# onsider the following differential equationd 2 y + 3 dy + 2

onsider the following differential equation:d 2 y + 3 dy + 2 y = udt2 dtWrite the state equations for this systemAdd a new state in which x&3 = y − yd where yd is the unit step and represents the desiredoutput of the system. Write the new state equations treating yd as another input.Now,pickavector k=[k1,k2,k3]suchthatifu=−kx,thenewstateswillhaverootsofthecharacteristic equation at ‐2, ‐3, and ‐4.Simulate the system and observe the output y and compare the response for yd = step inputto the step response of the system without control.