PID Controllers, 2nd Edition

Chapter 7.4 - Control Paradigms: Model Following

When discussing PID-control in Chapter 4 the main emphasis was on load disturbance response. The setpoint response was shaped by setpoint weighting. In some cases it is desirable to have more accurate control of the setpoint response. This can be achieved by using a reference model that gives the desired response to setpoint changes. A simple approach is then to use the scheme shown in Figure 7.8 where the output of the reference model is fed into a simple feedback loop.

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Figure 7.8 Block diagram of a system based on model following.

07_4-2.jpg

Figure 7.9 Block diagram of a system that combines model following and feedforward from the command signal.

The reference model is typically chosen as a dynamic system of first or second order. In this case we obtain model following by combining a simple controller with a model. It is necessary that the feedback loop be very fast relative to the response of the reference model.

The system can be improved considerably by introducing feedforward as shown in Figure 7.9. In this system we have also feedforward from the command signal. (Compare with Section 7.3.) The signal uff is such that it will produce the desired output if the models are correct. The error e will differ from zero when the output deviates from its desired behavior. The feedback path will then generate the appropriate actions. When implementing the system the boxes labeled model and feedforward are often combined into one unit which has the command signal yc as input and ysp and uff as outputs.

The system is called a two-degree-of-freedom system because the signal paths from setpoint to control and process output to control can be chosen independently. Use of setpoint weighting (see Section 3.4) is one way to obtain this to a small degree. The system in Figure 7.9 is the general version. For such systems it is common to design the feedback so that the system is insensitive to load disturbances and process uncertainties. The model and the feedforward elements are then designed to obtain the desired setpoint response. The feedback controller is often chosen as a PID controller. Model following is used when precise setpoint following is desired, for example, when several control loops have to be coordinated.

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