%
% Calculate PID parameters given gamma1, gamma2, beta,
% omega, zeta, and alpha
%
format compact

if ~(exist('gamma1')==1 && exist('gamma2')==1 && exist('delta')==1 ...
     && exist('omega')==1 && exist('zeta')==1 && exist('alpha')==1)
  error('gamma1, gamma2, delta, omega, zeta, and alpha must be defined first.')
end

% Given constants
x10 = 0.5;
x20 = 0.5;

% Process parameters
rho = delta;
tau1 = 2*sqrt(x10)/gamma1;
tau2 = 2*sqrt(x20)/gamma2;

% PID parameters
K = tau1/rho*(omega^2*(1+2*zeta*alpha)-1/(tau1*tau2))
Ti = rho*K/(tau1*alpha*omega^3)                       
Td = tau1/(rho*K)*(omega*(alpha+2*zeta)-1/tau1-1/tau2)