The effect of filtering on closed loop dynamics Your boss has discussed implementing a level controller on a troublesome boiler drum that contains a boiling liquid. The manipulated variable is the feedwater control valve. The level transmitter is quite noisy and that such a system will require a noise filter on the measurement. a) Use a block diagram to show how a filter can be implemented. Assume that the filter is implemented through a first order transfer function with filter time constant f. and the level process is represented by the following transfer function: Gp(s)=s(2s+1)K(1s+1) b) Develop the closed loop relationships between the level setpoint and measurement assuming the measurement and valve dynamics are unity (Gm=Gv=1) and a proportional only controller. The valve characteristics are assumed to be linear. c) Comment on choice of the filter time constant frelative to the process time constant. 2. d) Can the presence of the filter lead to instability of the closed loop