Nonlinear Control Sy.. - Free

1.10. EXERCISES 27
Figure 1.18: Ball-and-beam experiment.
g, and r and 0 are shown in Figure 1.18. Defining now state variables xl = r, x2 = r, x3 = 0,
and x4 = 0, we obtain the following state space realization:
1.10 Exercises
x2
-mg sin x3 + mx1x4
m+ R
X4
T - rngx1 COS X3 - 2mxlx2x4
mxi+J+Jb
(1.1) For the following dynamical systems, plot ± = f (x) versus x. From each graph, find
the equilibrium points and analyze their stability:
(a) a=x2-2.
(b) ±=x3-2x2-x+2.
(c) x=tanx - 2