drydemo.html

交流 模糊控制 交流 模糊控制

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--><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium;">Overview</p><ul xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd"><li><a href="#Nonlinear system identification">Nonlinear system identification</a></li></ul><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;">Nonlinear system identification<a name="Nonlinear system identification"></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">This demo addresses the use of ANFIS function in the Fuzzy Logic
Toolbox for nonlinear dynamical system identification. This demo also
requires the System Identification Toolbox, as a comparison is made
between a nonlinear ANFIS and a linear ARX model.
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">Copyright 1994-2002 The MathWorks, Inc.
$Revision: 1.9 $
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px"><span style="color:green">% Exit if the IDENT toolbox is not on the path</span>
<span style="color:blue">if</span> exist(<span style="color:#B20000">'arx.m'</span>,<span style="color:#B20000">'file'</span>) == 0
  errordlg(<span style="color:#B20000">'DRYDEMO requires the System Identification Toolbox.'</span>);
  <span style="color:blue">return</span>;
<span style="color:blue">end</span></pre><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">The data set for ANFIS and ARX modeling was obtained from a laboratory
device called Feedback's Process Trainer PT 326, as described in Chapter
17 of Prof. Lennart Ljung's book "System Identification, Theory for the
User", Prentice-Hall, 1987. The device's function is like a hair dryer:
air is fanned through a tube and heated at the inlet. The air temperature
is measure by a thermocouple at the outlet. The input u(k) is the voltage
over a mesh of resistor wires to heat incoming air; the output y(k) is
the outlet air temperature. Here is a the system model
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">a=imread(<span style="color:#B20000">'dryblock.jpg'</span>, <span style="color:#B20000">'jpg'</span>);
image(a); 
axis image;
axis off;</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" src="drydemo_img02.gif"><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">Here are the results of the test.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">load dryer2;
data_n = length(y2);
output = y2;
input = [[0; y2(1:data_n-1)] <span style="color:blue">...</span>
        [0; 0; y2(1:data_n-2)] <span style="color:blue">...</span>
        [0; 0; 0; y2(1:data_n-3)] <span style="color:blue">...</span>
        [0; 0; 0; 0; y2(1:data_n-4)] <span style="color:blue">...</span>
        [0; u2(1:data_n-1)] <span style="color:blue">...</span>
        [0; 0; u2(1:data_n-2)] <span style="color:blue">...</span>
        [0; 0; 0; u2(1:data_n-3)] <span style="color:blue">...</span>
        [0; 0; 0; 0; u2(1:data_n-4)] <span style="color:blue">...</span>
        [0; 0; 0; 0; 0; u2(1:data_n-5)] <span style="color:blue">...</span>
        [0; 0; 0; 0; 0; 0; u2(1:data_n-6)]];
data = [input output];
data(1:6, :) = [];
input_name = str2mat(<span style="color:#B20000">'y(k-1)'</span>,<span style="color:#B20000">'y(k-2)'</span>,<span style="color:#B20000">'y(k-3)'</span>,<span style="color:#B20000">'y(k-4)'</span>,<span style="color:#B20000">'u(k-1)'</span>,<span style="color:#B20000">'u(k-2)'</span>,<span style="color:#B20000">'u(k-3)'</span>,<span style="color:#B20000">'u(k-4)'</span>,<span style="color:#B20000">'u(k-5)'</span>,<span style="color:#B20000">'u(k-6)'</span>);
trn_data_n = 300;
index = 1:100;
subplot(2,1,1);
plot(index, y2(index), <span style="color:#B20000">'-'</span>, index, y2(index), <span style="color:#B20000">'o'</span>);
ylabel(<span style="color:#B20000">'y(k)'</span>);
subplot(2,1,2);
plot(index, u2(index), <span style="color:#B20000">'-'</span>, index, u2(index), <span style="color:#B20000">'o'</span>);
ylabel(<span style="color:#B20000">'u(k)'</span>);</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" src="drydemo_img03.gif"><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">The data points was collected at a sampling time of 0.08 second. One
thousand input-output data points were collected from the process as the
input u(k) was chosen to be a binary random signal shifting between 3.41
and 6.41 V. The probability of shifting the input at each sample was 0.2.
The data set is available from the System Identification Toolbox; and the
above plots show the output temperature y(k) and input voltage u(t) for
the first 100 time steps.
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">A conventional method is to remove the means from the data and assume a
linear model of the form:
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">y(k)+a1*y(k-1)+...+am*y(k-m)=b1*u(k-d)+...+bn*u(k-d-n+1)
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">where ai (i = 1 to m) and bj (j = 1 to n) are linear parameters to be
determined by least-squares methods. This structure is called the ARX
model and it is exactly specified by three integers [m, n, d]. To find an
ARX model for the dryer device, the data set was divided into a training
(k = 1 to 300) and a checking (k = 301 to 600) set.  An exhaustive search
was performed to find the best combination of [m, n, d], where each of
the integer is allowed to changed from 1 to 10 independently. The best
ARX model thus found is specified by [m, n, d] = [5, 10, 2], with a
training RMSE of 0.1122 and a checking RMSE of 0.0749. The above figure
demonstrates the fitting results of the best ARX model.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">trn_data_n = 300;
total_data_n = 600;
z = [y2 u2];
z = dtrend(z);
ave = mean(y2);
ze = z(1:trn_data_n, :);
zv = z(trn_data_n+1:total_data_n, :);
T = 0.08;

<span style="color:green">% Run through all different models</span>
V = arxstruc(ze, zv, struc(1:10, 1:10, 1:10));
<span style="color:green">% Find the best model</span>
nn = selstruc(V, 0);
<span style="color:green">% Time domain plot</span>
th = arx(ze, nn);
th = sett(th, 0.08);
u = z(:, 2);
y = z(:, 1)+ave;
yp = idsim(u, th)+ave;

xlbl = <span style="color:#B20000">'Time Steps'</span>;

subplot(2,1,1); 
index = 1:trn_data_n;
plot(index, y(index), index, yp(index), <span style="color:#B20000">'.'</span>);
rmse = norm(y(index)-yp(index))/sqrt(length(index));
title([<span style="color:#B20000">'(a) Training Data (Solid Line) and ARX Prediction (Dots) with RMSE = '</span> num2str(rmse)]);
disp([<span style="color:#B20000">'[na nb d] = '</span> num2str(nn)]);
xlabel(xlbl);

subplot(2,1,2); 
index = (trn_data_n+1):(total_data_n);
plot(index, y(index), index, yp(index), <span style="color:#B20000">'.'</span>);
rmse = norm(y(index)-yp(index))/sqrt(length(index));
title([<span style="color:#B20000">'(b) Checking Data (Solid Line) and ARX Prediction (Dots) with RMSE = '</span> num2str(rmse)]);
xlabel(xlbl);</pre><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:gray; font-style:italic;">[na nb d] = 5 10  2
</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" src="drydemo_img05.gif"><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">The ARX model is inherently linear and the most significant advantage is
that we can perform model structure and parameter identification rapidly.
The performance in the above plots appear to be satisfactory. However, if
a better performance level is desired, we might want to resort to a
nonlinear model.  In particular, we are going to use a neuro-fuzzy
modeling approach, ANFIS, to see if we can push the performance level by
using a fuzzy inference system.
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">To use ANFIS for system identification, the first thing we need to do is
input selection. That is, to determine which variables should be the
input arguments to an ANFIS model.  For simplicity, we suppose that there
are 10 input candidates (y(k-1), y(k-2), y(k-3), y(k-4), u(k-1), u(k-2),
u(k-3), u(k-4), u(k-5), u(k-6)), and the output to be predicted is y(k).
A heuristic approach to input selection is called sequential forward
search, in which each input is selected sequentially to optimize the
total squared error. This can be done by the function seqsrch; the result
is shown in the above plot, where 3 inputs (y(k-1), u(k-3), and u(k-4))
are selected with a training RMSE of 0.0609 and checking RMSE of 0.0604.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">trn_data_n = 300;
trn_data = data(1:trn_data_n, :);
chk_data = data(trn_data_n+1:trn_data_n+300, :);
[input_index, elapsed_time]=seqsrch(3, trn_data, chk_data, input_name);
fprintf(<span style="color:#B20000">'\nElapsed time = %f\n'</span>, elapsed_time);