%LTSROB Loop transfer function for reduced-order-observer based tracking system.
% LTSROB is a script that calculates a state-space description
% of the loop transfer function for a reduced-order-observer based
% tracking system. Such a tracking system can be designed using
% the functions DTS and ROO.
%
% INPUTS:
%
% phi,gamma ZOH equivalent plant model.
% Cm Measurement matrix: ym[k] = Cm x[k]
% c Output matrix: y[k] = c x[k]
% F,G,H,K,P Reduced-order observer matrices
% phia,gammaa State space matrices for additional dynamics
% L1,L2 Feedback gains for cascade of plant and additional
% dynamics.
%
% OUTPUTS:
%
% phi_L,gamma_L,c_L State-space description of loop transfer function.
%
% To find stability margins, use SM(phi_L,gamma_L,c_L).
% R.J. Vaccaro 11/94,11/98
[nn_4,nn_1]=size(Cm);
nn_2=length(F);
nn_3=length(phia);
Lb1=L1/P;
Lb_11=Lb1(:,1:nn_4);
Lb_12=Lb1(:,nn_4+1:nn_1);
phi_L=[phi zeros(nn_1,nn_2+nn_3);...
(G-H*(Lb_11+Lb_12*K))*Cm F-H*Lb_12 -H*L2;...
gammaa*c zeros(nn_3,nn_2) phia];
gamma_L=[gamma;zeros(nn_2+nn_3,length(gamma(1,:)))];
c_L= [(Lb_11+Lb_12*K)*Cm Lb_12 L2];
clear nn_1 nn_4 Lb1 Lb_11 Lb_12 nn_2 nn_3
sm(phi_L,gamma_L,c_L)
