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A Real-Time Approach to Process Control, 3rd Edition by William Svrcek, Donald Mahoney, Brent Young

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9

Using Steady-State Methods in a Multi-loop Control Scheme

Control scheme selection for a unit operation, a process or a total plant is straightforward provided each controlled variable is only affected by one manipulated variable. However, interactions are often present between the various control loops in multi-loop control schemes. Interactions occur when a manipulated variable affects a controlled variable of another loop. For instance, in a distillation column a manipulated variable, such as reflux flow rate, may affect several different controlled variables, such as distillate flow rate, distillate composition and/or reboiler duty. Hence, selecting the best control scheme for pairing manipulated and controlled variables is not straightforward. This chapter explores different methods for designing multi-input/multi-output control schemes for processes using steady-state methods such as relative gain array (RGA), the Niederlinski index (NI) and singular value decomposition (SVD).

9.1 Variable Pairing

When multiple, single-loop control schemes interact, the closure of one loop can change the closed loop gain of one or all the other control loops in the scheme. The SISO control loops may become unstable or respond sluggishly to disturbances since the overall loop gain has been altered (Equation 2.6). The interaction between two control loops, in block diagram form, is illustrated in Figure 9.1 and is described mathematically as follows:

(9.1)

(9.2)

where yi is the controlled ...

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