Spring 2003 16.61AC26 Longitudinal Response Final response to a step input u =i/s, y=G(s)u, use the FVT lim y(t)= lims G(s) =lim y(t)=G(O)u=-CA B)i Initial response to a step input, use the IVT ()=s(G(s)=)=iG(s)i For your system, G(s)=C(sI-A)B+D, but D=0, so linG(s)→0 Note: there is No immediate change in the output of the motion variables in response to an elevator input =y(0)=0 Consider the rate of change of these variables y(0) i(t)=CX=CAX+CBu and normally have that CB#0. Repeat process above to show that i(0+)=CBi, and since C=I, (0+)=Bi Looks good. Now compare with numerical values computed in MATLAB Q Plot u, a, and fight path angle ?=8-a(since 00=10=0) See ac 1-10 I Note that C(sI-A)-B+D=D+CB+CArE+