On/Off and PID ("proportional integral derivative") are the most frequently used control algorithms in the process industries, and SSF plants are not an exception. Therefore, we will describe below both algorithms in detail and will provide some hints about how to achieve a good performance.
27.2.1 On/Off Control
The simplest algorithm that can be implemented is On/Off control, which explains its widespread use, from home appliances to industrial facilities. This algorithm switches the controller output between two values; the switching is triggered when the measured value crosses the set point, that is, when the error (difference between the measured value and the set point) changes sign. Hence, this algorithm can be written as:
with e(t) = measured value - set point value
Here, e(t) is the error computed at time t, u is the controller output, and uj and u2 are the two possible process input values that must be defined by the process engineer. If the difference u2 - u is large, the process will reach the set point fast, but the maximum error will be large and the controller will switch between uj and u2 very frequently. Hence, proper values of u1 and u2 should be tuned on-line to achieve a compromise between speed of response and maximum error.
To illustrate the effect of tuning, here we present two simulations with On/Off control applied to a double pipe heat exchanger as shown in Fig. 27.3. These simulations were generated with a MATLAB™ model provided by Brosilow and Joseph (2002).
In this model, the cold fluid outlet temperature, T1, (measured variable) is controlled by manipulating the cold fluid inlet flowrate, F1, (operating variable); the controller adjusts the value of F1 by moving the valve V-1 (actuator).
We will evaluate the controller performance using a set point step response. Here, the measured variable starts at a given steady state defined by the initial set point value. Next, we suddenly change the set point value to see how the measured value and the operating variable evolve until they reach a new steady state. This is the standard form to evaluate controlled processes in control engineering.
Figure 27.4 shows the process response when the two possible process inputs measured in gallons per minute (GPM) are u1 = 0.07 GPM and u2 = 0.12 GPM, resulting in a difference u2 - u1 = 0.05 GPM. Although the figure shows that the measured temperature presents small deviations from the reference value, the process takes more than 8 seconds to reach the new steady state, after the set point change at time 15 s. On the other hand, when a difference u2 - u1 of 0.2 GPM is used, the process takes less than one second to reach the new steady state, however, temperature deviations are larger and the switching between u1 and u2 is very frequent (see Fig. 27.5). It is possible to conceive a controller that achieves a fast response and a small maximum deviation, using for example a value of u2 - u1 of 0.2 when the system is far from the set point and a value of u2 - u1 of 0.05 when the system is near the set point. However, the controller would not be On/Off anymore, requiring now 4 input values, and being more difficult to implement.
set e2!ÜJ controller L
hot fluid outlet
Fig. 27.3. Temperature control in a double pipe heat exchanger hot fluid outlet cold fluid inlet hot fluid inlet
Fig. 27.3. Temperature control in a double pipe heat exchanger
With a little extra cost, as we illustrate below, a proportional (P) controller can achieve a much better performance.
Although effective, low cost, and simple, the On/Off algorithm is not appropriate to control critical variables that should be kept close to the required value (set point) when oscillations of input or output variables are deleterious to the process or when the process responds slowly. In these cases, PID controllers are a good option, therefore they are used in almost all industrial installations; they are the first choice when smooth control action and small deviations from the set point are required.
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