[q]=zn2fpd(input)

function [q]=zn2fpd(input)
% [q]=zn2fpd(input)
% Ziegler-Nichols controller for 2nd order processes
% This function computes parameters of the controller (q0, q1, q2, q3, q4).
% Controller is based on forward rectangular method of discretization
% replacing derivation by a four-point difference.
% Transfer function of the controller is as follows:
%
%            q0 + q1*z^-1 + q2*z^-2 + q3*z^-3 + q4*z^-4
% G(z^-1) = --------------------------------------------
%                           1 - z^-1
%
% Transfer function of the controlled system is:
%
%               b1*z^-1 + b2*z^-2 
% Gs(z^-1) = -----------------------
%             1 + a1*z^-1 + a2*z^-2
%
% Input: input ... input parameters
%                  input(1) ... a1
%                  input(2) ... b1
%                  input(3) ... a2
%                  input(4) ... b2
%                  input(5) ... sample time T0
% Output: qp ... controller parameters   
%                qp(1) ... q0
%                qp(2) ... q1
%                qp(3) ... q2
%                qp(4) ... p1
%                qp(5) ... p2

a1 = input(1);
b1 = input(2);
a2 = input(3);
b2 = input(4);
T0 = input(5);

% compute ultimate gain and frequency
[Kpu, Tu] =  ultim([b1 b2],[a1 a2],T0);

Kp = 0.6*Kpu;
Ti = Tu/2;
Td = Tu/8;

q0 = Kp*(1 + T0/Ti + Td/(6*T0));
q1 = Kp*(-1 + Td/(3*T0));
q2 = Kp*(-Td/T0);
q3 = Kp*(Td/(3*T0));
q4 = Kp*(Td/(6*T0));

q=[q0;q1;q2;q3;q4];