Comfort Control Techniques for the Users of a Room - Comfort Control in Buildings - page 182

index value equal to zero. A PNMPC strategy is used (Plucenio et al. 2007 ), see
Sect. 5.2.3 .

5.4.1.1 Cost Function

MPC algorithms are characterised by the explicit use of a process model to obtain
the control signal by minimising a cost function (Camacho and Bordons 2004 ).
In the case of study of the CDdI-CIESOL-ARFRISOL building the cost function
defined by Eq. 5.8 is used. This cost function tries to find out the best future change
in the control signal,

u , which is able to minimise the tracking error, that can be
defined as the difference between the future predicted output ( y ), the PMV index,

and the reference value for this index ( w ). In addition, at the same time, changes
in the future control action, that is, changes in the impulse air temperature, T a imp ,
are penalised by means of a weighting factor. Weighting factors, the one associated
to the setpoint tracking,

ˆ

, have been
chosen after several simulation tests and looking for a tradeoff between robustness
and performance.

˃ , and the other related to the control signal, ˉ

5.4.1.2 Constraints

Furthermore, the optimisation problem is subject to several system constraints given
by Eqs. 5.26 and 5.27 . On the one hand, the first constraint, Eq. 5.26 , limits the
maximum and minimum change in the control signal at each sample time. This
constraint is used to avoid abrupt changes in the impulse air temperature, since
they can produce abrupt changes on indoor air temperature which can affect users'
productivity. On the other hand, the second constraint, Eq. 5.27 , makes reference to
hard physical constraints of the fancoil unit, in other words, it takes into account
the minimum and maximum impulse air temperatures, [ u min , u max ], which can be

achieved with the current actuator.

u min ≤ u ( k + j − 1 ) ≤ u max ∀ j = 1 ,..., N u (5.26)

u min ≤ u ( k + j − 1 ) ≤ u max ∀ j = 1 ,..., N u . (5.27)

5.4.2 Control Layer (Lower Layer): Fancoil MISO Controller

As discussed in previous sections, this layer receives as input the impulse air
temperature setpoint optimised by the PNMPC and includes a control algorithm
which tries to efficiently lead the fancoil unit to this value.
The fancoil unit available in the CDdI-CIESOL-ARFRISOL building, whose
architecture can be observed in Fig. 5.22 , allows its users to change the impulse