The control of the fuel-to-air ratio in an automobile carburetor became of prime importance in the 1980s as automakers worked to reduce exhaust-pollution emissions. Thus, auto engine designers turned to the feedback control of the fuel-to-air ratio. A sensor was placed in the exhaust stream and used as an input to a controller. The controller actually adjusts the orifice that controls the flow of fuel into the engine [3]. Select the devices and develop a linear model for the entire system. Assume that the sensor measures the actual fuel-to-air ratio with a negligible delay. With this model, determine the optimum controller when we desire a system with a zero steady-state error to a step input and an overshoot for a step command of less than 10%.