The forward-path transfer function of a control system with unity feedback is where a and K are real constants. (a) Find the values of a and K so that the relative damping ratio of the complex roots of the characteristic equation is 0.5 and the rise time of the unit-step response is approximately 1 s. Use Eq. (7-98) as an approximation of the rise time. With the values of a and K found, determine the actual rise time using computer simulation. (b) With the values of a and K found in part (a), find the steady-state errors of the system when the reference input is (i) a unit-step function and (ii) a unitramp function.