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A feedforward-only control system is to be designed for
Chapter 15, Problem 15.11(choose chapter or problem)
A feedforward-only control system is to be designed for the stirred-tank heating system shown in Fig. E15.11. Exit temperature T will be controlled by adjusting coolant flow rate, qc. The chief disturbance variable is the inlet temperature T; which can be measured on-line. Design a feedforwardonly control system based on a dynamic model of this process and the following assumptions: 1. The rate of heat transfer, Q, between the coolant and the liquid in the tank can be approximated by Q = U(1 + qc)A(T- Tc) where U, A, and the coolant temperature Tc are constant. 2. The tank is well mixed, and the physical properties of the liquid remain constant. 3. Heat losses to the ambient air can be approximated by the expression QL = ULAL(T- Ta), where Ta is the ambient temperature. 4. The control valve on the coolant line and the T; sensor/ transmitter (not shown in Fig. E15.11) exhibit linear behavior. The dynamics of both devices can be neglected, but there is a time delay e associated with the T; measurement due to the sensor location.
Questions & Answers
QUESTION:
A feedforward-only control system is to be designed for the stirred-tank heating system shown in Fig. E15.11. Exit temperature T will be controlled by adjusting coolant flow rate, qc. The chief disturbance variable is the inlet temperature T; which can be measured on-line. Design a feedforwardonly control system based on a dynamic model of this process and the following assumptions: 1. The rate of heat transfer, Q, between the coolant and the liquid in the tank can be approximated by Q = U(1 + qc)A(T- Tc) where U, A, and the coolant temperature Tc are constant. 2. The tank is well mixed, and the physical properties of the liquid remain constant. 3. Heat losses to the ambient air can be approximated by the expression QL = ULAL(T- Ta), where Ta is the ambient temperature. 4. The control valve on the coolant line and the T; sensor/ transmitter (not shown in Fig. E15.11) exhibit linear behavior. The dynamics of both devices can be neglected, but there is a time delay e associated with the T; measurement due to the sensor location.
ANSWER:Step 1 of 8
We are given the following information:
- The controller used is feedforward control only.
- is the coolant flow rate which is changed to control the outlet temperature .
- is the disturbance variable.
- which is the rate of heat transfer can be expressed by:
- The internal energy of the fluid , and the coolant temperature are constant
- There is no change in the physical properties of the liquid
- The relation between the heat losses and the ambient temperature is expressed by:
- The control valve and the sensor are behaving linearly with negligible dynamics.
- The sensor has a time delay .