
Later, in Section 5.6, Equations 5.50 and 5.51 will be converted into a pair of equations, one for
€
x
and the other with
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u where both are explicit functions of the state variables u and
_
u.
A Simu link diagram of the system is shown in Figure 5.33.
The algebraic loop shown in bold is broken by the insertion of a ‘‘Memory’’ block, eliminating
the need for the Newton–Raphson iterative root solving at each integration step.
A simulation of the inverted pendulum when u(t) ¼0, t 0 was run for a period of 10 s using a
fixed-step numerical integrator. All initial conditions are zero except the initial pendulum deflection,
u(0) ¼p=2 rad. The output u(t) is