1. the block diagram of a closed-loop feedback control system for making set point changes is shown below. the process is second-order. the sensor exhibits first-order dynamics with time constant . the PI controller was tuned for a sensor with time constant =1. however, this sensor with response time =1 is now broken and is very expensive to replace. cheaper sensors are on the market; however, these sensors suffer from a larger response time . our objective is to study how the response time of the sensor we employ affects the stability of this closed loop-with the PI controller settings fixed. (a) (1 point) write the open loop transfer function (in terms of ). (b) (3 points) write the characteristic equation (in terms of ) that determines the boundedinput, bounded-output (BIBO) stability of the closed loop response-as a polynomial in s. 1. the block diagram of a closed-loop feedback control system for making set point changes is shown below. the process is second-order. the sensor exhibits first-order dynamics with time constant . the PI controller was tuned for a sensor with time constant =1. however, this sensor with response time =1 is now broken and is very expensive to replace. cheaper sensors are on the market; however, these sensors suffer from a larger response time . our objective is to study how the response time of the sensor we employ affects the stability of this closed loop-with the PI controller settings fixed. (a) (1 point) write the open loop transfer function (in terms of ). (b) (3 points) write the characteristic equation (in terms of ) that determines the boundedinput, bounded-output (BIBO) stability of the closed loop response-as a polynomial in s