
(a) Find the matrix A in the state equations
_
x ¼ A
x for the continuous-time model.
(b) Find the matrix G in the discrete-time state equations
x
A
(n þ1) ¼Gx
A
(n) resulting from
the use of improved Euler integration to approximate the response of the continuous-time
system.
(c) The syst em parameters are k ¼4lb=ft and m ¼1 slug. Fill in the following table:
Nx
A
(n) T ¼0.05 s x(nT ) nx
A
(n) T ¼001 s x(nT )
00
15
210
315
420
525
630
735
840
945
10 50
3.25 By trial and error, determine an acceptable value for the step size T in simulating the nonlinear
pendulum response in Example 3.12 using implicit Euler integration. The initial conditions
are x
1
(0) ¼p=6 rad and x
2
(0) ...