Question

13.2 Consider the system (a) Is the system input-output linearizable? 0.05 t-0.25 2 1.5 1.5 output -reference output -reference 0.5 0.5 0.5 1.5 0.5 1.5 0.05 τ = 0.25 2 0.5 1.5 0.5 1.5 Time Figure 13.3: Simulation of the tracking control of Example 13.22 (b) If yes, transform it into the normal form and specify the region over which the transformation is valid (c) Is the system minimum phase?

Answer 1

[x_1 x_2 x_3] = [- 1 - 1 - 1 1 1 0 - 1 1 0] [x_1 x_2 x_3] + [0 1 1] [4] y = [0 0 1] [x_1 x_2 x_3] from the above Transfer function is Therefore = c [S J - A]^- 1 B + D = [0 0 1] [s + 1 1 1 - 1 s + 1 0 1 - 1 s] [0 1 1] = [0 0 1] [s^2 + s - s - 1 - s - 1 s s^2 + s - 1 - s s + 2 s^2 + 2s + 2] [0 1 1] [s^2 + 25 + 1]/1 m Y (s)/X (s) = 1/s rightarrow (1) Apply inverse Laplace transform \r\n d y (t)/dt = x (t) rightarrow (2) from (2) we can say that d y_1/dt = x (t) d y_2 (t)/dt = x_2 (t) y_3 = y_1 + y_2 rightarrow Linear From (1) we see that y (s) = x (s)/s rightarrow y (t) = x (t) u (t)