The dynamic behavior of a physical process can be represented by the transfer function: y(s) x(s) = 18 s2 + 3s + 9 (a) After a step change of x(t) = 2S(t) (where S(t) represents the unit step function), what is the new steady-state value of y? (b) For physical reasons, it is required that y(t) 2 throughout the transient response. What is the largest step change in x that the process can tolerate without exceeding this limit? Hint: First check to see whether the response would be oscillatory, then proceed as appropriate. (c) If the system is oscillatory, determine for the response to the step in (b), (i) the period of oscillation. (ii) the decay ratio, and (iii) the time to first peak. (d) Confirm your answers in (b) and (c) using the step function in Matlab.