{foptd,pid}={(TransferFunctionModel[((1. (E^(- s)))/(1+0.125s)), ]),TransferFunctionModel[1+(1/(10 s))+(s/8),s]};

nsys=SystemsModelFeedbackConnect[foptd,pid]

OutputResponse[nsys,UnitStep[t-1],{t,0,10}];
Plot[{%,UnitStep[t-1]},{t,0,10},PlotStyle->{Automatic, Dashed}]

OutputResponse[nsys,Cos[t],{t,0,10}];
Plot[{%,Cos[t]},{t,0,10},PlotStyle->{Automatic, Dashed}]

OutputResponse[nsys,SquareWave[t/8.5],{t,0,10}];
Plot[{%,SquareWave[t/4]},{t,0,10},PlotStyle->{Automatic, Dashed}]