involved in the process, and the other is based on an analysis of the input–output
data of the process. In the first method, the process behavior is incompletely
known, and physical modeling is not easy considering the complexity of the
system that translates high order models with lot of parameters which are difficult
to adjust due to the nonlinear behavior of the greenhouse model (Herrero et al.
2008). The second method consists in approximate the behavior without a priori
information, for instance, polynomial fitting, ANNs, FLS, etc. However, they do
not have physical meaning but are easier to obtain.
How was previously mentioned, modeling by physic laws is complicated
because in order to achieve a reliable model, lot of parameters have to be included
in the model. But, it has proved that physic-laws models had a better goodness-of-fit
that black-box models (Blasco et al. 2007). However, adjusting these parameters is
complicated. An alternative was purposed by Guzmán-Cruz et al. (2009), which
used and compared different evolutionary algorithms (EA) such as GAs, Evolutionary Strategies (ES) and Evolutionary Programming (EP) to calibrate the
parameters that defines the greenhouse inside temperature and relative humidity
within a greenhouse with tomato crop. The calibration consisted in an optimization
problem which works altering model parameters until getting a better fit between
estimated and measured data. Results show a better performance of EP to predict
the air temperature and RH behavior; however, least squares (LSQ) and sequential
quadratic programming (SQP) methods slightly improve the estimation of temperature, but present lot of inaccuracy for RH. This assertion is supported by
(Speetjens et al. 2010), which also indentified the key parameters of a physic-based
model using a controlled random search (CRS). The model is composed by a
limited number of states, which keep the computational load in an acceptable level.
This model enhances practical applicability for in situ purposes.
However, in all aforementioned works, important sets of data are required.
Measurements in the greenhouse during 2 years or more were necessary to calibrate the models; otherwise the risk to get trapped in a local minimum is highly
probable. Other problematic relies in controlling greenhouses are strongly
dependent on the geographical area; and solution that are valid in some regions
must be adapted in order to fit others (Herrero et al. 2007). This problematic was
partially solved developing a reduced thermal and mass (water vapor) model of the
greenhouse by an on-line estimation of its parameters. This estimation was carry
out using the particle swarm optimization (PSO), which present a better performance than GAs in some cases (Coelho et al. 2005; Hasni et al. 2011). Also,
several advantages were reached, such as energy savings, soft optimal control
effort a low computational burden (El Ghoumari et al. 2005). Automatic, on-lined
estimation and adaptation of parameters in physic-based models were proposed by
Speetjens et al. (2009) using Extended Kalman Filtering (EKF). This technique
could deal with changing circumstances like plant growth, changes in material
properties and modification in greenhouse design and layout. Then, EKF improves
the model fit over a longer period. After tuning of the filter, the parameters were
automatically adapted, so that changes in system were dealt with. The unique
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M. S. Acosta-Navarrete et al.
data of the process. In the first method, the process behavior is incompletely
known, and physical modeling is not easy considering the complexity of the
system that translates high order models with lot of parameters which are difficult
to adjust due to the nonlinear behavior of the greenhouse model (Herrero et al.
2008). The second method consists in approximate the behavior without a priori
information, for instance, polynomial fitting, ANNs, FLS, etc. However, they do
not have physical meaning but are easier to obtain.
How was previously mentioned, modeling by physic laws is complicated
because in order to achieve a reliable model, lot of parameters have to be included
in the model. But, it has proved that physic-laws models had a better goodness-of-fit
that black-box models (Blasco et al. 2007). However, adjusting these parameters is
complicated. An alternative was purposed by Guzmán-Cruz et al. (2009), which
used and compared different evolutionary algorithms (EA) such as GAs, Evolutionary Strategies (ES) and Evolutionary Programming (EP) to calibrate the
parameters that defines the greenhouse inside temperature and relative humidity
within a greenhouse with tomato crop. The calibration consisted in an optimization
problem which works altering model parameters until getting a better fit between
estimated and measured data. Results show a better performance of EP to predict
the air temperature and RH behavior; however, least squares (LSQ) and sequential
quadratic programming (SQP) methods slightly improve the estimation of temperature, but present lot of inaccuracy for RH. This assertion is supported by
(Speetjens et al. 2010), which also indentified the key parameters of a physic-based
model using a controlled random search (CRS). The model is composed by a
limited number of states, which keep the computational load in an acceptable level.
This model enhances practical applicability for in situ purposes.
However, in all aforementioned works, important sets of data are required.
Measurements in the greenhouse during 2 years or more were necessary to calibrate the models; otherwise the risk to get trapped in a local minimum is highly
probable. Other problematic relies in controlling greenhouses are strongly
dependent on the geographical area; and solution that are valid in some regions
must be adapted in order to fit others (Herrero et al. 2007). This problematic was
partially solved developing a reduced thermal and mass (water vapor) model of the
greenhouse by an on-line estimation of its parameters. This estimation was carry
out using the particle swarm optimization (PSO), which present a better performance than GAs in some cases (Coelho et al. 2005; Hasni et al. 2011). Also,
several advantages were reached, such as energy savings, soft optimal control
effort a low computational burden (El Ghoumari et al. 2005). Automatic, on-lined
estimation and adaptation of parameters in physic-based models were proposed by
Speetjens et al. (2009) using Extended Kalman Filtering (EKF). This technique
could deal with changing circumstances like plant growth, changes in material
properties and modification in greenhouse design and layout. Then, EKF improves
the model fit over a longer period. After tuning of the filter, the parameters were
automatically adapted, so that changes in system were dealt with. The unique
390
M. S. Acosta-Navarrete et al.