 4 MATLAB .m les: (a) hw_421_s06_07.m (b) root_locus.m (c) breakpts.m (d) plotax.m 2. Extract the MATLAB les from the .zip le and store them in your working MATL
ECE 421, Spring 2006, HW Assignment #13 Bode Compensator Design Problems Due 4:00 p.m., Friday, May 5, 2006
For each problem, design a compensator Gc (s) such that all of the specications are satised. Use MATLAB to draw the uncompensated and compensated B
% hw_421_s06_07 % f function [] = hw_421_s06_07; c close all dp = [1 6 11 6 0]; z = [8 4 2.75 2.25 1.75 1.25 0.75 0.1 -1]; for i = 1:length(z) np = [1 z(i)]; figure(i),clf, subplot(121),root_locus(np,dp),title(['Open-Loop Zero is at s = ' num2str(z(i) ',
ECE 421, Spring 2006 Solutions to HW Assignment #1
Problem 1 For the given time-domain expression x1 (t), the Laplace transform is 2 4 3 2 (s + 3) (s 2) 4s3 (s 2) + 3s3 (s + 3) + = 3 s s+3 s2 s3 (s + 3) (s 2) 2s2 + 2s 12 4s4 + 8s3 + 3s4 + 9s3 s3 (s + 3) (
ECE 421, Spring 2006 Solutions to HW Assignment #2
Problem B-3-1 A parallel conguration is dened by two or more blocks having the same input signal and the outputs of the blocks being added together at a summing junction. Therefore, blocks G1 and G2 are i
ECE 421, Spring 2006 Solutions to HW Assignment #3
Problem B-5-1 Assume that the thermometer is modeled by a rst-order system with output c(t) representing the thermometer reading and the input r(t) representing actual temperature, and the relationship C
ECE 421, Spring 2006 Solutions to HW Assignment #4
Problem B-5-9 For the original conguration, n = 10 = 3.162 r/s and = 1/2 n = 0.158. In the second conguration, the equivalent open-loop transfer function is Geq (s) = 1 2 10 n = s s + 1 + 10Kh s (s + 2 n
ECE 421, Spring 2006 Solutions to HW Assignment #5
Problem #B-5-23 From the given G(s), the closed-loop transfer function and closed-loop characteristic equation are C (s) G(s) K K = = =3 R(s) 1 + G(s) s (s + 1) (s + 2) + K s + 3s2 + 2s + K
TCL (s) =
(1)
ECE 421, Spring 2006 Solutions to HW Assignment #7
1. Zero located at s = 8 G1 (s)H1 (s) = K (s + 8) s (s + 1) (s + 2) (s + 3) (1)
(a) K > 0: For small values of K, the closed-loop pole on each of the branches of the root locus is in the left-half plane,