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function varargout = predict(varargin)
// K-steps ahead output predictor
//
// Calling Sequence
// predict(plantData,sys)
// predict(plantData,sys,k)
// [yData,tData,fData] = predict(plantData,sys)
// [yData,tData,fData] = predict(plantData,sys,k)
//
// Parameters
// plantData : iddata type or nx2 matrix
// sys : idpoly type polynomial
// k : non-neagtive integer prediction step
// yData : k step ahead predicted output response,default value is 1
// tData : time series data
// fData : initial state
//
// Description
// predict function consider the inital conditions as zero and predict the k step ahead output response of the sys ,idpoly type, model.
//
// Examples
// a = [1 0.2];b = [0 0.2 0.3];
// sys = idpoly(a,b,'Ts',0.1)
// u = idinput(1024,'PRBS',[0 1/20],[-1 1])
// y = sim(u,sys)+rand(1024,1)
// plantData = iddata(y,u,0.1)
// predict(plantData,sys)
// figure();clf();
// k = 5
// predict(plantData,sys,k)
//
// Authors
// Ashutosh Kumar Bhargava
[lhs,rhs] = argn(0)
// ------------------------------------------------------------------------------
// checking the number of inputs
if rhs < 2 || rhs > 3 then
error(msprintf(gettext("%s:Wrong number of input arguments.\n"),"predict"))
end
// ------------------------------------------------------------------------------
data = varargin(1)
model = varargin(2)
if rhs == 3 then
kStep = varargin(3)
elseif rhs == 2 then
kStep = 1
end
// ------------------------------------------------------------------------------
// k step analysis
if typeof(kStep) <> 'constant' || isnan(kStep) then
error(msprintf(gettext("%s:Prediction horizon(k) must be a non-negative integer number or inf.\n"),"predict"))
end
// if given k step is infinity or []
if isinf(kStep) || ~size(kStep,'*') then
kStep = 1
end
// checking the dimensions
if size(kStep,'*') <> 1 || (ceil(kStep)-kStep) then
error(msprintf(gettext("%s:Prediction horizon(k) must be a non-negative integer number or inf.\n"),"predict"))
end
// ------------------------------------------------------------------------------
// checking the plant model
if typeof(model) ~= 'idpoly' then
error(msprintf(gettext("%s:Plant model must be ""idpoly"" type.\n"),"predict"))
end
modelSampleTime = model.Ts
modelTimeUnit = model.TimeUnit
// ------------------------------------------------------------------------------
// checking the data type
if typeof(data) <> 'iddata' && typeof(data) <> 'constant' then
error(msprintf(gettext("%s:Sample data must be ""iddata"" type or ""n x 2"" matrix type.\n"),"predict"))
end
// checking the plant data
if typeof(data) == 'iddata' then
if ~size(data.OutputData,'*') || ~size(data.InputData,'*') then
error(msprintf(gettext("%s:Number of sample data in input and output must be equal.\n"),"predict"))
end
plantSampleTime = data.Ts
plantTimeUnit = data.TimeUnit
data = [data.OutputData data.InputData]
// disp('iddata')
elseif typeof(data) == 'constant' then
if size(data,'c') ~= 2 then
error(msprintf(gettext("%s:Number of sample data in input and output must be equal.\n"),"predict"))
end
plantSampleTime = model.Ts
plantTimeUnit = model.TimeUnit
end
// ------------------------------------------------------------------------------
// comparing the sampling time
if modelSampleTime-plantSampleTime <> 0 then
error(msprintf(gettext("%s:The sample time of the model and plant data must be equal.\n"),"predict"))
end
// Comparing the time units
if ~strcmp(modelTimeUnit,plantTimeUnit) then
else
error(msprintf(gettext("%s:Time unit of the model and plant data must be equal.\n"),"predict"))
end
// ------------------------------------------------------------------------------
// ckecking the k step size. if it greater than number of sample size then the
// k step will become 1
if kStep >= size(data,'r') then
kStep = 1
end
// ------------------------------------------------------------------------------
// storing the plant data
// B(z) C(z)
// y(n) = ---------- u(n) + ---------- e(n)
// A(z)*F(z) A(z)*D(z)
aPoly = poly(model.a,'q','coeff');
bPoly = poly(model.b,'q','coeff');
cPoly = poly(model.c,'q','coeff');
dPoly = poly(model.d,'q','coeff');
fPoly = poly(model.f,'q','coeff');
Gq = bPoly/(aPoly*fPoly)
Hq = cPoly/(aPoly*dPoly)
if kStep == 1 then
Wkq = Hq^-1
elseif kStep > 1 then
adCoeff = coeff(aPoly*dPoly);adCoeff = adCoeff(length(adCoeff):-1:1);
adPoly = poly(adCoeff,'q','coeff')
cCoeff = model.c;cCoeff = cCoeff(length(cCoeff):-1:1);
cPoly = poly(cCoeff,'q','coeff')
hBar = clean((ldiv(cPoly,adPoly,kStep))',0.00001)
hBarPoly = poly(hBar,'q','coeff')
Wkq = hBarPoly*Hq^-1
end
WkqGq = Wkq * Gq
tempWkqGq = coeff(WkqGq.den)
if tempWkqGq(1) <> 1 then
WkqGq.num = WkqGq.num/tempWkqGq(1)
WkqGq.den = WkqGq.den/tempWkqGq(1)
end
Wkq1 = 1-Wkq
tempWkq1 = coeff(Wkq1.den)
if tempWkq1(1) == 1 then
Wkq1.num = Wkq1.num/tempWkq1(1)
Wkq1.den = Wkq1.den/tempWkq1(1)
end
// pause
// ------------------------------------------------------------------------------
// storing the plant data
uCoeff = coeff(WkqGq.num*Wkq1.den)
yCoeff = coeff(WkqGq.den*Wkq1.num)
yCapCoeff = coeff(WkqGq.den*Wkq1.den)
// pause
lengthuCoeff = length(uCoeff)
lengthyCoeff = length(yCoeff)
lengthyCapCoeff = length(yCapCoeff)
// ------------------------------------------------------------------------------
// keeping initial conditions equal to zero
uData = zeros(lengthuCoeff,1)
yData = zeros(lengthyCoeff,1)
yCapData = zeros(lengthyCapCoeff-1,1)
uData = [uData;data(:,2)]
yData = [yData;data(:,1)]
sampleData = size(data,'r')
// pause
// reversing the coefficients
if ~size(uCoeff,'*') then
uCoeff = 0
else
uCoeff = uCoeff(lengthuCoeff:-1:1)
end
if ~size(yCoeff) then
yCoeff = 0
else
yCoeff = yCoeff(lengthyCoeff:-1:1)
end
if ~size(yCapCoeff,'*') then
yCapCoeff = 0
else
yCapCoeff = -yCapCoeff(lengthyCapCoeff:-1:2)
end
// pause
for ii = 1:sampleData+1
// pause
if ~size(uData(ii:ii+lengthuCoeff-1),'*') then
tempu = 0
else
tempu = uCoeff*uData(ii:ii+lengthuCoeff-1);
end
if ~size(yData(ii:ii+lengthyCoeff-1),'*')
tempy = 0
else
tempy = yCoeff*yData(ii:ii+lengthyCoeff-1);
end
if ~size(yCapData(ii:ii+lengthyCapCoeff-2),'*') then
tempyCap = 0
else
tempyCap = yCapCoeff*yCapData(ii:ii+lengthyCapCoeff-2);
end
yCapData = [yCapData;tempu+tempy+tempyCap];
end
// pause
extraSample = abs(size(yCapData,'r')-sampleData)
yCapData = yCapData(extraSample+1:$)
timeData = ((modelSampleTime:modelSampleTime:(size(yCapData,'r')*modelSampleTime))');
if lhs == 1 then
clf()
plot(timeData,yCapData)
axisData = gca()
tempTimeUnit = 'Time('+modelTimeUnit+')'
xtitle('Predicted Response',tempTimeUnit,'y')
xgrid
varargout(1) = 0
elseif lhs == 2 then
varargout(1) = yCapData
varargout(2) = 0
elseif lhs == 3 then
varargout(1) = yCapData
varargout(2) = timeData
varargout(3) = 0
end
endfunction
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