Answer Happy

Q3) [30 points total] Consider the following input/output differential equation that described the equation of motion of a system: y + 5y – 60y = 3 sin u – - 1543, where y is the output, u is the input. a) Define the state variables of the system above. Convert the equation of motion into two 1st-order ODE's that are functions of the state variables and input u. Write the ODE's in the nonlinear state-space form i = f (x, u) (u is a scalar in this case). [10 points]
= b) Compute the matrices A and B of the linearized state-space model, is Axg + Bug, that you obtain by linearizing the nonlinear model about: Xo = , uo = 0. [10 points) [01 :
c) Is the nonlinear system above with input u=0 asymptotically stable or unstable? [10 points]