1. Design an air-fuel ratio controller for a four cylinder SI engine with manifold fuel injection. Assume that you can model the engine with a first order transfer function and a dead time. The transfer function would have the following form. A(s) U(s) 1+T where A(s) is the air-fuel ratio, U(s) is the control variable (e.g. fuel injection time). Assume that Kle -1.1; Tie 0.07 sec; and Tae 0.05 sec. Design a Proportional plus Integral (PID) controller (i.e. determine the P+I gain values) to obtain the following step response characteristics: Rise time (90%-0.4 sec; Max overshoot