系统辨识作业解析

Answer to Program testing
1. generating input-output signalsby mean of MATLAB
Input u(t)
u(t) is the maximum length PRBS with amplitudea 1 and trend ut t 0.0001t
ut t 0.0001t , other parmateres of M-PRBS will be determined by the
examined-students.
Disturbance e t is the Gaussian-distribution white noise with zero mean and
900 1000
t
②the programme of the output signal
%output of system1
A=1;
C=1;
B= [0 1 0.5];
D= [1 -1.5 0.7];
F= [1 -1.5 0.7];
m0= idpoly(A,B,C,D,F);
y1=sim(m0, [u' e1]);
Disturbance e t :
e t is the Gaussian-distribution white noise with zero mean and variances ,Let 0.2 and 1.2 respectively
(1) we choose the data length L=1000 and select the =0.2 as the variance
about it including order and parameters. The unique information is just above data. Please identify the process model, B/F, based on the data and using MATLAB package. Take reference of the examples in the texbook 17.3 to get preliminary models, further models and final choice of model by proper identification method. 3. Compare the obtained models with the true system(original transfer-function). Compare the models obtained under different conditions with each other. Note:The examined-student should give a clear procedure of solving problems and offer flow-chart,etc.
variances ,Let 0.2 and 1.2 respectively. 1. For every system , generate input-output signals by means of MATLAB, select
the data length L=1000. 2. Suppose,now, you view the systemas a black-box ,you don’t know anything
of e(t)
①the programme of the input signal and disturbance signal
N=[1000 1];
BAND1=[0 1];
BAND2=[0 1];
LEVEL1=[-1 1];
LEVEL2=[-sqrt(0.2) sqrt(0.2)];
%input of system1
'e1' ),title(
'white noise with zero mean and variance
0.2' );

figure(2)
plot(t,u,
'b' )
xlabel( 't' ),ylabel(
'u' ),title(
' pseudorandom binary signal'
);
pseudorandom binary signal 1.5
PROBLEM:PROGRAMME TESTING
Given the following SISO systems described by transfer-function containing 4 polynomials:
e
C D
u(t)
B F
Aq 1
Fq
1 1.5 q 1 0.7 q 2
1
2
1.
Bq
q
0.5 q
Cq Dq
1
1
2
1 1.5 q
0.7 q
+ y(t)
Aq 1
Fq
1
2
1 1.5 q
0.7 q
2.
Bq
q 1 0.5 q 2
Cq
1
2
1q
0.2 q
Dq
1 1.5 q 1 0.7 q 2
Input signal u(t) is the Maximum Length PRBS with amplitude a 1 and trend
1
0.5 u
0
-0.5
-1 0
1.5
100 200 300 400 500 600 700 800 900 1000 t
white noise with zero mean and v
ariance 0.2
1
0.5
0 e2
-0.5
-1
-1.5
-2
0
100 200
300 400
500 600 700 800
figure(3)
plot(t,y1)
xlabel( 't' ),ylabel(
'y1' ),title(
' output of the system1'
u1=idinput(N,
'prbs' ,BAND1,LEVEL1);
u2=idinput(N,
'rgs' ,BAND2,LEVEL2);
e1=u2;
for t=1:1000
u(t)=u1(t)+0.0001*t;
end
t=1:1000;
figure(1)
plot(t,e1,
'b' )
xlabel( 't' ),ylabel(