polydet.m

Software for design and tuninig of SISO and MIMO contol systems

function [num,den,dead]=polydet(nummt,denmt,deadmt,use_Pade)
% function [num,den,dead]=polydet(nummt,denmt,deadmt)
% compute a determinant of n x n transferfunction matrix described by
% a cell array of nominator (nummt)and denominator (denmt) polynomial 
% matrices. The nummt and denmt are defined in IMCTUNE as cell arrays
% of polynomial matrices. The deadmt is a matrix of dead times of the 
% system. The function can also approximate dead times by
% Pade's method with the order given in the use_Pade variable.

if nargin <= 3, use_Pade = 0; end
if ~iscell(nummt)
    errordlg('Not a cell array defined for IMCTUNE !');
    return
end
[m,n]=size(nummt);
if m ~= n
    errordlg('Not a square matrix!');
    return
end
tempx=iscell(deadmt);
if tempx % Take care in case that A is cell array
	temp=zeros(n,n);
   for i=1:n
      for j=1:n
         temp(i,j)=mt2dt(deadmt{i,j},[]);
      end
   end
   deadmt=temp;
end
if isempty(denmt) | any(iscellempty(denmt))
   for i=1:n
      for j=1:n
         denmt{i,j}=1;
      end
   end
end   
if use_Pade & ~all(deadmt(:)==0)
   for i=1:n
      for j=1:n
         [temp,temp1]=pade(deadmt(i,j),use_Pade);
         nummt{i,j}=conv(nummt{i,j},temp);
         denmt{i,j}=conv(denmt{i,j},temp1);
      end
   end
   deadmt=zeros(n,n);
end
if m > 1
   num={0};
   den={1};
   dead=0;
   depth=1;
   for i=1:n
      if ~all(nummt{1,i}==0)
         nummt1=nummt;
         nummt1(1,:)=[];
         nummt1(:,i)=[];
         denmt1=denmt;
         denmt1(1,:)=[];
         denmt1(:,i)=[];
         deadmt1=deadmt;
         deadmt1(1,:)=[];
         deadmt1(:,i)=[];
         [num1,den1,dead1]=polydet(nummt1,denmt1,deadmt1,use_Pade);
         dead1=dead1+deadmt(1,i);
         temp=(-1)^(1+i);
         for j=1:length(dead1)
           num1{j}=conv(num1{j},nummt{1,i});
           den1{j}=conv(den1{j},denmt{1,i});
           [num1{j},den1{j}]=z_p_cancel1(num1{j},den1{j},1);
           num1{j}=num1{j}*temp;
           if any((dead1(j)==dead))
              temp1=min(find(dead1(j)==dead));
              temp2=conv(den1{j},num{temp1});
              num{temp1}=polyadd(temp2,conv(num1{j},...
                 den{temp1}));
              den{temp1}=conv(den{temp1},den1{j});
              [num{temp1},den{temp1}]=z_p_cancel1(num{temp1},den{temp1},1);
           else
              if (length(num)>1 | ~all(num{1}==0)) 
                 depth=depth+1;
              end
              num{depth}=num1{j};
              den{depth}=den1{j};
              dead(depth)=dead1(j);
           end
        end
      end
  end
else
   num=nummt;
   den=denmt;
   dead=deadmt;
end
for j=1:length(dead) % get rid of the dead time with zero coef.
   if  all(num{j}==0)
      num(j)=[];
      den(j)=[];
      dead(j)=[];
   end
end
if tempx % if input deadtime is a cell array, so does the output
   temp=cell(1,1);
   for i=1:depth
      if all(dead==0)
         temp{i}=0;
      else
         temp{i}=dead(i);
      end
   end
   dead=temp;
end