Instrumentation and Control Systems
All real chemical processes are dynamic, which means they change with time. This is to say they are unsteady state. Steady state describes a system without disturbances. The intention of a process control system is to counter disturbances to create a metastable state process. Instrumentation measures process variables. Controllers calculate changes required to counter changes in signals from instrumentation. Actuators receive signals from controllers and make changes in the process.
The bottoms product of a distillation column flows into a tank before it is loaded into barges for shipment. The maximum temperature limit in the tank is 200 degrees Fahrenheit. If the stream is cooled too much, it may become too viscous to pump, so the minimum temperature is 150 degrees Fahrenheit. A thermocouple is installed on the inlet pipe to the tank. The thermocouple measures the temperature of the stream and sends a signal to a controller. The controller uses the signal from the thermocouple to calculate a signal to give to the actuator on a control valve which may open or close to adjust the flow bypassing a heat exchanger which cools the stream as it leaves the process unit.
Types of Control Loops:
In the above example, the temperature leaving the distillation column would be known as the input variable. The changes in the amount of cooling from the heat exchanger would be called disturbances. The input and the disturbances to the process change the output. In the case above, the output is the tank inlet temperature.
The example above is a feedback control loop. A feedback control loop is one which measures the output to control the process.
A feedforward control loop is one that measures the input and/or the disturbances to control the process.
An open control loop does not measure the process inputs, outputs or disturbances. It controls without information that closes the loop.
Most simple control loops have a set-point to which they control. Setpoints may be constant or they may be changed by an operator or another controller. When a control loop changes the setpoint of another control loop, it is known as cascaded control.
The equations a controller uses to choose the signal for an actuator (in the example above, the position of the control valve) most commonly incorporate a sum of one, two or three terms. These are "proportion", "integral" and "derivative" terms.
The most simple control is called proportional control. In proportional control, the signal is equal to the difference between the setpoint and the measured variable multiplied by a constant. In the example above, if the tank inlet temperature setpoint was 175 degrees Fahrenheit, the thermocouple signal read 177 degrees, and the chosen constant was 3% valve position per degree, the control signal would be (175deg-177deg)*3%/1deg = -6%. The controller would signal the control valve to close 6% to divert more flow through the heat exchanger. The chosen constant is a tuning parameter. If it were chosen too small, it wouldn't make large enough changes to the process to control the tank inlet temperature. If it were too large, it may make changes to the process which cause the output to frequently overshoot the setpoint. For this reason, it is critical to appropriately choose the constant. This may be done experimentally or by modeling the process.
A second type of control is called proportion, integral control. Abbreviated as P,I control, the signal is chosen by the sum of two terms. The first term is calculated as described above in proportional control. The second is the integral term. The integral term seeks to improve control by accounting for the amount of time a process output has been above or below the setpoint. The integral term is equal to a second tuning parameter multiplied by the integral of the difference in the output and the setpoint over a chosen period of time. For example, if the integral term measures the previous 10 seconds of data, the tank inlet was 2 degrees too hot for 6 seconds, 1 degree too cold for 4 seconds, and the constant was chosen as 0.1%/deg*sec, then the integral term would be (2deg*6sec-1deg*4sec)*0.1%/deg*sec = +0.8%. The control signal would be the sum of the proportion term and the integral term. -6%+0.8% = -5.2%.
The derivative term may be used to improve control by accounting for how quickly the process output is changing. It's important to note that a derivative term may harm control in certain circumstances because it amplifies the effect of error in measurement of the output variable and actuation of the controller. Nonetheless, the derivative term may be useful for making the controller act quickly to large changes in the process. For instance if the temperature of the distillation column bottoms in the example above were to suddenly increase, the derivative term in the controller would help quickly close the bypass valve. The derivative term is the product of a third constant and the derivative, or rate of change, of the difference between the measured variable and the setpoint over a chosen period of time. For example, if the derivative term measures the previous 5 seconds, each of those 5 seconds, the tank inlet temperature increased two degrees and the chosen constant were -1%/deg/sec, then the derivative term would be 2deg/s*-1%/deg/sec = -2%. If the controller was a PID controller, it would sum the proportion, integral and derivative term. -6%+0.8%-2% = -7.2%. The controller would signal the actuator on the control valve to close it 7.2% because the tank inlet temperature was too hot and continuing to heat up.