Internal Model Control

IMC INTRODUCTION • The main advantage to IMC is that it provides a transparent

framework for control-system design and tuning.

• This is pleasing because we can use standard equipment and algorithms to implement an "advanced" control concept.

• The IMC design procedure is exactly that of the open-loop "control" design procedure developed.

• Thus a factorization of the process model was performed so that the resulting controller would be stable.

• If the controller is stable and the process is stable, then the overall controlled system is stable.

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Contd..

In process control applications, model based control systems are often used

to track set points and reject low disturbances.

The internal model control (IMC) philosophy relies on the internal model

principle which states that if any control system contains within it, implicitly

or explicitly, some representation of the process to be controlled then a

perfect control is easily achieved.

In particular, if the control scheme has been developed based on the exact

model of the process then perfect control is theoretically possible.

Development of the IMC Structure We now consider a process model that receives the same manipulated variable signal as the actual process. We can now subtract the difference between the process output (actually measured) and the process model output (model predicted) to determine the model error. This is shown in Figure 1. We must also realize that disturbances can enter the system, as shown in Figure 3.

1. Process model in parallel with the actual process.

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2. Calculating model error.

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3. Incorporating the process disturbance.

Notice that Figure 2 shows the calculation of model uncertainty (which includes unmeasured disturbances). This information can now be used by the controller, to compensate for the model uncertainty. This creates a feedback system, as shown in Figure 4.

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4. Feedback structure derived from the open-loop structure

Figure 4 is also known as the IMC structure, which is discussed in depth in the next sections.

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• Although the IMC design procedure is identical to the open-loop "control" design procedure, the implementation of IMC results in a feedback system.

• Thus, IMC is able to compensate for disturbances and model uncertainty, while open-loop "control" is not.

• Note that the internal model controller must be detuned to assure stability if there is model uncertainty.

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IMC Structure • The IMC structure is shown in Figure 5. The distinguishing characteristic of this structure is

the process model, which is in parallel with the actual process (plant). Note that (~) is generally used to represent signals associated with the model. Other literature sources may use a subscript (such as m) to represent the model. Figure 6 illustrates that both the controller and model exist as computer computations; it is convenient to treat them separately for design and analysis.

5. The internal model control structure.

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6. The IMC strategy. The dotted line indicates the calculations performed by the model-based controller

A list of transfer function variables shown in the IMC block diagram are given below.

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Recapitulating, the reasons for feedback control include the following:

•Unmeasured disturbances

•Model uncertainty

•Faster response than the open-loop system (with a static controller)

•Closed-loop stability of open-loop unstable system

The primary disadvantage of IMC is that it does not guarantee stability of open-loop unstable systems.

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