Internal model control

Internal model control loop

Internal Model Control ( IMC ) is a control method from control engineering that is the implicit basis of all predictive controllers . Controllers based on the IMC principle contain a mathematical model of the process that is as identical as possible to the process and a compensation element . ${\displaystyle G(s)}$ ${\displaystyle G_{m}(s)}$ ${\displaystyle Q(s)}$

Basic principle

The model is supplied with the same manipulated variables as the real process ; with a perfect model, the difference between the model output and the measured actual value y is the estimate for the non-measurable disturbance . Without this disturbance, this value and thus the negative input of the compensator is zero. Then applies and thus the theoretical ideal (actual value = target value) can be achieved through . ${\displaystyle G_{m}(s)}$ ${\displaystyle G(s)}$ ${\displaystyle {\overline {d}}}$ ${\displaystyle {\overline {y}}_{d}}$ ${\displaystyle {\overline {u}}(s)=Q\cdot {\overline {w}}(s)}$ ${\displaystyle {\overline {y}}(s)=G\cdot {\overline {u}}(s)=G\cdot Q\cdot {\overline {w}}(s)}$ ${\displaystyle G\cdot Q=I\Leftrightarrow Q=G^{-1}}$

In real processes, this cannot be achieved due to the delay, but only feedforward controllers and no feedback controllers are required. So, with a perfect model, only one control (feedforward) is necessary. Model errors and non-measurable disturbances are corrected by the controller component (controller). In the case of an ideal model and stable process, it is also true that the entire closed control loop is stable if the sufficient condition Q (s) is stably fulfilled.

Conventional regulation

For a conventional controller K arises in the formula for an IMC controller by switching finally , this parameterization is also Q parameterization mentioned. ${\displaystyle {\overline {u}}=K\cdot ({\overline {w}}-{\overline {y}})}$ ${\displaystyle {\overline {u}}=Q\cdot ({\overline {w}}-({\overline {y}}-G_{m}{\overline {u}}))}$ ${\displaystyle K=Q\cdot (I-G_{m}Q)^{-1}}$

literature

• Garcia, EC and M. Morari: Internal Model Control: 1. A Unifying Review and Some New Results . In: Industr. and Eng. Chemistry Process Design and Development . tape 21 , 1982, pp. 308-323 .
• Dirk Abel, Ulrich Epple, Gerd-Ulrich Spohr: Integration of Advanced Control in the process industry . Wiley-VCH, 2008, ISBN 978-3-527-31205-4 , pp. 64-66 .
• Kai Müller: drafting robust regulations . 1st edition. Teubner-Verlag, Stuttgart 1996, ISBN 3-519-06173-2 .