Question

Problem 1: Feedback Control of an Integrating Process The process model for a liquid storage system shown in the process diagram below is given by the following transfer function: $G_p(s) = \frac{H(s)}{F(s)} = \frac{K_p e^{-\theta s}}{s}$ $K_p = 0.2$ $\theta = 7.4$ The objective is to control the level by manipulating the inlet flow rate. The outlet flow is directed to a chemical reactor and is kept constant under flow control. The inlet flow rate acts both as the manipulated variable(MV) and as a disturbance(DS). A PID controller is considered for this task 1. Using the Internal Mode Control (IMC) tuning method derive expressions for the controller gain, reset and rate parameters 2. Draw a block diagram for this control loop and derive the transfer functions for the level response to (a) a set point change and (b) to a disturbance change 3. Using MATLAB or the PIDController.xlsm control loop simulator, prepare plots for the level response to unit step change in the disturbance variable for various values of the design parameter $\tau = \{4, 8, 16\}$. Based on your simulations select what you consider to be the most suitable design parameter. 4. Calculate the maximum process gain for which the PID controller you have designed is stable. Calculate an approximate value with the Routh criterion and the exact value using the frequency response analysis method.

          Problem 1: Feedback Control of an Integrating Process
The process model for a liquid storage system shown in the process diagram below is given by
the following transfer function:
$G_p(s) = \frac{H(s)}{F(s)} = \frac{K_p e^{-\theta s}}{s}$  $K_p = 0.2$  $\theta = 7.4$
The objective is to control the level by manipulating the inlet flow rate. The outlet flow is
directed to a chemical reactor and is kept constant under flow control. The inlet flow rate acts
both as the manipulated variable(MV) and as a disturbance(DS). A PID controller is considered
for this task
1. Using the Internal Mode Control (IMC) tuning method derive expressions for the
controller gain, reset and rate parameters
2. Draw a block diagram for this control loop and derive the transfer functions for the level
response to (a) a set point change and (b) to a disturbance change
3. Using MATLAB or the PIDController.xlsm control loop simulator, prepare plots for
the level response to unit step change in the disturbance variable for various values of the
design parameter $\tau = \{4, 8, 16\}$. Based on your simulations select what you consider to
be the most suitable design parameter.
4. Calculate the maximum process gain for which the PID controller you have designed is
stable. Calculate an approximate value with the Routh criterion and the exact value using
the frequency response analysis method.

$Problem 1: Feedback Control of an Integrating Process The process model for a liquid storage system shown in the process diagram below is given by the following transfer function: Gp(s) = (H(s))/(F(s)) = (Kp e^-θ s)/(s) Kp = 0.2 θ = 7.4 The objective is to control the level by manipulating the inlet flow rate. The outlet flow is directed to a chemical reactor and is kept constant under flow control. The inlet flow rate acts both as the manipulated variable(MV) and as a disturbance(DS). A PID controller is considered for this task 1. Using the Internal Mode Control (IMC) tuning method derive expressions for the controller gain, reset and rate parameters 2. Draw a block diagram for this control loop and derive the transfer functions for the level response to (a) a set point change and (b) to a disturbance change 3. Using MATLAB or the PIDController.xlsm control loop simulator, prepare plots for the level response to unit step change in the disturbance variable for various values of the design parameter τ = {4, 8, 16}. Based on your simulations select what you consider to be the most suitable design parameter. 4. Calculate the maximum process gain for which the PID controller you have designed is stable. Calculate an approximate value with the Routh criterion and the exact value using the frequency response analysis method.$

Added by Jessica L.

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