Page 464 - Design and Operation of Heat Exchangers and their Networks

Optimal control process of heat exchanger networks 447

Eq. (9.41) demonstrates that the deviations of the controlled output vari-
ables Δz θ will be affected by the deviations in the thermal capacity rates of
_
_
the process streams C h, j ( j¼1, 2, …, N h ) and C c,k (k¼1, 2, …, N c ) and the
manipulation of the bypass fractions c h,i and c c,i (i¼1, 2, …, N E ).
If the HEN is flexible, for a given u2R u , an optimal control vector
c2R c (R c ¼{0 c h, i 1,0 c c, i 1jy i ¼1;i¼1,2,…,N E }) can be found
such that the total utility cost reaches the minimum,
n o
X X
ð
ð
min C x, c, uð Þ ¼ min a Q HU x, c, uÞ + b Q CU x, c, uÞ (9.42)
c2R c c2R c
s:t: Δzx, c, uÞ ¼ 0
ð
hx, c, uÞ ¼ 0
ð
gx, c, uÞ 0
ð
9.4 The dynamic control of heat exchanger networks
Operation analysis (static optimal) of a given HEN gives us the information
on which variables (or which bypasses) should be manipulated and how
much should be manipulated upon disturbances in order to maintain the
target temperatures so that the utility consumption at the same time is min-
imized. The dynamic control analysis and control strategy design will decide
how to manipulate those selected bypasses within a limited time to recover
the nominal operation outputs, namely, how to arrange the temporary
manipulations and how fast the change should be carried out. The dynamic
control process is depended on the choice of control system and its strategy.

9.4.1 Basic concepts of the model predictive control

Feedback and feedforward are two types of control schemes for systems that
react automatically to the dynamical disturbance inputs. The control of any
dynamic system, including heat exchangers and HENs, should be executed
on the basis of automatic control principle. Traditional automatic control is
based on PID feedback method, by which the feedback is the sum of propor-
tional plus integral plus derivative. As is shown in Fig. 9.5 as an example, for
controlling the outlet temperature of the hot stream at the set value, t h,set ,the
00
00
deviation Δz¼z z ref between the measured outlet temperature t h and its
target temperature t h,set are sent to the feedback controller. According to Δz
00
and its variation history, the controller sends a manipulating signal y to adjust
the bypass fraction so that the deviation Δz will approach zero again. Like all
other PID feedback control systems, during the control process, the