Answer Happy

1. True/False, multiple choice, and short answer (5 points each) (a) State the definition for the system y = f{u} to be linear time-invariant. There are two parts to this definition (i.e., linear and time-invariant). Make sure that you use mathematical notation for both parts 1 (b) Suppose the Laplace transform of f(t) is F(s) (s + 2)(+3) What are the values of f(0) = lim f(t) and lim f(t)? 1 () List two properties of the state transition matrix (t) = <-'[(sl - A)-'). (d) What are the conditions for marginal stability? (e) Which parameters of the prototype second order system affect the settling time? i. the natural frequency w, only ii. the damping factor only iii. both the damping factor and the natural frequency iv, neither the damping factor (nor the natural frequency (1) Which type of system results in a zero steady state error for a ramp input? i type 0 system fi. type 1 system iii. type 2 system iv. none of the above