# 1736

A stirred tank is used in a reaction in which A is converted to B. The stirred tank is perfectly mixed and the reaction is performed at constant volume with the rate of reaction given as ??- = ?? ? where ? ?is the concentration of the reactant A. The inlet concentration of A is ? ??and the inlet flow rate is ?) ?kg/s). The inlet concentration ? ??varies with time. The objective is to control the outlet concentration ? ?by keeping it at a desired set point using the feedback control system shown in the diagram. In the diagram, the controller manipulates the inlet flow rate ? ?through the control valve to keep ? ?at a required set-point. ? The controller set-point calibration ? ,?the analyzer AT, and the current to pressure transducer (I/P) have negligible dynamics, hence their transfer functions are gains ? = ?1.0, ??? = 1.0, and ? = ?1.0 respectively. ? The control valve has a dynamics with the transfer function given as ?= ? ? ??? (a) Derive the process and disturbance transfer function: ?? ? ?? (s?(? = (?) ??? (s(??+(?)? ? (?) [Hint: Perform linearization of process variables around steady-state values for ? ,?? ,??and ? .?See data in the table given] (10 points) (b) Draw a block diagram for the feedback control of the outlet concentration ?) ?10 points) ?? = (?)?? :Controller Proportional (c) Derive the closed loop transfer function relating the change in concentration to change in set-point, ?? ?(?) ???? ?(?) (10 points) (d) For a step change of magnitude 0.15 in the set point (i) Determine the steady state offset for ? = ?0.1, 1 ??? 10 (10 points) (ii) Plot the closed loop response for the controller gains (plot within the rangeA stirred tank is used in a reaction in which A is converted to B. The stirred tank is perfectly mixed and the reaction is performed at constant volume with the rate of reaction given as ??- = ?? ? where ? ?is the concentration of the reactant A. The inlet concentration of A is ? ??and the inlet flow rate is ?) ?kg/s). The inlet concentration ? ??varies with time. The objective is to control the outlet concentration ? ?by keeping it at a desired set point using the feedback control system shown in the diagram. In the diagram, the controller manipulates the inlet flow rate ? ?through the control valve to keep ? ?at a required set-point. ? The controller set-point calibration ? ,?the analyzer AT, and the current to pressure transducer (I/P) have negligible dynamics, hence their transfer functions are gains ? = ?1.0, ??? = 1.0, and ? = ?1.0 respectively. ? The control valve has a dynamics with the transfer function given as ?= ? ? ??? (a) Derive the process and disturbance transfer function: ?? ? ?? (s?(? = (?) ??? (s(??+(?)? ? (?) [Hint: Perform linearization of process variables around steady-state values for ? ,?? ,??and ? .?See data in the table given] (10 points) (b) Draw a block diagram for the feedback control of the outlet concentration ?) ?10 points) ?? = (?)?? :Controller Proportional (c) Derive the closed loop transfer function relating the change in concentration to change in set-point, ?? ?(?) ???? ?(?) (10 points) (d) For a step change of magnitude 0.15 in the set point (i) Determine the steady state offset for ? = ?0.1, 1 ??? 10 (10 points) (ii) Plot the closed loop response for the controller gains (plot within the range

Attachments:

CHE489-Projec….pdf