1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
|
function sys = estpoly(varargin)
// Parameters Estimation of generalized discrete time model using Input Output time-domain data
//
// Calling Sequence
// sys = bj(ioData,[na nb nc nd nf nk])
//
// Parameters
// ioData : iddata or [outputData inputData] ,matrix of nx2 dimensions, type plant data
// na : non-negative integer number specified as order of the polynomial A(z^-1)
// nb : non-negative integer number specified as order of the polynomial B(z^-1)+1
// nc : non-negative integer number specified as order of the polynomial C(z^-1)
// nd : non-negative integer number specified as order of the polynomial D(z^-1)
// nf : non-negative integer number specified as order of the polynomial F(z^-1)
// nk : non-negative integer number specified as input output delay, Default value is 1
// sys : idpoly type polynomial have estimated coefficients of A(z^-1), B(z^-1),C(z^-1),D(z^-1) and F(z^-1) polynomials
//
// Description
// Fit generalized discrete time model on given input output data
// The mathematical equation of the generalized discrete time model
// <latex>
// begin{eqnarray}
// A(q)y(n) = \frac {B(q)}{D(q)}u(n) + \frac {C(q)}{D(q)}e(t)
// end{eqnarray}
// </latex>
// It is SISO type model. It minimizes the sum of the squares of nonlinear functions using Levenberg-Marquardt algorithm.
//
// sys ,an idpoly type class, have different fields that contains estimated coefficients, sampling time, time unit and other estimated data in Report object.
//
// Examples
// u = idinput(1024,'PRBS',[0 1/20],[-1 1])
// a = [1 0.2];b = [0 0.2 0.3];
// model = idpoly(a,b,'Ts',0.1)
// y = sim(u,model) + rand(length(u),1)
// ioData = iddata(y,u,0.1)
// sys = estpoly(ioData,[2,2,2,2,2,1])
//
// Examples
// u = idinput(1024,'PRBS',[0 1/20],[-1 1])
// a = [1 0.2];b = [0 0.2 0.3];
// model = idpoly(a,b,'Ts',0.1)
// y = sim(u,model) + rand(length(u),1)
// ioData = [y,u]
// sys = estpoly(ioData,[2,2,2,2,2,1])
//
// Authors
// Ashutosh Kumar Bhargava
[lhs , rhs] = argn();
if ( rhs < 2 ) then
errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while should be 2"), "estpoly", rhs);
error(errmsg)
end
z = varargin(1)
if typeof(z) == 'iddata' then
Ts = z.Ts;unit = z.TimeUnit
z = [z.OutputData z.InputData]
elseif typeof(z) == 'constant' then
Ts = 1;unit = 'seconds'
end
if ((~size(z,2)==2) & (~size(z,1)==2)) then
errmsg = msprintf(gettext("%s: input and output data matrix should be of size (number of data)*2"), "estpoly");
error(errmsg);
end
if (~isreal(z)) then
errmsg = msprintf(gettext("%s: input and output data matrix should be a real matrix"), "estpoly");
error(errmsg);
end
n = varargin(2)
if (size(n,"*")<5| size(n,"*")>6) then
errmsg = msprintf(gettext("%s: The order and delay matrix [na nb nc nd nf nk] should be of size [5 6]"), "estpoly");
error(errmsg);
end
if (size(find(n<0),"*") | size(find(((n-floor(n))<%eps)== %f))) then
errmsg = msprintf(gettext("%s: values of order and delay matrix [nb nc nd nf nk] should be nonnegative integer number "), "estpoly");
error(errmsg);
end
na = n(1); nb = n(2); nc = n(3); nd = n(4);nf = n(5);
if (size(n,"*") == 5) then
nk = 1
else
nk = n(6);
end
// storing U(k) , y(k) and n data in UDATA,YDATA and NDATA respectively
YDATA = z(:,1);
UDATA = z(:,2);
NDATA = size(UDATA,"*");
function e = G(p,m)
e = YDATA - _oestpolyfun(UDATA,p,na,nb,nc,nd,nf,nk);// _oestpolyfun(UDATA,p,nd,nc,nf,nb,nk);
endfunction
tempSum = na+nb+nc+nd+nf
p0 = linspace(0.0001,0.001,tempSum)';
[var,errl] = lsqrsolve(p0,G,size(UDATA,"*"));
// disp(errl)
err = (norm(errl)^2);
// disp(err)
opt_err = err;
resid = G(var,[]);
x = var
// b = poly([repmat(0,nk,1);var(1:nb)]',"q","coeff");
// c = poly([1; var(nb+1:nb+nc)]',"q","coeff");
// d = poly([1; var(nb+nc+1:nb+nc+nd)]',"q","coeff");
// f = poly([1; var(nb+nd+nc+1:nd+nc+nf+nb)]',"q","coeff");
a = poly([1; x(1:na)]',"q","coeff");
b = poly([repmat(0,nk,1);x(na+1:na+nb)]',"q","coeff");
c = poly([1; x(na+nb+1:na+nb+nc)]',"q","coeff");
d = poly([1; x(na+nb+nc+1:na+nb+nc+nd)]',"q","coeff");
f = poly([1; x(na+nb+nd+nc+1:na+nd+nc+nf+nb)]',"q","coeff");
t = idpoly(coeff(a),coeff(b),coeff(c),coeff(d),coeff(f),Ts)
// t = sys;// idpoly(1,coeff(b),coeff(c),coeff(d),coeff(f),Ts)
// estimating the other parameters
[temp1,temp2,temp3] = predict(z,t)
[temp11,temp22,temp33] = pe(z,t)
// pause
estData = calModelPara(temp1,temp11,na+nb+nc+nd+nf)
// pause
t.Report.Fit.MSE = estData.MSE
t.Report.Fit.FPE = estData.FPE
t.Report.Fit.FitPer = estData.FitPer
t.Report.Fit.AIC = estData.AIC
t.Report.Fit.AICc = estData.AICc
t.Report.Fit.nAIC = estData.nAIC
t.Report.Fit.BIC = estData.BIC
t.TimeUnit = unit
sys = t
// sys.TimeUnit = unit
endfunction
function yhat = _oestpolyfun(UDATA,x,na,nb,nc,nd,nf,nk)// (UDATA,x,nd,nc,nf,nb,nk)
x=x(:)
q = poly(0,'q')
tempSum = na+nb+nc+nd+nf
// making polynomials
a = poly([1; x(1:na)]',"q","coeff");
b = poly([repmat(0,nk,1);x(na+1:na+nb)]',"q","coeff");
c = poly([1; x(na+nb+1:na+nb+nc)]',"q","coeff");
d = poly([1; x(na+nb+nc+1:na+nb+nc+nd)]',"q","coeff");
f = poly([1; x(na+nb+nd+nc+1:na+nd+nc+nf+nb)]',"q","coeff");
bd = coeff(b*d); cf = coeff(c*f); fc_d = coeff(f*(c-a*d));
if size(bd,"*") == 1 then
bd = repmat(0,nb+nd+1,1)
end
// pause
maxDelay = max([length(bd) length(cf) length(fc_d)])
yhat = [YDATA(1:maxDelay)]
for k=maxDelay+1:size(UDATA,"*")
bdadd = 0
for i = 1:size(bd,"*")
bdadd = bdadd + bd(i)*UDATA(k-i+1)
end
fc_dadd = 0
for i = 1:size(fc_d,"*")
fc_dadd = fc_dadd + fc_d(i)*YDATA(k-i+1)
end
cfadd = 0
for i = 2:size(cf,"*")
cfadd = cfadd + cf(i)*yhat(k-i+1)
end
// pause
yhat = [yhat; [ bdadd + fc_dadd - cfadd ]];
end
endfunction
|
