For the inertia system represented by the equation: T = Jθ¨ + Bθ˙ and using the velocity and position as state variables, determine:
a. State space model matrices (A, B, C, and D) for the system assuming that the position (x1) is used as the output.
b. The state feedback gains for desired closed-loop poles of -5 + 3i and -5 - 3i. Use the same B and J values as those used in Figure 9.9.
A plot of this equation is shown in Figure 9.9 for a system with J = 0.7 kg m^2 and B = 0.5 N·m·s/rad. These same parameters are used for all the simulations shown in this chapter.
Figure 9.9
2 1.8 1.6 1.4 1.2 Speed (rad/s)
1 0.8 0.6 0.4 0.2 0 0
-1
-2
-3
-4 5 6 Time (s)
7
8
9
10