Elsevier

Applied Soft Computing

Volume 7, Issue 3, June 2007, Pages 1092-1101
Applied Soft Computing

Fuzzy identification of a greenhouse

https://doi.org/10.1016/j.asoc.2006.06.009Get rights and content

Abstract

Nonlinear dynamic systems’ modelling is difficult. The solutions proposed are generally based on the linearization of the process behaviour around the operating points. Other researches were carried out on this technique of linearization not only around the operating points, but also in all the input–output space allowing the obtaining of several local linear models. The major difficulty with this technique is the model transition. Fuzzy logic makes it possible to solve this problem thanks to its properties of universal approximator. Indeed, many techniques of modelling and identification based on fuzzy logic are often used for this type of systems. Among these techniques, we find those based on the fuzzy clustering technique. The proposed method uses in a first stage the fuzzy clustering technique to determine both the premises and the consequent parameters of the fuzzy Takagi–Sugeno rules. In a second stage these consequent parameters are adapted by using the recursive weighted least squares algorithm with a forgetting factor. We will try in this paper to apply this method to model the air temperature and humidity inside the greenhouse.

Introduction

The agricultural greenhouses were used to protect the crop against the weather changes. With technical progress, the greenhouses have become a production means used to control the crop environment in order to obtain higher quality thus, making it possible to increase the economic benefit of the producer. Indeed, the producers aim is to minimize the production costs by reducing the consumption of water, fertilisers, CO2 and energy.

Thus, the agricultural greenhouses objectives are:

  • To obtain the highest productivity.

  • To ensure a production quality which is in conformity with the commercial objectives by setting quality standards as for flowers: length and diameter of the floral stems, absence of deformation, colouring, etc.

  • To control the calendars of production, i.e. to program the date of the beginning of the plant production and this can be achieved through the control of photosynthesis, breathing and the temperature cycles and alternations required by certain plants to be able to flower.

  • To save energy. In fact, greenhouses are energy consuming, as they need to be heated, costs a lot to producers. In Europe, for example, the expenditure of heating represents between 10 and 30% of the running costs for the greenhouse crops. The reduction in the expenditure of energy should not be made at the expense of the productivity. But, an “intelligent” energy saving can be made with understanding well the heat transfers in the greenhouses and which also permits to be able to measure the heating installation correctly.

These four objectives can be achieved by developing, in a first stage a good prediction model of the inside air temperature and humidity, and in a second stage a control law to permit to these outputs to follow specific values depending on the plants nature. In this paper, we are interested only in the modelling phase.

This contribution deals with modelling a class of nonlinear dynamic processes by local linear models. The latter are Takagi–Sugeno fuzzy models [1]. The output of these fuzzy systems is calculated as an interpolation of locally valid linear models. On the one hand, this allows a linguistic interpretation of the fuzzy rules. On the other, classical linear control concepts can be applied to the local linear models [2], [3]. The information process from the fuzzy models can be utilised by a great variety of control methodologies. Indeed, the control performance strongly depends on the model accuracy. Hence, a great portion of the design effort has to be spent on modelling. Moreover, time-variant behaviour of the plant which is caused by disturbances or aging components should be considered in the process model. Therefore, an on-line adaptation of the process model is required. Here, the local linear models in the rule consequents of Takagi–Sugeno fuzzy models are updated. Assuming that the nonlinear structure of the process does not change significantly, the premises of the fuzzy rules are kept fixed and only the linear parameters in the consequents are locally updated by a recursive weighted least squares algorithm (RWLS).

The outline of this paper is as follows: first, a problem of MIMO systems modelling is introduced. In Section 3, the Takagi–Sugeno fuzzy model as well as a suitable off-line identification algorithm is presented. Section 4 describes the procedure of on-line adaptation of the fuzzy model including a forgetting factor. Section 5 shows the application of the proposed method on the greenhouse climate modelling. Section 6 concludes the paper.

Section snippets

Fuzzy process models

Modelling and identification are important steps in the design of control system. In fact, the establishment of a “good” model permits on the one hand to test a controller before its implementation in the real process and on the other hand to make possible to use it, as in an adaptive control scheme. Typical applications of these models are the simulation, the prediction or the control system design [4], [5], [6].

We consider a MIMO system with ni inputs named u and no outputs named y. This

Takagi–Sugeno type fuzzy models

The TS model has attracted the attention of many searchers. In fact, this model consists of if-then rules with fuzzy antecedents and mathematical functions in the consequent part [8]. The antecedents of fuzzy sets divide the input space into a number of fuzzy regions, while the consequent functions describe the system's behaviour in these regions [9], [10].

MISO models are estimated of an independent manner, so, to simplify the notation, the output index l is omitted and we will be interested

On-line adaptation of the fuzzy model

There are two reasons for applying on-line identification. First, a too simplistic (e.g. linear) model may be used, which is only capable of describing the process behaviour within a small operating regime. The need for on-line adaptation then emerges from the process nonlinearities that are not represented by the model. This strategy is employed in classical linear adaptive control [19]. However, the second reason for the requirement of on-line adaptation is time-variant behaviour of the

Greenhouse climate modelling

The main objective of greenhouse crop production is to increment the economic benefits of the farmer compared to traditional agriculture methods [20]. The implementation of an adequate automatic control system for controlling the climate of the greenhouse (temperature, humidity) can lead to an increased production and quality of the horticultural products, reducing pollution and energy consumption [21].

In recent years, there have been many researches on analysis and control of the environment

Conclusion

This paper proposes a study on the application of the fuzzy method to the identification problem of MIMO process. This method is based on the fuzzy clustering technique using the Takagi–Sugeno (TS) fuzzy models. The local models automatically obtained, are adapted by the weighted recursive least squares algorithm with forgetting factor.

The performance of the proposed technique is demonstrated on the air temperature and humidity inside greenhouse modelling.

The obtained results are satisfactory

Acknowledgment

I would like to thank Mr. Duplaix, professor in automatic control to have provided us the greenhouse data files containing the different data which are used in our simulation for greenhouse modelling.

References (37)

  • R. Linker et al.

    Robust controllers for simultaneous control of temperature and CO2 concentration in greenhouses

    Control Eng. Pract.

    (1999)
  • R. Linker et al.

    Greenhouse temperature modelling: a comparison between sigmoid neural networks and hybrid models

    Mathematics Comput. Simul.

    (2004)
  • K. Zeng et al.

    A comparative study on sufficient conditions for Takagi–Sugeno fuzzy system as universal approximation

    IEEE Trans. Fuzzy Syst.

    (2000)
  • J.C. Bakker et al.

    Greenhouse Climate Control: An Integrated Approach

    (1995)
  • P. Salgado et al.

    Greenhouse climate hierarchical fuzzy modelling

    Control Eng. Pract.

    (2004)
  • F. Lafont et al.

    Fuzzy logic to the identification and the command of the multidimensional systems

    Int. J. Comput. Cognition

    (2004)
  • A. Trabelsi et al.

    Identification of nonlinear multivariable systems by adaptive fuzzy Takagi–Sugeno model

    Int. J. Comput. Cognition

    (2004)
  • T. Takagi et al.

    Fuzzy identification of systems and its application to modeling and control

    IEEE Trans. Syst. Man Cybernetics

    (1985)
  • Cited by (39)

    • Modeling and optimization of environment in agricultural greenhouses for improving cleaner and sustainable crop production

      2021, Journal of Cleaner Production
      Citation Excerpt :

      For the above category, the model by the latter two methods is referred to as the Greenhouse Black-box Model (GBM) in this paper, which means that these methods do not have to pay attention to the law and principles of physics in the greenhouse. In addition to the above three kinds of methods, the fuzzy theory, Peteri Nets, and other technologies are applied to greenhouse modeling by some researchers (Salgado and Cunha, 2005; Tovany et al., 2013; Trabelsi et al., 2007; Yaofeng et al., 2018). Greenhouse Mechanism Model (GMM) uses the law of physiological and physics principles to analyze related factors in the greenhouse quantitatively.

    • Verification and predicting temperature and humidity in a solar greenhouse based on convex bidirectional extreme learning machine algorithm

      2017, Neurocomputing
      Citation Excerpt :

      Wang et al. [10] used online sparse least-squares support vector machines regression with linear kernel function to model the greenhouse environment. Amine Trabelsi et al. [11] proposed a study on the application of the Takagi–CSugeno (TS) fuzzy models to the identification problem of greenhouse modeling. Based on the BP neural network model, He et al. [12] analyze the influencing factors importance of inside air humidity which the inside temperature, outside temperature and humidity, open ration of sunshade curtain, wind speed, solar radiation and open angle of top and side vent.

    • Temperature control in a MISO greenhouse by inverting its fuzzy model

      2016, Computers and Electronics in Agriculture
      Citation Excerpt :

      Through the production in greenhouses the plants are protected against plagues and atmospheric events, so its application is very common (Bennis et al., 2008). In (Trabelsi et al., 2007) it was made a fuzzy identification by clustering in a greenhouse, the Takagi–Sugeno (TS) fuzzy system used had linear functions as rules consequents, also a multi-model approach was presented without a control application, and in Gorrostieta-Hurtado et al. (2010) the clustering returns the key parameters for modeling. In Salgado and Cunha (2005) a fuzzy model for a greenhouse was presented, it uses a hierarchical structure to reduce the number of fuzzy rules; and the actualization of the model was made on-line with climatic measures.

    View all citing articles on Scopus
    View full text