Environmental Control for Plants using Intelligent Control Systems

Contents

Acknowledgements

Synopsis

List of Figures

List of Tables

List of Symbols

Abbreviations

1. Introduction
1.1. Preliminaries
1.2. The greenhouse climate: characteristics and determinism
1.3. Research objectives
1.4. Outline of the thesis

2. Background to fuzzy logic, Neural Networks, Optimizers, Greenhouses and Fault Detection/Isolation Systems
2.1. Preliminaries
2.2. Fuzzy Logic Systems and their Applications
2.2.1. Fuzzy sets and fuzzy logic
2.2.2. Architecture of fuzzy logic systems
2.2.2.1. Fuzzification interface
2.2.2.2. Knowledge base
2.2.2.3. Fuzzy approximate reasoning
2.2.2.4. Defuzzification interface
2.2.3. Fuzzy logic systems in control
2.2.3.1. Static fuzzy logic systems
2.2.3.2. Adaptive fuzzy logic systems
2.2.3.3. Features and applications of fuzzy logic systems
2.3. Adaptive control
2.4. Feedforward neural networks
2.4.1. Multi-layer perceptron
2.4.2. Learning in Neural Networks
2.4.2.1. Supervised learning
2.4.2.2. Reinforcement learning
2.4.2.3. Unsupervised learning
2.4.3. Applications of feedforward neural networks
2.5. Modern Optimization Techniques
2.5.1. Genetic algorithms
2.5.2. Principal attractions of genetic algorithms
2.5.3. Construction of Genetic Algorithms
2.5.3.1. Solution representation
2.5.3.2. Data structure
2.5.3.3. Reproduction
2.5.3.4. Crossover
2.5.3.5. Mutation
2.6. Greenhouses
2.7. Fault detection and isolation systems
2.8. Summary

3. Mathematical models of Greenhouse
3.1. Preliminaries
3.2. Hierarchical decomposition of greenhouse climate management
3.3. Greenhouse crop production process
3.4. Greenhouse dynamical model
3.5. Control of the greenhouse ventilation model
3.5.1. Control model
3.5.2. Feedback/feedforward linearization and decoupling
3.6. Modeling with neural networks
3.6.1. Multi-layer perceptron
3.6.2. Radial basis function networks
3.6.3. Including prior knowledge: hybrid modeling
3.7. Summary

4. Greenhouse climate controls
4.1. Preliminaries
4.2. Pseudo-derivative feedback controller
4.2.1. Controller structure
4.2.2. Optimization approaches
4.3. Simulation experiments
4.3.1. Setpoint tracking test
4.3.2. Disturbance rejection test
4.4. Fuzzy logic control
4.4.1. Controller structure
4.4.2. Fuzzy PI controller
4.4.3. Fuzzy PDF controller
4.4.4. GA-based Fuzzy controller
4.5. Simulation experiments
4.5.1. Setpoint tracking test
4.5.2. Disturbance rejection test
4.6. Summary

5. Fault diagnosis and its application on greenhouses
5.1. Preliminaries
5.2. Robust detection and isolation
5.2.1. Residual generation
5.2.2. Residual interpretation
5.3. Adopted approach and limitations
5.4. Greenhouse climate modeling
5.5. Fuzzy neural failure detection and isolation
5.6. Simulation results
5.7. Summary

6. Conclusions and Further Work
6.1. Preliminaries
6.2. Contributions and conclusions
6.3. Future work

References

Related publications

Acknowledgements

I would Firstly, I would like to thank my supervisors for their kind support and supervision during the entire duration of the thesis d like also to extend my sincere thanks to all who have extended their support in helping me carry out my work efficiently.

Finally, I would like to thank my family and friends for their complete support and encouragement throughout the duration of this work.

Synopsis

Environmental control for commercial plant production affects the productivity and the quality of the crop. The efficiency of plant production in greenhouses depends significantly on the adjustment of several components particularly, the greenhouse interior temperature, relative humidity and Co2 concentration. In warm climates, the greenhouse air temperature and relative humidity are controlled by means of a simultaneous ventilation and humidification. Humidification usually requires some sort of evaporative devices such as misters, fog units or sprinklers, all of which cool and add water vapour to the greenhouse air. Dehumidifiers are very expensive, thereby in warm countries the only available solution for dehumidification is ventilation. Ventilation is required during most of the day to exchange the moist air with drier outside air. Moreover, it is very important in all greenhouses even if they are not controlled since it decreases the so-called “Greenhouse effect” which is mainly due to the confining of the air in the greenhouse enclosure and less to the radiative properties of the cover. Conventional controllers (e.g. Pseudo-Derivative Feedback Controller) are employed to maintain, at any time, optimal temperature and relative humidity inside the greenhouse, and to overcome the load effect of the outdoor undesirable climatic conditions. Since greenhouses are continually exposed to changing conditions, e.g. the outside climate and the thermal effect of the growing plant inside it, the greenhouse moves between different operating points within the whole growing season. That leads to a complex control problem requiring effective intelligent controllers.

In practice, conventional controllers were used to control the system however their parameters are empirically adjusted. Besides, the operation of these controllers relies on the measurements provided by sensors located inside and near the greenhouse. If the information provided by one or several of these sensors is erroneous, the controllers will not operate properly. Similarly, failure of one or several of the actuators to function properly will impair the greenhouse operation. Therefore, an automatic diagnosis system of failures in greenhouses is proposed. The diagnosis system is based on deviations observed between measurements performed in the system and the predictions of a model of the failure-free system. This comparison is done through a bank of fuzzy observers, where each observer becomes active to a specific failure signature and inactive to the other failures. Neural networks are used to develop a model for the failure-free greenhouse.

The main objective of this thesis is to explore and develop intelligent control schemes for adjusting the climate inside a greenhouse. The thesis employs the conventional Pseudo- Derivative Feedback (PDF) Controller. It develops the fuzzy PDF controller (FPDF). The thesis also, develops two genetic algorithm (GA) based climatic control schemes, one is genetic PDF (GPDF) and the other is genetic FPDF (GFPDF). The former uses GA to adjust the gains of the Pseudo-Derivative Feedback Controller (GPDF) and the later uses genetic algorithm to optimize the FPDF controller parameters (i.e., scale factors and/or parameters of the membership functions). Finally, the thesis develops a fuzzy neural fault detection and isolation system (FNFDIS), in which a bank of fuzzy observers are designed to detect faults that may occur in the greenhouse end items (e.g.., sensors and actuators). Simulation experiments are performed to test the soundness and capabilities of the developed control schemes for controlling the greenhouse climate. The proposed schemes are tested through two experiments, setpoint tracking test and regulatory control test. Also, the proposed diagnostic system was tested through four experiments. Compared with the results obtained using the conventional controllers, best results have been achieved using the proposed control schemes.

List of Figures

2.1. A typical fuzzy logic system

2.2. Graphical interpretation of Mamdani's minimum rule

2.3. Graphical interpretation of Larsen's product operation rule

2.4. Adaptive control system

2.5. Model reference adaptive system

2.6. Schematic representation of a fully connected feedforward neural network with one hidden layer and a single output

2.7. Genetic algorithm flowchart

2.8. Mapping between chromosome and solution set

2.9. One-point crossover

2.10. Two-point crossover

2.11. Uniform crossover mechanism

2.12. Schematic representation of a greenhouse and the main factors influencing its climate

3.1. A schematic diagram of the greenhouse crop production process

3.2. Overall control strategy in case of small time delays and/or a slow desired response

3.3. Hybrid modeling schemes

4.1. The I-DF control system

4.2. The PDF control system

4.3. The PD-0F control structure applied to the process model

4.4. Codification of the controller gins (chromosome length =40 bits)

4.5. Setpoint tracking test using CPDF and GPDF controllers

4.6. Disturbance test using CPDF and GPDF controllers

4.7. Uncertainty test using CPDF and GPDF controllers

4.8. A fuzzy controller with two inputs and one single output

4.9. Membership functions

4.10. FPI control structure

4.11. FPDF control structure

4.12. GA-based FPDF (GFPDF) control structure

4.13. Triangle membership function

4.14. Parameters to be tuned for each control variable

4.15. Chromosome structure of a control variable

4.16. Setpoint tracking test using FPI (thin line) and FPDF (heavy line) controllers

4.17. Optimized Scale factors and membership functions of the GFPDF control structure

4.18. Controller outputs for step changes in both humidity and temperature using FPDF (thin line) and GFPDF (solid line) controllers

4.19. Controller outputs for step changes in external disturbances using FPI and FPDF controllers

4.20. Controller outputs for step changes in external disturbances using FPDF (thin line) and GFPDF controllers (solid line)

4.21. RMSE for the proposed controllers for the two experiments

5.1. The general structure of a diagnostic system

5.2. The proposed failure detection and isolation scheme

5.3. Membership functions of the input (top frame)/output (bottom frame) of the proposed fuzzy 5.4. MATLAB/SIMULINK implementation of the fuzzy neural fault detection and isolation system

5.5. MATLAB/SIMULINK implementation of the greenhouse climate control model

5.6. Surface view of fuzzy observers: (a) r1, (b) r2 and (c) r

5.7. Predicted against actual temperature (top frame) and humidity (bottom frame)

5.8. Normalized data and model prediction of the greenhouse climates, the top frame for the air temperature and the bottom one for the humidity

5.9. Residuals calculated with no failure (failure free case)

5.10. Residuals calculated with a failure of the greenhouse ventilation (Greenhouse ventilation not working)

5.11. Residuals calculated with a failure of the greenhouse fog system ventilation (Greenhouse watering system not working)

5.12. Residuals calculated with a failure of the indoor sensor (Aspiration fan of indoor sensor not working

List of Tables

3.1. A hierarchical decomposition of greenhouse climate management

4.1. CPDF and GPDF controller parameters

4.2. RMS errors computed after 50 min

4.3. Output variables description

5.1. Description of the failures

5.2. Expected deviations of the residuals in response to failures

5.3. Rule base of the fuzzy observer bank

6.1. RMS errors

List of symbols

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Abbreviations

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1. Introduction

1.1. Preliminaries

A greenhouse can be considered as a nonlinear time variant system. The environment of the system is composed by (i) the outside climate and (ii) the grower, who acts on the greenhouse equipments in order to control the internal environments (external control). The greenhouse system can be divided into three main components that interact in a more or less strong way: the internal atmosphere, the crop and the soil. The latter is often considered as the main thermal mass of the system. The behavior of the whole system depends on these interactions, but also on the outside climate (driving forces) and on the actions that are exerted on the components of the system via the climate control equipment (heating, cooling and CO2 enrichment). The presence of the crop, with its own internal control processes (i.e. stomatal regulation), is fundamental in the determinism of the system behavior. If the greenhouse climate can be maintained whatever the outside climate and the plant response, the control of the system is perfect, and the growth and development of the crop is optimal in the sense that it will correspond to the objectives and planning of the grower [Albright et al., 2001]. This chapter can be organized as follows. Section 1.2 briefly describes the problem and its treatment strategies. The research objectives of this thesis are summarised in section 1.3. Section 1.4 is dedicated to the organization of the thesis.

1.2. The greenhouse climate: characteristics and determinism

- Feedback and coupling in the greenhouse

There are many different interactions between the crop and the greenhouse atmosphere. There are several negative feedback loops (thermal and hydraulic) that tend to stabilize the transpiration rate. On the contrary, stomatal regulation is a positive feedback loop that tends to enhance the trend either to higher or lower transpiration rate. In recent years, the concept of "transpiration set point" was introduced [Stanghellini, 1987], which is the basis for calculating the couple of temperature and humidity set points to maintain a given transpiration rate. The simultaneous control of temperature and humidity is one of the most difficult control tasks, because these two variables are strongly influenced not only by outside temperature and humidity, but by radiation and the physiological response of the crop. In unheated greenhouses, the only mean to control these two variables is ventilation, which is nearly the only way to avoid condensation on plants at night. Also, the degree of coupling between the crop and the outside atmosphere is governed mainly by the ventilation rate.

- The main problems to be solved

Radiation: during the summer period, the high number of clear days and the long day length, allow the crop to receive enough solar radiation for its growth and development, without the need to add CO2 or artificial light.

Temperature: with too low temperature during winter nights and too high temperature during summer days. The problem of too low temperature can be solved by some heat that is supplied to the greenhouse during the critical periods. The problem of too high temperature during late spring and summer is one of the most important aspects to deal with.

Humidity: the low efficiency of the ventilation systems gives rise to impaired humidity conditions. During summer, very low humidity conditions are induced because of inadequate management of the openings, when the grower gives priority to temperature control by ventilation.

CO2 concentration: during winter, CO2 concentration could be a limiting factor when the shelter is closed in order to rise temperature. There are several reasons that explain why this technique is not usually practiced: (i) it is expensive, (ii) the potential period of CO2 enrichment is limited due to the necessity of aeration early in the season [Enoch et al., 1988] and (iii) it is not really necessary as the amount of radiation in winter is generally enough for plant growth.

- Equipment for climate control

The basic device for environmental control is ventilation, for its strong influence on all the climatic variables (except radiation). Equipments that are commonly used for controlling the temperature and humidity in greenhouses are briefly discussed below:

(1) Temperature control

Greenhouse air temperature is controlled using heating and cooling devices. Heating have to increase productivity, quality and earliness [Abou-Hadid et al., 1995]. Heating is not a technical problem, but the problem is to take a decision or not to use a heating system, and this must be done from an economical point of view. Cooling is the most important and strategical aspect. There are several methods for cooling, static or forced ventilation, evaporative cooling (pads, misting and sprinkling) and shading (screens and white washing). Evaporative cooling is the most efficient way to cool the environment [Cohen et al., 1983; Giacomelli et al., 1985; Montero et al., 1990], especially if the outside atmosphere is dry.

(2) Dehumidification

Dehumidifiers are very expensive, thereby the common solution adopted for dehumidification is the simultaneous use of heating and ventilation, which is an energy consuming and expensive solution. Therefore, in warm countries the only available solution for dehumidification is ventilation.

(3) CO2 enrichment

This technique is not really necessary in warm countries. The periods of enrichment are very limited, due to ventilation requirements [Enoch, 1984; Bellamy and Kimball, 1986]. This is not a technical problem, but an economical one.

1.3. Research objectives

The main objective of this thesis is to develop intelligent control algorithms to maintain optimal climate setpoints inside the greenhouse, as well as, to cope with the continually changing conditions to which the greenhouse usually be exposed. The operation of these controllers relies on the measurements provided by the sensors located inside and near the greenhouse. If the information provided by one or several of these sensors is erroneous, the controllers do not operate properly. Similarly, failure of one or several of the actuators (fans, valves, heaters, etc.) to function properly, impairs the greenhouse operation. Thus the thesis proposes an effective fault detection system for protection reasons. Research objectives can be achieved as follows:

- Employing a PD-0F Control scheme.

This scheme is a modification of the Pseudo-Derivative Feedback (PDF) algorithm [Phelan, 1971]. PD-0F (or simply, PDF) control scheme was first applied to greenhouse temperature control by [Setiawan, 1998] and then later by [Albright et al., 2001]. The controller has a better load handling capability than PID controller however it has two constants that can be varied compared to three in PID controller [Ohm, 1994].

- Development of a FPDF control scheme.

This thesis introduces fuzzy set theory to enhance the PDF controller. This fuzzy PDF control scheme has two inputs: the error between desired and actual output, and the process output derivative, and has one output, the change of control input to the plant. This scheme is nonlinear, flexible, understandable and well suited for ill defined processes.

- Development of GA-based control scheme s.

The thesis also employs genetic algorithms (GAs) to tune the parameters of the above schemes. It proposes two GA-based control schemes; one is GPDF and the other GFPDF. The former employs the well-known binary GA to adapt its parameters while the latter employs the real-valued GA either to optimize the scale factors or to optimize the membership functions of the fuzzy controller.

- Development of a fuzzy neural fault detection and isolation.

Finally, the thesis proposes a FNFDI scheme. This fuzzy neural fault detection and isolation scheme is based on the comparison between the current measurements and the predictions of a failure-free model of the greenhouse climates. This comparison is done through a bank of fuzzy observers where each observer is designed to respond only for a specific failure signature. Also, in this scheme, a feed forward neural network, FFNN, is used to model the greenhouse climates in the case of its ideal operation (i.e., to develop a failure-free model).

1.4. Outline of the thesis

Chapter 2: provides the essential background information on fuzzy systems, neural networks, genetic algorithms, greenhouses and fault detection and isolation systems.

Chapter 3: describes the plant physical model, the nonlinear relationship and the coupling between greenhouse indoor air temperature and relative humidity and the assumptions taken into account in simplifying the greenhouse climate model. It also describes the feedback-feedforward linearization and decoupling (FFLD), the overall control strategy and the neural network models of the greenhouse climate.

Chapter 4: proposes Pseudo-Derivative Feedback (PDF) control scheme and the PDF like fuzzy control scheme (FPDF) for controlling the greenhouse climate. This chapter also employs the genetic algorithm to tune/adapt the proposed controller schemes. It develops GA-based PDF control scheme (GPDF) and GA-based FPDF control scheme (GFPDF).

Chapter 5: details the importance of the fault diagnosis for greenhouse automation. It develops a hybrid fuzzy neural fault detection and isolation scheme (FNFDI) for detecting unfavorable conditions that may occur in the greenhouse climate control system.

Chapter 6: concludes the thesis by summarizing the contributions made and presenting suggestions for future work.

2. Background to fuzzy logic, Neural Networks, Optimizers, Greenhouses and Fault Detection/Isolation Systems

2.1. Preliminaries

In this chapter, the essential background for understanding the subsequent chapters is briefly introduced. The rest of the chapter is organised as follows. Section 2.2 briefly reviews fuzzy logic systems and their applications. Adaptive control is reviewed in section 2.3. In section 2.4, feedforward neural networks and learning schemes are summarized. Section 2.5 briefly reports on the three most popular, modern optimization techniques (simulated annealing, tabu search, and genetic algorithms). Section 2.6 is dedicated for greenhouses. Section 2.7 briefly describes the fault detection and isolation system developed. Section 2.8 summaries these topics.

2.2. Fuzzy logic systems and their applications

This section briefly explains fuzzy set theory and its applications to the control of dynamic systems.

2.2.1. Fuzzy sets and fuzzy logic

Linguistic terms and numerical values are classified into three categories namely, singletons, crisp sets and fuzzy sets [Zadeh, 1965 and 1973]. Three notable points are associated with them. First, a numerical quantity named a singleton is not a flexible description of real values. Second, crisp sets could be described by a group of singletons. This description is more flexible. Third, a fuzzy linguistic term can be defined by a membership function to represent real values such as room temperature and chamber pressure and natural language [Yamakawa, 1993].

A fuzzy linguistic term could be regarded as a fuzzy set that is a set of singletons with grades of membership which range from 0 to 1 [Zadeh, 1973]. The definitions of the fuzzy sets, its properties and its operations are all summarized in [Awad, 2001]. The dynamic behaviour of a process is characterised by a set of fuzzy rules (relations) that can be constructed from many sources such as expert knowledge, operator’s control actions, data extracted from the controlled process and/or control engineering information. These fuzzy rules normally take the form:

IF (a set of conditions is satisfied) THEN (a set of consequents can be inferred)

This rule consists of two main parts, an antecedent and a consequent. A Multi-Input Single-Output (MISO) fuzzy system can be described by a set of rules an example of which is given below:

IFx₁ is big and x₂ is mediumand x₃ is big THEN yis medium (2.1)

where x₁is , x₂is ,x₃is and y

are linguistic variables that represent three process state variables and one control variable respectively. "Medium" and "big" are fuzzy sets of the linguistic variables in the universe of discourse, U1, U2, U3 and U4 respectively. Another example of a rule, but in the case of Multi-Input Multi-Output (MIMO) system, is:

IF x₁is is big and x₂ is mediumand x₃ is big THEN y₁ is mediumand y₂ is big (2.2)

This rule can be decomposed into two rules, R₁ and R₂ :

R₁ :IFx₁ is big and x₂ is mediumand x₃ is big THEN y₁ is medium

R₁ :IFx₁ is bigand x₂ is mediumand x₃ is bigTHEN y₂ is b g

2.2.2. Architecture of fuzzy logic systems

Although fuzzy set theory was proposed in 1965, the link between it and the area of control systems was not introduced until the year 1974 [Mamdani, 1974]. Since that date, a great deal of research based on fuzzy set theory has been conducted in the field of the identification and control of dynamic systems [Batur et al., 1995; Li, 1999]. A fuzzy logic controller basically consists of four components named a fuzzification interface, a knowledge base, an inference engine and a defuzzification interface. Fig. 2.1 depicts the general configuration of a fuzzy logic system. Its components are described below:

2.2.2.1. Fuzzification interface

A fuzzification interface basically has the effect of transforming crisp data from the crisp domain to the fuzzy domain. That is:

y Fuzz(x) (2.3)

where x is a crisp input value, y is a fuzzy set and Fuzz(.) stands for a fuzzy operator. The fuzzification interface generally performs the following functions:

1: Scaling the range of the input and output data into corresponding universes of discourse,

2: Fuzzifyingthe scaled data.

2.2.2.2. Knowledge base

The knowledge base contains information about the controlled process and consists of two components, a database and a fuzzy rule base. The database includes three operations namely quantisation/normalisation of universes of discourse, fuzzy partitioning and definition of fuzzy sets.

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Fig. 2.1. A typical fuzzy logic system

The quantisation process is for discretising continuous universes. Normalisation is adopted to deal with large data ranges. Partitioning of a universe of discourse is carried out to determine the initial number of fuzzy subsets required to represent that universe. Fuzzy sets are usually selected to cover the whole universe of discourse. These fuzzy sets can either be represented as a vector of numbers or in function forms such as triangle-shaped, bell-shaped and trapezoidal-shaped membership functions. There is no systematic method to decide either the shape and/or number of the fuzzy sets or their degree of overlap. These parameters strongly depend upon the designer’s experience.

Defining the fuzzy rule base includes the choice of the input and the output variables of the controlled process and a set of fuzzy rules that describe the control policy in the domain of expertise. Fuzzy rules normally describe process and/or controller behaviour in a fuzzy logic control system. Derivation methods for these fuzzy rules are the corner stone in a fuzzy logic system. The following methods have been proposed to obtain the fuzzy rules for the controlled process [Wang and Mendel, 1992; Pedrycz, 1993; Rojas et al., 2000].

1. Using the operator’s experience
2. Copying the operator’s control actions
3. Employing the control engineer’s knowledge
4. Modelling the controlled process.

2.2.2.3. Fuzzy approximate reasoning

Fuzzy approximate reasoning is a method for inferring a fuzzy output based on an employed fuzzy inference scheme. Two important fuzzy approximate reasoning strategies are respectively Generalised Modus Ponens (GMP) and Generalised Modus Tollens (GMT) [Dubois and Prade, 1984; Lee, 1990].

Mamdani’s inference model basically follows the GMP strategy. It begins with a set of given data then looks for fuzzy rules in the knowledge base whose antecedents match these data and then fires the selected rules. Some properties of the GMP scheme can be found in [Fukami et al., 1980]. While the GMT strategy starts with a desired goal then tries to establish the facts needed to prove it by examining the fuzzy rules with the desired goal as the consequent part [Batur et al., 1995; Li, 1999]. Some properties of the GMT scheme are listed in [Li, 1999].

The fuzzy approximate reasoning strategy is the kernel of fuzzy logic control systems. It basically mimics human thinking. Based on a fuzzy inference scheme, the fuzzy approximate reasoning strategy infers a set of conclusions using a set of fuzzy relations from the rule base that describe a process model or a controller. The singleton strategy is commonly used in control systems for fuzzy inference. In general, a fuzzy inference scheme strongly depends on the compositional operators employed. In the literature, four main compositional operators have been described, the sup-min, sup- product, sup-bounded-product and sup-drastic-product operators respectively [Zadeh, 1973; Kaufmann, 1975; Larsen, 1980; Mizumoto, 1981]. For the sake of clarification, Mamdani’s minimum and Larsen's product operation rules are represented in Fig. 2.2 and Fig. 2.2.

2.2.2.4. Defuzzification interface

A defuzzification function basically maps fuzzy inference results as described above, from the fuzzy domain into crisp outputs in a crisp domain. These crisp outputs should

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Fig. 2.2. Graphical interpretation of Mamdani's minimum rule

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Fig. 2.3. Graphical interpretation of Larsen's product operation rule best represent the distributed fuzzy control action. A defuzzifier for this mapping can be expressed as:

z Defuzz(Y) (2.4)

where z is the crisp control action, Y is the fuzzy set that represents the distribution of the fuzzy control action and Defuzz(.) stands for the defuzzification operator. A general strategy for deciding on which defuzzification method to adopt in a particular application does not exist [Saade, 1996; Runkler, 1997]. Popular strategies adopted in solving identification and control problems are the maxima and the centroid approximation function strategies. Among these strategies, there are three commonly used defuzzification methods. The first method is the maximum criterion. The max criterion produces the point z in the output universe Z that has the maximum degree of membership in the output fuzzy set. A problem arises with this method when more than one element of Z possesses this maximal value and thus z is not uniquely determined. The second method is the Mean Of Maxima (MOM). If there is more than one element in Z possessing the maximal membership value, then MOM produces the average value of the maxima. In the discrete universe of discourse, the crisp control action z can be expressed as:

illustration not visible in this excerpt

where w_j stands for the support value at which the membership function reaches the maximum value and m is the cardinality that is card(Z) m . However, MOM does not take account of rules fired below the maximum level [Saade, 1996]. The third and the most commonly used method is the Centre Of Area (COA). COA attempts to overcome the drawback of MOM by considering rules that can be fired below the maximum level.

COA generates the centre of gravity z of the possibility distribution of a control action as follows:

illustration not visible in this excerpt

where n is the number of quantisation levels of a universe Z and w _k is the point in the kth quantisation level in a universe Z at which (w) achieves its maximum value μ(wk ) . Although this method yields the exact COA, it is computationally demanding. Thus the approximate COA method, named height defuzzification [Driankov et al., 1993], is employed in this work to obtain results quickly. The approximate COA is given by:

illustration not visible in this excerpt

where[Abbildung in dieser Leseprobe nicht enthalten] is the firing strength of the kth fuzzy rule, C _k is the centre (or mean) of the kth membership function and m is the number of fired fuzzy rules.

2.2.3. Fuzzy logic systems in control

Fuzzy logic systems can mainly be classified into two types, static and adaptive.

2.2.3.1. Static fuzzy logic systems

Experienced human operators are the kernel source of information when designing a fuzzy logic controller. Accordingly, such a controller belongs to the class of knowledge-based controllers. Efforts have been made to achieve the best knowledge base for the controlled process [Takagi and Sugeno, 1983; Peng and Wang, 1988; Shenghaog and Kreifeldt, 1989]. The knowledge base includes a database and a set of fuzzy rules as mentioned previously. The fuzzy rules are not updated in this scheme during the control period and hence the scheme is called static fuzzy logic control.

2.2.3.2. Adaptive fuzzy logic systems

Although the static fuzzy logic control scheme is capable of dealing with complex and/or ill-defined processes, it has no on-line adaptation and hence it cannot cope with large changes that may occur during the operation of the controlled system. The adaptive fuzzy logic control scheme performs on-line adaptation of the rule base and hence overcomes the drawbacks of the static scheme [Sun, 1994; Lotfi and Tsoi, 1994]. It alters three major items of a fuzzy logic system, the membership functions, the fuzzy rule base and the scaling factors, to yield a robust fuzzy system. These items strongly influence the performance of a fuzzy logic controller [Saade, 1996]. In general, there are two important adaptive fuzzy control strategies to alter these items, namely, the direct and indirect strategies [Moore, 1991; Moore and Harris, 1994].

2.2.3.3. Features and applications of fuzzy logic systems

Because of the intrinsic features of fuzzy set theory, there has been a rapid growth in the use of fuzzy logic systems for controlling complex and ill-defined processes. These features can be summarised as follows. First, a fuzzy logic system transparently maps process dynamics. Second, unlike conventional control schemes, it is a tool to model phenomena associated with human thinking and perception in an understandable manner. Third, it has a simple structure. By virtue of these features, fuzzy logic techniques have the ability to cope with different type of available data such as numerical values and linguistic information. Since 1974, the control of processes has become a very fertile application area for fuzzy set theory. Examples of applications based on fuzzy logic systems include:

1. Manipulation of robot arms [Lin and Lee, 1993].
2. Chemical bath control [Dohmann, 1994].
3. Control of a feed-water system in a nuclear-power plant [Iijima et al., 1995].
4. Control of a ship-mounted satellite tracking antenna [Tseng and Teo, 1998].
5. Improved control of a pressurised water nuclear reactor [Fodil et al., 2000].
6. Plant and animal environment (i.e, temperature) control [Gates et al., 1999 ].

2.3. Adaptive control

If a controller adjusts the control strategy without human intervention it is adaptive. In daily conversation to adapt means to modify according to changing circumstances, for example: ‘ they adapted themselves to the warmer climate ’. An adaptive controller is therefore intuitively a controller that can modify its behaviour after changes in the controlled plant or in the environment. Some objectives for using adaptive control are

- The character of the plant varies, or
- The character of the disturbances varies.

Adaptive controllers are essential in the field of greenhouses climate control, since greenhouses are continually exposed to changing conditions. For example, the dynamics of a greenhouse change with changing, for example, the speed and direction of the outside air, the outside climate such as air temperature, humidity, and CO2 concentration, the greenhouse altitude, and the thermal effect of the growing plant inside the greenhouse. Therefore, the greenhouse moves between different operating points within the hole growing season and the controller is aware of the present operating conditions and accordingly adjusts its gains to the newly conditions. Research in adaptive control started in the early 1950s. An adaptive controller is consisting of two loops: a control loop and a parameter adjustment loop (Fig. 2.4) [Åström and Wittenmark, 1995]. Model reference adaptive system (MRAS) is an adaptive system in which the performance specifications are given by a reference model (Fig. 2.5). In general the model returns the desired response ym to a command signal uc. The parameters are changed according to the model error, which is the deviation of the plant response from the desired response.

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Fig. 2.4. Adaptive control system. The inner loop (solid line) is an ordinary feedback control loop around the plant. The outer loop (dashed line) adjusts the parameters of the controller.

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Fig. 2.5. Model reference adaptive system, MRAS. The outer loop (dashed line) adjusts the controller parameters such that the error em= ym- y becomes close to zero.

2.4. Feedforward neural networks

2.4.1. Multi-layer perceptron

Rosenblatt [Rosenblatt, 1958] coined the name perceptron for the Multi-Layer

Perceptron (MLP) networks that have received much attention. MLP feedforward

networks consist of at least three layers named input, output and hidden (Fig. 2.6).

Mathematically, the operation of a MLP could be represented by:

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ˆf k (x)is the kth output of the network, xiis the ith input, p is the number of input units, N is the number of hidden units, wji is the weight between the input and hidden layers, w _kj is the weight between the hidden and output layers, Bj is the bias on the hidden layer, Bk is the bias on the output layer and (.) is the activation function.

The most popular choices for (.) are the hyperbolic tangent and sigmoid functions [Zurada, 1992]. A MLP implements a non-linear mapping that can approximate a continuous function up to a predetermined degree of accuracy [Hornik, 1991; Hunt et al., 1992; Hush and Horne, 1993]. MLP networks have many drawbacks. The major shortcoming is that in practice they are not universal approximators. In other words, if the operating region of a real system changes, the behaviour of the MLP network will be distorted owing to its global-support-function. This means that for the MLP to function correctly all weights will need to be changed. This is true because the training of a MLP network is basically a non-linear optimisation problem. This optimisation is usually performed using the error Back Propagation (BP) algorithm and all weights have to be modified. In short, this type of network lacks plasticity. This means that the learning of new information causes previously stored data (as represented by the values of the weights) to be destroyed. Using NNs in greenhouse climate modeling will be discussed in details in chapter 3.

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Fig. 2.6. Schematic representation of a fully connected feedforward neural network with one hidden layer and a single output.

2.4.2. Learning in Neural Networks

Two phases, the learning phase and the recall phase, are employed to build a particular neural network. The former consists of two learning segments, one structural and the other parameter-based. A trained neural network basically represents a static knowledge base. Some important features have been added to the traditional neural network to yield evolving connectionist systems. These features are on-line learning, knowledge base adaptation and incremental learning. Learning schemes in neural networks can be classified generally into three categories, supervised, reinforcement and unsupervised.

2.4.2.1. Supervised learning

In this scheme, a system should be directed by an external signal to achieve a desired performance. A common supervised learning method, the error BP scheme, is based on the steepest descent method. The major drawback of this method is its slow speed of learning and the local minimum problem that makes it not suitable for real-time application. Adding a momentum term to this scheme can sometimes stabilise and speed up the network convergence in training. A number of powerful second-order techniques have also been proposed to accelerate MLP as mentioned previously. The BP algorithm with these modifications has successfully been used in many networks.

Mathematically, each weight,w

[Haykin, 1994]:

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2.4.2.2. Reinforcement learning

A reinforcement learning scheme basically refers to the concept that if a satisfactory response of a system is obtained, then the action that produced this response should be rewarded. Conversely, if the response due to a certain action is unsatisfactory, the action should be penalised.

Both the supervised learning and reinforcement learning schemes are directed by an external agent. These schemes are functionally similar. However, they have different information forces. In the case of reinforcement learning, the feedback information only provides an evaluative feedback signal (reinforcement signal), while in the case of supervised learning a precise feedback signal is supplied to the learning system.

2.4.2.3. Unsupervised learning

Unlike the supervised learning scheme, an unsupervised learning algorithm basically needs no external signal, and hence is commonly used in competitive learning systems. Competitive learning systems are normally employed for pattern clustering.

2.4.3. Applications of feedforward neural networks

The main application areas are statistical analysis, in particular data/text mining, analysis/control of industrial processes, telecommunications and medical/biological applications. Among these applications, the area of identification and control of dynamic systems is very promising.

1. Modelling the dynamic response of pH in a stirred tank reactor [Bhat and McAvoy, 1990].
2. Function approximation [Srinivasa, 1997].
3. Identification and control of a distillation column [Cheung, 1997].
4. Temperature control of rapid thermal processing [Lai and Lin, 1999].
5. Water treatment control [Zang and Stanley, 1999].

2.5. Modern Optimization Techniques

In recent years several heuristic search techniques have been developed for solving combinatorial optimization problems. The word ‘heuristic’ has come from the Greek word ‘heuriskein’ that means ‘to discover or find’ and which is also the origin of ‘Eureka’, derived from Archimedes’ reputed exclamation, ‘Heurika’ (for ‘I have found it’), uttered when he had discovered a method for determining the purity of gold [Polya, 1957]. However, three methods, that go beyond simple local search techniques and become particularly popular as global optimization techniques, are simulated annealing [Kirkpatrick, 1983], tabu search [Glover, 1989, 1993, 999; Revees, 1996; Glover and Laguna, 1997], and genetic algorithms [Goldberg, 1989]. These methods have all arisen at least in part from a study of natural and physical processes which perform an analogy of optimization [Reeves, 1996]. These methods, when used to optimize an objective function with multivariables, take guesses about the settings for these variables. The variable settings are then modified in some logical or “intelligent” way and presented to the objective function to determine whether this combination of variable settings results in an improvement.

2.5.1. Genetic algorithms

The genetic algorithm (GA) method is a global search technique based on an analogy with biology in which a group of solutions evolves through natural selection and survival of the fittest [Goldberg, 1989]. GA represents each solution by a binary bit string or directly in its real value. Such a string is made up of sub-strings, each sub- string representing a different parameter. In the terminology of GAs the bits are referred to as ‘genes’ and the total string as a ‘chromosome’. Several chromosomes representing different solutions comprise a ‘population’. GA is not gradient based, and uses an implicitly parallel sampling of the solution space. The population approach and multiple sampling means that it is less subject to becoming trapped in local optima than traditional optimization techniques, and can explore a large solution space. GA has been shown to be powerful at reaching an optimal or a very near optimal solution in a computationally efficient manner.

The structure of GA is quite simple. The GA starts with random generation of initial population strings, and evaluation of each string’s fitness. The algorithm then proceeds by selecting, according to whatever strategy is used, two ‘parent’ solutions, interchanging portions of their strings and thus generating two ‘offspring’ solutions. This process is called a ‘crossover’. The process is repeated until the new population size is completed. The selection of a chromosome is generally based on its fitness relative to the fitness of other chromosomes in the population. In each generation, relatively ‘good’ chromosomes (solutions) are more likely to survive and produce offspring, and relatively ‘bad’ chromosomes are more likely to die out. To ensure further variety the ‘mutation’ operator with a small probability is applied during the crossover for random switching of one or more bits. Finally, the new population replaces the old (initial) one. This procedure continues until a certain termination condition is reached. A simple flowchart of a GA is shown in Fig. 2.7. There are several aspects in which GAs differ from other search techniques:

1. GAs optimize the trade-off between exploring new points in the search space and exploiting the information discovered thus far.

2. GAs have the property of implicit parallelism. Implicit parallelism means that the GAs effect is equivalent to an extensive search of hyperplanes of the given space, without directly testing all hyperplanes values.

3. GAs are randomized algorithms, in that they use operators whose results are governed by probability. The results of such operations are based on the value of a random number.

4. GAs operate on several solutions simultaneously, gathering information from current search points to direct subsequent search. Their ability to maintain multiple solutions concurrently makes GAs less susceptible to the problems of local optima.

The interest in GAs has been growing rapidly in recent years among researchers in various fields such as computer science, engineering and operational research.

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Fig. 2.7. Genetic algorithm flowchart.

2.5.2. Principal attractions of genetic algorithms

The principal attractions of GAs as listed in [Reeves, 1995; Khalifa, 1997] are domain independence, non-linearity, robustness, ease of modification, and multi objectiveness.

Domain independence: GAs work on a coding of a problem, so that it is easy to write a general computer program for solving many different optimization problems.

Non-linearity: Many conventional optimization methods depend on restricting assumption for the search space, e.g., linearity, continuity, convexity, differentiability, etc. None of these limitations are needed for GAs. The only requirement is the ability to calculate some measure of performance, which may be highly complicated and non- linear.

Robustnes s: As a result of the above two properties, GAs are inherently robust. They can cope with a diversity of problem types; they can not only just work with highly non-linear functions, but also do it in a very efficient manner. Further, empirical evidence shows that although it is possible to fine-tune a GA to work better on a given problem, it is nevertheless true that a wide range of GA parameter settings (selection criterion, population size, crossover and mutation rates, etc.) will give very acceptable results.

Ease of modification: Even relatively minor modifications to a particular problem may cause severe difficulties to many heuristic methods. In contrast, it is easy to change a GA to model variations of the original problem.

Multi objectiveness: One of the most important features that GAs can provide is the multi objectiveness of the fitness function which can be formulated as to optimize for more than a single criterion. Also, GAs are very flexible in the choice of an objective function.

These characteristics give GAs the ability to solve many complex real-world problems.

2.5.3. Construction of genetic algorithms

In section 2.5.1 a brief explanation of the basics of GAs has been given. This section presents more detailed description of GAs’ components and genetic operations, viz. reproduction, crossover, and mutation.

2.5.3.1. Solution representation

Before the GAs are applied to find a solution of an optimization problem, a suitable coding is necessary which means that each possible solution in the search space can be coded into a unique representation. The solution (optimized parameters) is usually encoded into a string (chromosome) of binary bits {0’s and 1’s}. The binary representation is not the only way to represent the solution. It is also possible to use the real parameters’ values directly to form a chromosome. However, the binary representation offers the maximum number of schemata per bit of information. Moreover, it is simple to create and implement.

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