Your boss has discussed implementing a level controller on a troublesome process tank that contains a boiling liquid. Someone told him that a level transmitter used with such a system has a very noisy output and that a P or PI controller will require a noise filter on the measurement. (a) Show how a measurement noise filter can be implemented with a PI controller by drawing a block diagram of the controller, modified with a first order transfer function in the appropriate location. (b). How would fig be modified to illustrate the response of a PI controller to a step change in the filtered measurement? If necessary, calculate the time response. (c). Your company purchased a digital control system several years ago that provides a first order digital filter as one of its many features. Can you suggest why this required noise filter ought to be implemented using an analog instrument, instead of using the available digital implementation? Assume that the digital controller utilizes a sampling interval of 1 S