A mixing process consists of a single stirred tank instrumented as shown in Figure 3. The...

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A mixing process consists of a single stirred tank instrumented as shown in Figure 3. The concentration of single species A in the feed stream varies. The controller attempts to compensate for this by varying the flow rate of pure A through the control valve using PI controller (K. = 5, = 0.25). All the transmitter dynamics are negligible. The following data are %3D given. GA Pu MP V Traasfer line Stirred tank AT AC Figure 3: Mixing Process Control System The process transfer function is given by 1 G, s' +2s+1 The disturbance transfer function is given by 5 G, 2s +1 a) Construct the block diagram of the process by mentioning all the transfer functions (10 Marks) b) Formulate the closed-loop transfer function for set-point change and disturbance change (8 Marks) c) Evaluate the stability of the system using Routh stability criterion. Also determine the number of roots on the LHP and RHP. (10 Marks) d) If the PI controller is replaced by P controller, for what value of Ke the system will be on the verge of instability and also determine the roots on the imaginary axis. (12 Marks) The steady-state gain and time constant for the control valve are given as 2 and 1 respectively. The input range of composition transmitter is 0 to 1 and the output range is 4 to 20 mA. The input range of set point transmitter is 0.5 to 1 and the output range is 4 to 20 mA. The input range of I/P transmitter is 4 to 20 mA and the output range is 3-15 psig. A mixing process consists of a single stirred tank instrumented as shown in Figure 3. The concentration of single species A in the feed stream varies. The controller attempts to compensate for this by varying the flow rate of pure A through the control valve using PI controller (K. = 5, = 0.25). All the transmitter dynamics are negligible. The following data are %3D given. GA Pu MP V Traasfer line Stirred tank AT AC Figure 3: Mixing Process Control System The process transfer function is given by 1 G, s' +2s+1 The disturbance transfer function is given by 5 G, 2s +1 a) Construct the block diagram of the process by mentioning all the transfer functions (10 Marks) b) Formulate the closed-loop transfer function for set-point change and disturbance change (8 Marks) c) Evaluate the stability of the system using Routh stability criterion. Also determine the number of roots on the LHP and RHP. (10 Marks) d) If the PI controller is replaced by P controller, for what value of Ke the system will be on the verge of instability and also determine the roots on the imaginary axis. (12 Marks) The steady-state gain and time constant for the control valve are given as 2 and 1 respectively. The input range of composition transmitter is 0 to 1 and the output range is 4 to 20 mA. The input range of set point transmitter is 0.5 to 1 and the output range is 4 to 20 mA. The input range of I/P transmitter is 4 to 20 mA and the output range is 3-15 psig.