Question

Problem 3 Consider the following system: 2 213+w. where w denotes control input. Here we design a control system based on passivity. (a) Suppose that w =-r1 + x2 + 2.123 + u for a new control input u. Show that the state equation can be written as the following cascade form: i fa(2) +F(z)y, 22u yT2, where z = [ri, r3]T e R2. Find the expression for fa (z) and F(z). (b) Show that when y0, the origin 0 of the following driven system is asymptotically stable. ( Hint: W(2)-ドー树+]小 (c) Show that the following driving system is passive: (d) Based on the passivity property, design u such that the origin 0 of the complete system is asymptotically stable. Give the corresponding expression for the original control input w (Hint: U(z, x2) = W(z) + V(T2))

Answer 1

Jhis gives, ㄥ 1) rep lie xi 0 х.

2 군군 х. excpt m