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Applied Process Control by Michael Mulholland

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3Modelling

The most important skill that the process engineer brings to bear on the field of process control and optimisation is his/her ability to describe the dynamics and relationships of process variables. The model (Figure 3.1) may serve several purposes:

  • insight and understanding;
  • basis for controller/optimiser design;
  • offline testing of controller/optimiser;
  • basis of filter for online estimation of process variables.
A flowdiagram depicting general open-loop process model, where on the left-hand side are rectangles placed vertically, denoting MV 1–M and DV 1–L, pointing arrows (rightward) at a bigger rectangle denoting process. From process various rightward arrows point at rectangles denoting PV 1–N (top to bottom).

Figure 3.1 General open-loop process model.

In the distant past, models sometimes ran on analogue computers – using capacitors and resistors to convert signals. However, what is being thought of here is an algorithm which will run on a digital computer. Variations to bear in mind include

  • theoretical versus regressed (black box);
  • continuous versus discrete equations;
  • logical versus analogue;
  • online versus offline;
  • linear versus nonlinear;
  • lumped versus distributed;
  • continuous versus discrete versus mixed inputs and outputs;
  • single versus multiple behaviour regimes (modes);
  • numerical versus analytical solution;
  • multi-input, multi-output (MIMO) versus single-input, single-output (SISO);
  • differential versus algebraic;
  • open loop versus closed loop;
  • state-space versus input–output;
  • deterministic versus stochastic;
  • approximate versus accurate;
  • stable versus unstable;
  • transfer function form versus equation form.

In this chapter, the focus will be on the modelling ...

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