R=[6,-4;-4,14] % Resistance matrix.
R =
6 -4
-4 14
V=[9;0], % Voltage vector.
V =
9
0
I=inv(R)*V
I =
1.8529
0.5294
A=[-4,-4;2,-4], % System matrix of RLC circuit.
A =
-4 -4
2 -4
B=[4;0], % Input matrix
B =
4
0
C=[0,2], % Output matrix
C =
0 2
ssRLC=ss(A,B,C,0), % State-space Representation of RLC circuit.
a =
x1 x2
x1 -4 -4
x2 2 -4
b =
u1
x1 4
x2 0
c =
x1 x2
y1 0 2
d =
u1
y1 0
Continuous-time model.
eA=eig(A)
eA =
-4.0000 + 2.8284i
-4.0000 - 2.8284i
step(ssRLC)
tfRLC=tf(ssRLC)
Transfer function:
16
--------------
s^2 + 8 s + 24
bode(ssRLC)
grid
% Plotting signals.
t=0:0.01:5; % Time vector.
who
Your variables are:
A C R eA t
B I V ssRLC tfRLC
s=sin(2*t); % Sinusoid with a frequency of 2 rad/sec.
figure
plot(t,s)
e=exp(-0.5*t);
figure
plot(t,e)
size(s)
ans =
1 501
size(e)
ans =
1 501
ds=s.*e;
figure
plot(t,ds)
title('Damped Sinusoid')
ylabel('Output Response')
xlabel('Time (seconds)')
figure(3)
title('Exponential Decay')
uiopen('Z:\mlab\340\demos\stp_fn.m',1)
x=2*stp_fn(t)-2.5*stp_fn(t-1.5)+0.5*stp_fn(t-4);
figure
plot(t,x)
axis([-1 6 -1 3])
help eig
EIG Eigenvalues and eigenvectors.
E = EIG(X) is a vector containing the eigenvalues of a square
matrix X.
[V,D] = EIG(X) produces a diagonal matrix D of eigenvalues and a
full matrix V whose columns are the corresponding eigenvectors so
that X*V = V*D.
[V,D] = EIG(X,'nobalance') performs the computation with balancing
disabled, which sometimes gives more accurate results for certain
problems with unusual scaling. If X is symmetric, EIG(X,'nobalance')
is ignored since X is already balanced.
E = EIG(A,B) is a vector containing the generalized eigenvalues
of square matrices A and B.
[V,D] = EIG(A,B) produces a diagonal matrix D of generalized
eigenvalues and a full matrix V whose columns are the
corresponding eigenvectors so that A*V = B*V*D.
EIG(A,B,'chol') is the same as EIG(A,B) for symmetric A and symmetric
positive definite B. It computes the generalized eigenvalues of A and B
using the Cholesky factorization of B.
EIG(A,B,'qz') ignores the symmetry of A and B and uses the QZ algorithm.
In general, the two algorithms return the same result, however using the
QZ algorithm may be more stable for certain problems.
The flag is ignored when A and B are not symmetric.
See also condeig, eigs, ordeig.
Overloaded functions or methods (ones with the same name in other directories)
help lti/eig.m
help sym/eig.m
Reference page in Help browser
doc eig
edit
xx=dummy(t);
check=xx-t;
plot(check)
diary off