14.2.5 Robust Control
Robust control is an approach that attempts to design stable controllers in spite of
the uncertainties and disturbances generally acting on the system (Morari and
Zafiriou 1989). The control system specifications are given in time-domain and
then translated to the frequency-domain using a second- or third-order model for
the closed-loop system. The model uncertainties are also considered in the design
procedure using Nichols charts. The design method allows for closed-loop stability
and meeting the specifications of the system. This approach has only rarely been
applied to control the greenhouse system. Linker et al. (1999) applied robust
controllers for simultaneous control of temperature and CO 2 concentration in
greenhouses. They applied the Horowitz’s method to their design. Moreno et al.
(2002) also designed a robust controller for temperature inside a greenhouse using
the Horowitz’s method. The system was modeled as a first-order system with
uncertainty. More recently, the approach of H 2 robust control has been applied to
control temperature and humidity of a greenhouse (Bennis et al. 2008). Their
research work looks for closed-loop stability and variations of the controlled
variables within acceptable ranges and proportions given by the operating conditions of the greenhouse system. They used the Linear Matrix Inequality (LMI)
formalism to synthesize the controller. Recently, Linker et al. (2011) designed
robust controllers using quantitative feedback theory (QFT) in order to guarantee
good performance of the system in spite of modeling uncertainties and disturbances. The model considered air enthalpy and humidity ratio. The method starts
with a nominal model and the computation of value-sets that describe the model
uncertainties. These values are combined with the design specifications to calculate bounds that the nominal open-loop have to satisfy in such a way that the
closed-loop system will be stable and meet the requirements. At the end a pre-filter
is obtained.
14.2.6 Adaptive Control
In order to deal with uncertainties of the greenhouse system, the approach of
adaptive control (Astrom and Wittenmark 1994) has been proposed by several
researchers. For instance, multirate-output controllers were proposed to control
greenhouse temperature. The multirate-sampled data of the system coming from a
given sampling period is used to control the closed-loop system (Arvanitis et al.
2000). A space-state model for greenhouse air temperature was approximated with
a first-order transfer function with dead time. Two design methods were tested: a
multirate-output control based on adaptive pole placement and a multirate-output
control based on an LQ optimal regulator. Other authors have used hybrid
approaches to control temperature and humidity inside a greenhouse. For example,
an adaptive hierarchical control has been proposed (Rodríguez et al. 2008). Both
408
I. L. López-Cruz et al.
Robust control is an approach that attempts to design stable controllers in spite of
the uncertainties and disturbances generally acting on the system (Morari and
Zafiriou 1989). The control system specifications are given in time-domain and
then translated to the frequency-domain using a second- or third-order model for
the closed-loop system. The model uncertainties are also considered in the design
procedure using Nichols charts. The design method allows for closed-loop stability
and meeting the specifications of the system. This approach has only rarely been
applied to control the greenhouse system. Linker et al. (1999) applied robust
controllers for simultaneous control of temperature and CO 2 concentration in
greenhouses. They applied the Horowitz’s method to their design. Moreno et al.
(2002) also designed a robust controller for temperature inside a greenhouse using
the Horowitz’s method. The system was modeled as a first-order system with
uncertainty. More recently, the approach of H 2 robust control has been applied to
control temperature and humidity of a greenhouse (Bennis et al. 2008). Their
research work looks for closed-loop stability and variations of the controlled
variables within acceptable ranges and proportions given by the operating conditions of the greenhouse system. They used the Linear Matrix Inequality (LMI)
formalism to synthesize the controller. Recently, Linker et al. (2011) designed
robust controllers using quantitative feedback theory (QFT) in order to guarantee
good performance of the system in spite of modeling uncertainties and disturbances. The model considered air enthalpy and humidity ratio. The method starts
with a nominal model and the computation of value-sets that describe the model
uncertainties. These values are combined with the design specifications to calculate bounds that the nominal open-loop have to satisfy in such a way that the
closed-loop system will be stable and meet the requirements. At the end a pre-filter
is obtained.
14.2.6 Adaptive Control
In order to deal with uncertainties of the greenhouse system, the approach of
adaptive control (Astrom and Wittenmark 1994) has been proposed by several
researchers. For instance, multirate-output controllers were proposed to control
greenhouse temperature. The multirate-sampled data of the system coming from a
given sampling period is used to control the closed-loop system (Arvanitis et al.
2000). A space-state model for greenhouse air temperature was approximated with
a first-order transfer function with dead time. Two design methods were tested: a
multirate-output control based on adaptive pole placement and a multirate-output
control based on an LQ optimal regulator. Other authors have used hybrid
approaches to control temperature and humidity inside a greenhouse. For example,
an adaptive hierarchical control has been proposed (Rodríguez et al. 2008). Both
408
I. L. López-Cruz et al.