University of Maryland
Electrical Engineering Department
ENEE 463 DIGITAL CONTROL SYSTEMS
Spring 2007
Test 1 Take home due: 3/26/2006
You can use Matlab and any other software you would like to work on the problems.
1. The equation p(t ) = ap(t ) bp 2 (t
University of Maryland
Electrical Engineering Department
ENEE 463 DIGITAL CONTROL SYSTEMS
Spring 2011 2011-04-27
Test 2 Take-home due midnight 4/29/2011
Problem 1 (25 points): (a) Consider the damped second order continuous time system
n 2
G( s) 2
, 0, n
Problem 1.
c)
[t,x] = ode45('funky',[0 10],[2 4]);
plot(t,x(:,1),'-.r',t,x(:,2),'-b')
leg = legend('p(t)','r(t)');
set(leg,'Location','NorthWest')
function dx = funky(t,x)
a = 2; b = 3; c = 3; d = 4;
k1 = 2; k2 = 1/2;
dx = [a*x(1)-b*x(1)*x(2)+k1*x(1)+k2*x
Homework 6
Problem 1
syms h w b s
% continuous system
A = [0 w; -w 0];
B = [0; b];
% calculate controllability matrix W = [B AB]
W = [B A*B];
% if W is full rank, then the system is controllable
rank(W);
W=
[ 0, b*w]
[ b, 0]
ans =
2
The continuous system
PROBLEM 4.
syms a t
r1 = -a + sqrt(a^2 - 1);
r2 = -a - sqrt(a^2 - 1);
B = (2*a-r2)/(r1-r2);
A = (2*a-r1)/(r2-r1);
Y = A*exp(-r1*t) + B*exp(-r2*t);
% eq2 = int(Y^2, t, 0, inf) was calculated by hand because matlab was being
% dumb
eq2 = (A*A/(2*r1) + (2*A*
Lena Li
ENEE463
May 12, 2014
Homework 8
Problem 1
A = diag([-1 -2 -2 -3 -3]);
B = [0 1 0 1 0; 1 0 1 0 1]';
C = [1 -1 0 2 0; 0 0 1 1 -1];
% FULL ORDER OBSERVER
% check for observability
% Ob = obsv(A,C);
% rank(Ob) % has full rank of 5
Opoles = [-10 -5+2j
University of Maryland
Electrical Engineering Department
ENEE 463 DIGITAL CONTROL SYSTEMS Spring 2014
Problem Set 2 Due 2/10/2014
Problem 1. Use MATLAB to plot the root locus for the following system [command rlocus]
G( s) =
1
( s + 1)( s + 2 )( s + 3)
Fi
University of Maryland
Electrical Engineering Department
ENEE 463 DIGITAL CONTROL SYSTEMS
Spring 2014 Problem Set 1 due February 3
Problem 1. Consider the second order linear system defined by
y(t) + 2 n y (t) + n2 y(t) = 0, y(0) = y0 , y (0) = y1 , t 0
University of Maryland
Electrical Engineering Department
ENEE 463 DIGITAL CONTROL SYSTEMS
Spring 2011 2011-03-14
Test 1 - Solutions
All problems count 25 points
Problem 1: (a) Show that the damped second order continuous time system
n 2
G(s) 2
, 0, n 0
s
University of Maryland
Electrical Engineering Department
ENEE 463 DIGITAL CONTROL SYSTEMS
Spring 2008
Test 1 Solutions
Problem 1. Consider the damped second order system
G (s) =
1
2
s + 2n s + n
2
=
1
( s r1 )( s r2 )
Suppose the open loop poles are at -1
University of Maryland
Electrical Engineering Department
ENEE 463 DIGITAL CONTROL SYSTEMS
Spring 2008
Test 1 Solutions
Problem 1. Consider the damped second order system
G (s) =
1
2
s + 2n s + n
2
=
1
( s r1 )( s r2 )
Suppose the open loop poles are at -1