Applied Process Control Essential Methods by Unknown

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Language: eng
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251

7

Advanced Control Algorithms

This chapter focuses largely on multi-input multi-output (MIMO) controllers. The same equations

can be simplified where necessary for the SISO case.

7.1

Discrete z-Domain Minimal Prototype Controllers

This is a sampled data controller based on a model of the process. The design procedure seeks to

achieve a stipulated sampled response to a stipulated disturbance to the system. This may not

always be achievable, so an alternative desired response may have to be given. Figure 7.1 shows a

typical installation in which the manipulated variable values are updated by comparison of feedback

with setpoint only at fixed intervals T. The aim will be to achieve a particular form of measured

output y in response to particular forms of setpoint variation ys and/or load disturbance

variations d.

Recalling from Section 3.9.3.1 that the analogue sections must be combined between sampling

points, before transforming to ‘impulse-modulated’ (z) form, and being careful to preserve the

transfer function multiplication order so that MIMO systems are included, the system shown in

Figure 7.1 is seen to have a measured output determined by

y�z� � G

� MGLd� z

� � � �GMGPGH��z�GC z

� � y � � y� �

s z

z

(7.1)

that is

y�z� � I

f � G

� MGPGH��z�GC z

� �g 1 �GMGLd��z� � �GMGPGH��z�GC�z�ys z

� �

(7.2)

7.1.1

Setpoint Tracking Discrete Minimal Prototype Controller

Minimal prototype controllers will differ for setpoint or load disturbance, and for the particular

type of disturbance chosen, for example step versus ramp. In Examples 7.1 and 7.2, control of a

first-order system, with and without dead time, is considered, based on specifications for setpoint

tracking.

Applied Process Control: Essential Methods, First Edition. Michael Mulholland.

 2016 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2016 by Wiley-VCH Verlag GmbH & Co. KGaA.

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