PID Controllers, 2nd Edition

Chapter 7.5.3 - Control Paradigms: Ratio Control

Ratio Control

When mixing different substances it is desirable to control the proportions of the different media. In combustion control, for example, it is desirable to have a specified ratio of fuel to air. Similar situations occur in many other process control problems. Two possible ways to solve these problems are shown in Figure 7.15. One of the flows, yk, is controlled in the normal way, and the other flow y is controlled as in Figure 7.15A, where the setpoint is desired ratio a and the measured value is the ratio y/yk. This arrangement makes the control loop nonlinear, since the gain of the second controller depends on the signal yk. A better solution is the one shown in Figure 7.15B, where the signal obtained by multiplying yk by a and adding a bias b is used as the setpoint to a PI controller. The error signal is

07_5-7.jpg

where a is the desired ratio. If the error is zero it follows that

07_5-8.jpg

Ratio controllers can easily be implemented by combining ordinary PI and PID controllers with devices for adding and multiplying. The control paradigm is so common that they are often combined in one unit called a ratio controller, e.g., a Ratio PI controller (RPI). There are also PID controllers that can operate in ratio mode.

We illustrate ratio control with an example.

07_5-9.jpg

Figure 7.15 Block diagram of two ratio controllers.

EXAMPLE 7.6 Air-fuel control

Operation of a burner requires that the ratio between fuel flow and air flow is kept constant. One control system that achieves this can be constructed from an ordinary PI controller and an RPI controller as is shown in Figure 7.16. The fuel and the air circuits are provided with ordinary flow control. Fuel is controlled by a PI controller, the air flow is controlled with a ratio PI controller where the ratio signal is the fuel flow. The bias term b is used to make sure that there is an air flow even if there is no fuel flow. The system in Figure 7.16 is not symmetric. A consequence of this is that there will be air excess when the setpoint is decreased suddenly, but air deficiency when the setpoint is suddenly increased.

 

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