Control design of a thermal vacuum chamber cooling system based on artificial neural network

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Scuola di Ingegneria Industriale e dell’Informazione

Master’s degree in Space Engineering

CONTROL DESIGN OF A THERMAL

VACUUM CHAMBER COOLING SYSTEM

BASED ON ARTIFICIAL NEURAL

NETWORK

Alessandro Baroni

Advisor: Mauro Massari

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This thesis presents the design, finalized to experimental validation, of the controller for the cooling system of the thermal vacuum chamber (TVC) of the Department of Aerospace Science and Technologies of Politecnico di Mi-lano, through the use of artificial neural networks (ANN). The main problems of this kind of systems are overshoot of the temperature with respect a certain constant reference when trying to reach it, oscillations in regime and difficul-ties in following a prescribed thermal gradient. In the work all the phases of the ANN training are analyzed (data sets generation, network structure and controller inputs selection) searching for the optimum solution to counteract those problems. Moreover the design has to deal with intrinsic complications of the departmental TVC: no data sheets nor documentation of the system are available, the temperatures of the components are the only measurable quantities (through thermocouples) and mostly, there is no tunable control action so that the only way to act on the TVC is to switch ON or OFF the whole cooling system. It was impossible to find any training procedure in lit-erature (data sets for trainings are never discussed in papers and in scientific publications in general) so, the solution proposed, experimentally validated, is the result of an independent and original work that completely satisfied the problems of the overshoot and of the thermal gradient meanwhile the oscillation issue need a further improvement.

Part of the work was developed in simulation environment (Matlab/Simulink) so in the thesis also a detailed numerical model of the TVC is described; in the final chapter two possible ways of improvements of the control action, that were not developed to the experimental phase, are briefly discussed. This thesis demonstrated once more the versatility of ANN in the capability to identify an unknown system and in controlling it; ANN application to TVC temperature regulation is not a singularity but these devices, commonly, have always a controllable variable as the mass flow rate or the temperature of the refrigerant. instead, the departmental TVC with only the ON/OFF control action available, represents a very peculiar case and a harder system to work with.

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Abstract

In questa tesi viene descritta la progettazione per mezzo di reti neurali artificiali (ANN), finalizzata alla sperimentazione, del sistema di controllo dell’impianto di refrigerazione della camera termovuoto presente nel lab-oratorio dipartimentale di scienze e tecnologie aerospaziali del politecnico di Milano. I problemi principali di questo tipo di sistemi sono le sovrae-longazioni/sottoelongazioni di temperatura rispetto ad un valore di riferi-mento costante da raggiungere e mantenere, oscillazioni a regime attorno a questo valore e anche nel riuscire a far seguire alla temperatura un de-terminato gradiente di raffreddamento. Nel lavoro svolto sono state anal-izzate tutte le fasi che riguardano l’addestramento della rete neurale usata come controllore (dalla generazione dei data set migliori, alla struttura della rete fino alla selezione del tipo di input più adatti) al fine di contrastare i fenomeni sopra elencati. La progettazione del sistema di controllo è anche resa più difficile da alcune caratteristiche intrinseche della camera termovuoto dipartimentale in quanto non è disponibile alcuna documentazione né schede tecniche dell’impianto, non è possibile effettuare alcuna misura sul fluido re-frigerante (si può solo misurare la temperatura dei componenti per mezzo di termocoppie) e soprattutto non vi è alcuna azione di controllo regola-bile per cui l’unica maniera di agire sulla camera è l’accensione/spegnimento dell’intero sistema di refrigerazione. In letteratura non è reperibile alcuna procedura specifica di addestramento per reti neurali che abbiano questo scopo per cui la soluzione qui proposta, validata sperimentalmente, è il risultato di un lavoro indipendente ed originale che ha risolto il problema della sovraelongazione e del gradiente di raffreddamento mentre, per le os-cillazioni a regime, miglioramenti futuri sono necessari. Parte del lavoro è stato svolto nell’ambiente di simuazione Matlab/Simulink-Simscape per cui nella tesi viene anche descritto un dettagliato modello numerico della camera termovuoto. Nel capitolo finale vengono anche presentati due possibili modi di migliorare ulteriormente il sistema di controllo, che per ragioni di tempo non sono stati portati alla fase sperimentale. Questa tesi dimostra ancora una volta la versatilità delle reti neurali artificiali per quanto riguarda la capacità di identificare un sistema e controllarlo. La loro applicazione alle camere termovuoto non è certo un caso unico ma comunemente queste sono dotate di un qualche sottosistema capace di regolare una variabile di con-trollo come la portata massica o la temperatura del fluido refrigerante; nel caso della camera dipartimentale invece, la possibilità di agire sul sistema di raffreddamento con la sola azione di accensione o spegnimento rappresenta una situazione molto particolare e difficile da affrontare.

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Chapter 1 Introduction

The purpose of this thesis project is the desing, finalized to experimental validation, of the controller for the cooling system of the thermal vacuum chamber of the Department of Aerospace Science and Technologies of Po-litecnico di Milano, through the use of artificial neural networks.

The Thermal vacuum chamber (TVC) is a device aimed at testing com-ponents in a vacuum thermally controlled environment: it is born for the necessity of reproducing, within a certain volume, the space thermal envi-ronment inside which the tested components are designed to operate. For this purpose, the chamber has to maintain vacuum and determined temperature conditions in order to carry out qualification tests on the tested components. Typical procedure contemplates the identification of a point on the tested components surface, called Thermal Reference Point (TRP), whose function is to provide the reference temperature for the test. TRP corresponds to the point on which is placed the main thermocouple used for control reference. Tests are considered valid if the TRP temperature is kept for a prescribed time around a reference condition with a ±0.5°C tolerance; temperature is required to follow a predefined thermal gradient at necessity.

The control architecture is developed with empty chamber: the TRP is placed on the baseplate that is the rectangular support inside the chamber where test objects are located (figure 2.1). So, when a qualification test is performed for a given component, the thermal response of the system is altered and the performances of the control actions may drop drastically. This suggests that the controller should be able to regulate its action according to the observed behavior of the tested component and knowing the system dynamics in order to face these disturbances. In this, ANNs are particularly indicated due to

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their generalization capability that is the ability to handle unseen data[37]. Already two past thesis works dealt with the design of a controller for the heating system of the departmental TVC[35][29] meanwhile no study had never been performed on the developing of a cooling system controller. One of the main problems of the TVC is that it lacks of any documentation so that was impossible a complete and satisfactory identification of the system: in particular there is no data available on the cooling system so that is impos-sible to estimate correctly the pressure and mass flow rate of the refrigerant, quantities that are fundamental to estimate the cooling power delivered (i.e. the heat subtracted). ANNs are of great help in these cases because are ca-pable to identify the system, i.e. to reconstruct the inputs-outputs relation, without knowing any information about what really occurs inside the system but merely by observation of temporal histories of the inputs and outputs (this procedure is called training). For this, it is always convenient monitor-ing all the fundamental quantities that rules the workmonitor-ing of the system to allow the ANN a easier system identification.

ANN for thermal control is a common application nowadays, however most of the documented results (some examples are the references [2],[14] and [36]) concern systems or subsystems where all the important measurements for the identification are available; in particular “Artificial Neural Network Modelling of the Thermal Performance of a Compact Heat Exchanger”[36], is a clear example that shows how the knowledge of the mass flow rate is fundamental in the identification of the heat exchanges by the ANN. In the departmental TVC instead, no measures are available but the temperatures that can be registered placing thermocouples inside the chamber. In practice only the component temperatures can be monitored and so used as input for the training of the controller.

Another strong limitation is the kind of control action executable on the cooling system: it can only be switched on or off, there is no possibility to regulate the flow of the refrigerant inside the chamber. ANNs are capable to work with this kind of control action in thermal systems, as in “Development of a neural network heating controller for solar buildings”[2], but in this last case many measures are available meanwhile, as said above, the training of the controller for the departmental TVC can be performed only relaying on temperatures and knowing the state of the system (ON or OFF).

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Figure 1.1: in this thesis the control action will be always represented in the graphs as a line that has only two values, when it has the higher one the cooling system is ON, when it has the lower one the cooling system is OFF. The specific value has no meaning and is used only to be represented alongside the temperatures to see how this last behaves according to the control action.

About thermal control for TVC, in “enhancing temperature control method of thermal vacuum chamber for satellite testing using optimization algorithm: a review” , are discussed the most useful algorithms for this specific application and a lot of researches are taken into account and related revealing that the Genetic Algorithm (GA) is the more suitable for the application. However, from the diagram of figure 1.2 (taken from the same article[8]), it is evident that the ANN control development has been used more rarely than others, suggesting that lot to discover there may still be in the use of ANN for TVCs control. Moreover the application of ANN, and of the other algorithms, to TVCs discussed in [8] concerns the training of controllers aimed to gener-ate variable PID gains for the system control action, that may be the mass flow rate of the refrigerant or its temperature as occurs in “Thermal vacuum chamber identication through particle swarm optimization (PSO) fuzzy sys-tem and NARMAX ERR approach trade-off"[1]; the possibility to regulate

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somehow the source of cooling power is fundamental in the development of the controller.

Figure 1.2: number of researches in temperature control system using various optimization algorithms. GA=genetic algorithm, PSO=particle swarm opti-mization, FL=fuzzy logic, ANN=artificial neural network, ANFIS=adaptive neural fuzzy interference system. Details in reference [8]

In contrary, The departmental TVC with the simpler ON/OFF control ac-tion could represent a very singular case difficult to deal with; Stefano Tacca in his past thesis work on the departmental TVC[35] concluded that for the cooling system developement it should be installed an electro valve capable to modulate the amount of refrigerant provided and Attilio Restelli in “neural network inverse-model control of thermal vacuum chamber temperature”[29] (last work performed on the departmental TVC), asserted the necessity of a power regulation device for the compressor to extend the control, developed in his thesis for the heating system, to the cooling system. This same heating system showed difficulties in using the thermal resistances to regulate tem-perature due to a very high thermal inertia of the baseplate (characteristic found out also in this work) though in that case the power of the resistances was controllable with a PID. Again, in [31] and [20], and specifically for TVCs in [8], is highlighted how, though also with a tunable control action, the main problem of the big thermal systems, i.e. the overshoot of the temperature to control with respect to a constant reference, still remains sometimes.

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As a resume, there are three main aspects that render the development of the cooling system control hard and peculiar for the departmental TVC:

• There is no data sheet available about the system at all

• There is no possibility to monitor any of the refrigerant properties • There is no tunable control action, the only way to interact with the

cooling system is to switch it ON or OFF (by means of a relay). Despite all this, ANNs are a very powerful tool: with respect more conven-tional control techniques, they are good in modeling with nonlinear data with large number of inputs and are easy to use and understand compared to sta-tistical methods[45]. A more conventional relay control could not have any chance to predict how much earlier switching off the cooling system to avoid overshoot with the result, shown in figure 1.3, that the cooling continues up to the target temperature and only at this point the system is switched off by the relay, so that the cooling of the baseplate proceeds for a lot of time due to its thermal inertia. For this reason, a control action capable to predict how much time in advance to switch off the system, according to its present and past states, is fundamental and ANNs are the perfect candidate to ac-complish this, given their ability to identify the system behaviors without possessing any knowledge of its dynamics. To generate a controller which has prediction capability however is not so trivial: neural networks are black boxes, thus it is impossible to know how much each input is influencing the outputs, moreover they depend a lot on training data so that the search of the correct inputs and of the correct data sets represents a major issue of this approach. This thesis focused really a lot on the solution of these two problems leading to the developing of two similar training procedures (dis-cussed in section 3.3.7) named future reference and full future path trainings. It is important to highlight the fact that the cooling system can be conveyed in two different serpentines: one is located below the baseplate and the other one above the shroud, a semi-cylindrical structure that acts as a coating (figure 2.1). However, during the thesis development, the refrigerant was conveyed only in the serpentine below the baseplate to simplify the work to search for an ANN configuration capable to deal with all the complications listed above. A successful design of the controller for the restricted case of only one serpentine used, will be more easily extendable to the use of both in a further work.

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Figure 1.3: the classical relay control, tested on the departmental TVC[16], using two threshold values. Once the cooling begins, the relay switches off the cooling system when the baseplate temperature reaches the target value (reference temperature) Ttar = −33°C and switches it on if the baseplate

temperature rises above Ttar + 0.6°C. This approach gives rise to a 15°C

overshoot and to oscillations higher than ±3°C.

1.1 The structure of the thesis

The next three chapters represent the three main arguments in which the thesis work can be divided. The last one presents the results and some possible future developments.

• Chapter 2: here the modeling of the system, with the data available, is discussed and some assumptions are introduced where information could not be found. The modeling itself can be divided in three main parts (sections 2.3, 2.4 and 2.5):

– the model of the TVC structure and the heat transfers that occur between the main bodies inside it. It was developed in Simulink-Simscape environment

– the model of the refrigerant temperature, empirically obtained from the measurements of the duct temperature where fluid flows – the model of the heat exchange that occurs inside the ducts be-tween them and the fluid. Mathematically modeled through proper

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equations.

• Chapter 3: in this chapter all the aspects that led to the selection of the ANN final architecture and training procedure are presented. The two major issues, of identifying the correct types of data sets and the correct types of inputs for the controller training, are deeply analyzed finding valid solutions. More in detail, in this chapter, all the parts of the design that can be developed using the Simulink model are dis-cussed, then a first experimental test result is reported to highlight that the common procedure of training, in a high thermal inertia system, does not allow to control the temperature properly; finally two original training procedures are presented, to which was given the name of "fu-ture reference” and “full fu"fu-ture path” trainings, developed to overwhelm the problems revealed by the first experiment; both are validated in the simulation.

• chapter 4: this chapter concerns the experimentation of the training procedure developed in the previous one. First the hardware and soft-ware developed for the management of the experimental tests are de-scribed, then some aspects peculiar of the real system are analyzed. Moreover, conventional and unconventional techniques to estimate the quality of a controller at the end of its training, before its test, are explained (this is a fundamental aspect because an experimental test requires lot of hours and to test a controller that does not work would be a big loss of time); finally all the results obtained are reported and discussed.

• chapter 5: in the last chapter the most relevant results are summarized and discussed, then a couple of aspects not fully developed in this thesis (due to lack of time) are presented, explaining how they could be integrated in future works to give additional improvements to the control system.

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Chapter 2 TVC modeling

In this chapter all the aspects of the developing of the TVC model are de-scribed in detail: first a general description of the system is provided, with particular care to the cooling system, then all the main components that participate to the thermal exchanges are identified and it is mathematically analyzed how they interact each other through radiation and conduction (no convection occurs in vacuum). Next an empirical approach to find a function capable to describe the cooling and warming of the refrigerant inside the TVC is described and finally the numerical model developed to compute the cooling power delivered by the fluid is presented.

2.1 Description of the real system

The departmental TVC is a cylindrical structure of about 1 m3 _internal

volume: objects to be tested are placed inside it on the baseplate, a horizontal rectangular plate which is surmounted by a semi-cylindrical thin layer called shroud that acts as a coating (fig. 2.1).

To perform the tests, the TVC is provided of a two stages vacuum system capable of bringing down pressure to a minimum below 10−6 _{mbar and a}

thermal system differentiated in heating system and cooling system. The heating system is provided of six thermal resistances (350 W each) located inside the baseplate and six infrared lamps fixed on the shroud that radiate toward the baseplate; thermal resistances and lamps can be activated simul-taneously or separately and together can bring the inside temperature to a maximum value of 200°C. The cooling system is a two-stage refrigerant cycle where the low temperature cycle (the colder of the two) cools a refrigerant,

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Figure 2.1: The inside of the TVC, it can be observed the baseplate sur-mounted by the shroud.

the R23 – trifluoromethane, that subtracts heat inside the chamber, flow-ing in a serpentine located below the baseplate and in another one above the shroud (see figure 2.2); the refrigerant can be conveyed independently in both serpentines or just in one of them. Actually, the serpentine that cools the baseplate is constrained between two thin plates by means of bolts, one above and the other below it to keep the ducts firm (see figure2.3): the plate above the ducts is in contact with the baseplate so that the cooling power flow across it by conduction before arriving to the baseplate. Since the aim of the thesis is to control the cooling of the TVC, in below it follows a sec-tion that describes in detail the refrigerant system meanwhile, for a deeper description of the heating system the reader is referred to [35] and [29] that are two past thesis works on the development of the heating control system. Figures 2.11 and 2.10 are clear schems of the main bodies inside the TVC that take part in the cooling.

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Figure 2.2: The serpentine above the shroud. It can be observed also a Teflon connection between shroud and chamber.

Figure 2.3: The serpentine below the baseplate constrained between two thin plates

2.1.1 Cooling system

The cooling system of the departmental TVC is a cascade refrigeration system composed of two independently operated single-stage refrigeration systems (i.e. each stage has its own compressor though the electric system is setted to activate the low temperature cycle with a delay of 30 seconds with respect the high temperature one): the low temperature cycle works with R23 –

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Figure 2.4: scheme of a two stages refrigeration system.

trifluoromethane refrigerant, meanwhile the high temperature cycle works with R507a (a mixture of refrigerants R125 and R134a). In figure 2.4 it is shown a simplified scheme of the system, the main components are: low temperature compressor, high temperature compressor, condenser (an heat exchanger), cascade condenser and throttling devices for low temperature cycle and high temperature cycle. In this figure, during process 1-2 the low temperature cycle refrigerant R23 is compressed, it passes through cascade condenser where it gives heat to refrigerant R507a of higher temperature cycle (process 2-3) then R23 expands in low temperature expansion valve (process

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3-4) and further passes to evaporator (process 4-1) to produce necessary refrigerating effect (the role of the evaporator is played by the serpentines inside the TVC). In the higher stage refrigerant R507a is compressed in high temperature cycle compressor (process 5-6), then it is passed through condenser where it rejects heat with water coming from the water network (process 6-7). It expands in high temperature expansion valve (process 7-8) further passes to cascade heat exchanger where heat transfer between two refrigerants takes place. A wider overview of cascade refrigeration systems is available in the works of A. D. Parekh and P. R. Tailor, references [26] and [27] .

2.2 The TVC dynamics

Figure 2.5: cooling to regime temperature and warming of the baseplate. The red line represents the control action and it has only two values: the higher one represents the cooling system turned on and the lower one the cooling system turned off.

A good model of the system is fundamental to simulate the behaviors of the TVC because real tests require long times and, to find the best configuration of training for the ANN (in chapter 3), are necessary a lot of tests and a lot of data sets. For this reason, the chosen procedure was to model the same dynamics of the real system, find the best training configuration in the simulation environment and then use the same configuration for the real system (chapter 4).

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Figure 2.6: when the cooling system is switched on (represented by the black line that changes from the higher value to the lower one) the baseplate tem-perature keeps to decrease for a while (12K about).

Figure 2.7: It can be observed that when the duct temperature (green line) reaches the baseplate temperature (blue line) this latter stops to cool and starts a slow warming.

real system even if the cooling times are not perfectly respected (between simulation and real system), this because the purpose is to find a ANN architecture that is capable to identify and control these dynamics so that if the model dynamics are successfully controlled, the same ANN configuration should be able, hopefully, to control a real system which has the same kind of dynamics though are a bit faster or slower, because this last aspect is taken

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into account by the specific data sets. This will be clearer in section 3.3.2; for now, it is enough to know that the model must be capable to replicate the same kind of dynamics of the real system.

The temperature behavior of the baseplate, which is the temperature to control, is characterized by two dynamics:

• the first and more evident is the time needed to cool: when the cooling system is turned on, obviously, it takes some time to cool down to a certain temperature and the lower the temperature of the baseplate the higher the time to cool of another degree. If the cooling system is not turned off the baseplate reaches, after a long period, a regime temperature below -75°C about as can be seen in figure 2.5. On the contrary, when the system is switched off, it takes a lot of time to warm again to ambient temperature and the lower the temperature the lower the time to rise of one degree.

• the second dynamic (fig. 2.6) occurs when the system is switched off during the cooling: it happens that the baseplate keeps to cool down for a while, the higher the temperature the higher the time needed be-fore it starts to warm (to reverse the slope). Is this thermal inertia that makes the system difficult to control because the ANN should be able to predict how much earlier it has to switch off the system to reach a certain temperature without overshoot. This behavior is due to fact that, between the point where the baseplate temperature is measured and the serpentine that cools it, there is a significant difference of tem-perature: the ducts reach thermal equilibrium with refrigerant flowing inside them in few minutes, meanwhile the cooling of the upper face of the baseplate takes a longer time due to the very higher amount of mass (ducts are a small fraction of mass compared to baseplate); more-over when the cooling system is turned off, the refrigerant remains in the ducts so it starts to warm immediately but due to fact that they are colder than the baseplate this latter will continue to cool until it does not reach the same temperature of the ducts, then it too starts to warm (fig.2.7). Once temperature of ducts has reached the same value of the baseplate, their warming continues faster than baseplate due to smaller mass so that during warming of baseplate ducts are hotter than it. Similarly, for this reason, if the baseplate is warming and the cool-ing system is suddenly switched on, it keeps to warm for a bit before decrease of temperature begins; this interval of time is quite shorter with respect to the opposite case because ducts cool down very fast. The control of the shroud temperature is not discussed in this thesis, so

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its dynamics are not analyzed; indeed, refrigerant is conveyed only in the baseplate serpentine and no direct cooling of the shroud occurs at all.

2.3 Modeling of the thermal exchanges inside

TVC

The TVC lacks of documentation, this rendered the modeling quite difficult because no data about materials, sizes, weights and the system in general was available.

Modeling of the TVC was developed in the MatLab-Simulink/Simscape en-vironment according to the following assumptions and measurements:

1. the only masses considered were the ones of the following bodies (the sizes have been manually measured):

• The chamber i.e. the cylindrical structure made of steel, 1m of diameter and 1.13m of depth, with 6mm of thikness

• the baseplate, a rectangle of 0.8m depth and 0.63m width made of aluminum with 15mm of thickness

• the shroud made of copper, 269° of circumference with a radius of 0.45m and 0.8m in depth, 1mm of thickness

• two serpentines under the baseplate, made of copper for a total length of 13.6m, assumed of constant section, internal radius of 4mm and 1mm of thickness.

• the serpentine above the shroud made of copper for a total length of 15m assumed of constant section, internal radius of 4mm and 1mm of thickness

• the two thin plates above and below the baseplate serpentines, made of copper, rectangles of 0.8m depth and 0.63m width with 1.5mm of thickness

Masses were modeled as lumped in Simulink.

2. connections (made of Teflon) and structural supports between the main bodies (made of steel) were considered by means of thermal resistances (connections and supports can be seen in figures 2.2 and 2.8).

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Figure 2.8: Connections made of teflon connect the upper plate to the shroud and to the chamber also by means of a supporting structure.

3. thermophysical properties of masses and connections were assumed con-stant with temperature (conductivity, specific heat, emissivity); the values used were taken from references [39],[40] and [46].

4. Inside the chamber the heat exchange occurs only by means of conduc-tion and radiaconduc-tion, no convecconduc-tion happens in vacuum

• Conduction across a body was modeled using the specific Simulink-Simscape block that describe the equation:

˙

Q = λA s∆T

where ˙Q is the heat flux across the body, λ is the thermal con-ductivity, s is the length of the body along which the heat flux propagates, A is the cross secton area perpendicular to the heat flux and ∆T is the thermal difference between the two extremities of the body. As explained, connections and structural supports

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were considered only by means of a thermal resistances instead, for the masses considered, conduction was modeled splitting the thermal resistance across the mass in two equal parts (each with half the length of the body) and placing between them the lumped mass representing the body.

• Radiation between multiple bodies was modeled using the specific Simulink-Simscape blocks according to the scheme in figure 2.9 : this image describes the thermal resistances scheme between three bodies that radiate each other; in the model of the TVC the in-teractions between bodies are more complex (there are more than three masses) but the main concept is that each body presents a resistance to radiation that depends on the own emissivity and is described by 1−

A; once the heat is radiated it reaches the other

bodies and, the heat exchange between the radiating body and each of the other bodies, depends on the view factor F between them. In this case the thermal resistance between the two bodies is described by 1

AF, where A is the surface of the radiating body.

For details about radiation, reference [38] is recommended.

Figure 2.9: the scheme represents the thermal resistances circuit of the radi-ation between three bodies, together with the main equradi-ations that rule the model.

5. Outside the TVC, the environment exchanges heat with the external side of the chamber through conduction by means of its supports to the ground, through convection and through radiation.

According to previous points a simplified scheme of the modeled system is reported below in figure 2.10: it does not represents the real thermal resis-tances circuit developed for the model (that would be more complex) but it is a clear representation of how the masses taken into account (in point 1 above) interact each other and with the heat sources.

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Figure 2.10: the scheme represents how bodies exchange heat each other. This is not the thermal resistances circuit but just a representation of all the ways heat can move between the masses of the system. The only heat sources are the cooling power coming from the inside of the ducts (below the baseplate) and the heat from the environment that enters across the external surface of the TVC.

2.3.1 View factors computation

Particular care was dedicated to the computation of the view factors between the main bodies, to be able to estimate in which percentage cooling prop-agates between them: to do so a numerical code (available free online[43]) that computes the view factors between two planar surfaces in 3D-space was employed; for a theoretical description of the numerical approach used in the code see reference [9].

Baseplate and the plates that bind the serpentines are planar surfaces but shroud, tubes and the chamber structure are not; moreover the shroud radi-ates from both sides of its surface: the internal side radiradi-ates mainly toward the baseplate and in part toward the chamber, the external side radiates mainly toward the chamber, and with the ducts over the shroud itself (figure 2.11). To deal with these complications, using the code mentioned above, in the following are reported the procedures and assumptions made.

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Figure 2.11: In the image all the view factors needed to model the radiation heat exchanges, between the bodies considered, can be identified. In the representation Fb→c is missed due to 2D representation problems.

The view factor between baseplate and the internal side of the shroud Fb→sint

(i.e. the amount of radiation that leaves the baseplate of surface area Ab

and reach the shroud of surface As) was computed approximating the

semi-cylindrical structure with N rectangles (figure 2.12) then the code was used to compute the view factor Fi,b→sint between the base and the i

th rectangle

(that are two planar surfaces). The value Fb→sint was then computed as:

Fb→sint =

N

X

i=1

Fi,b→sint

With the law of reciprocity, Fsint→b can be calculated as Fsint→b =

Ab

AsFb→sint

and with the summation of view factors law the view factor between base and chamber Fb→c can be obtained:

Fb→c= 1 − Fb→sint

For an overview of the main properties of radiation heat transfer see [15]. Being concave, the internal side of the shroud radiate also toward itself, so this amount of heat radiated is not exchanged actually with the other bodies.

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To compute this amount of heat a simplified procedure was followed: it was computed, with the code, the view factor between a plane surface symmetric to the shroud and half the surface of the shroud approximated with the rectangles (figure 2.13); this value was assumed as the quantity of radiation that leaves and re-enters the shroud Fs0. In this way the value of Fsint→c,

view factor between the shroud internal side and the chamber was computed as:

Fsint→c = 1 − Fs0− Fsint→b

The computation of the view factor between the serpentine and the shroud

Figure 2.12: In the image the shroud is approximated with 15 rectangules; in reality, in the model, it was approximated using 200 rectangules.

external surface (Ft→sout) required a more radical assumption due to

complex-ity of the bodies: for simpliccomplex-ity it was assumed that 85% of heat radiated by serpentine reaches the chamber(Ft→c= 0.85) and the remaining 15% reaches

the shroud(Ft→sout = 0.15). Knowing the sizes of the bodies and using

reci-procity rule Fsout→t was obtained; it followed that:

Fsout→c = 1 − Fsout→t

The radiative surface of the ducts was assumed to be 7

8 of the whole surface

so 1

7 of it, was assumed as the contact surface with the shroud through which

conduction heat transfer occurs.

About the serpentines between the two plates, it was assumed that the view factor between each of the two plates and tubes is Fp→t = 2₃, so the view

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Figure 2.13: Half of the shroud is approximated by a vertical planar surface to compute the heat flux that leaves and re-enter the shroud due to concavity. factor between the two plates is Fpp = 1 − Fp→t; indeed the two plates see

each other. The radiative surface of the external area of the serpentines below the base was assumed to be 1

2 of the whole surface, so 1

2 too was assumed as

the contact surface with the plates through which conduction heat transfer occurs; this different value with respect to serpentine on shroud is due to fact that these ducts are in a stronger contacts due to the two bolted plates that bound them.

Finally, it must be considered also that the plate below the baseplate serpen-tine, on its outer side, radiates toward the chamber so that the view factor is Fp→c= 1.

2.4 Empirical model of the refrigerant

temper-ature

The description of the cooling system in section 2.1.1 explains only the work-ing with the main components of a general system of this kind however, the specific system of the TVC is supplied with many additional components that, without system documentation available, rendered the identification quite difficult; moreover some of the components are covered with insulating material so that was impossible to read the specifics for a correct

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identifica-tion. The final purpose of the modeling of the fluid cooling system should be to describe the temperature of the refrigerant entering the serpentines, but with all the uncertainties on the system it would have been so approximated that the work would have been useless. However, neither a constant enter-ing temperature of the fluid could have been assumed in the model because the varying entering temperature is a fundamental prerequisite to be able to model the same kind of dynamics: when the system is turned on the fluid takes some time to cool down and until it is warmer than baseplate this latter does not cool down; similarly, when the system is turned off the fluid is at rest inside the ducts and it starts to warm but, until it is colder than the baseplate, this one keeps to cool (already seen in figure 2.7). Lack of docu-mentation implies also impossibility to estimate the correct pressure of the fluid when it enters the ducts, its speed, its mass flow rate and the mass that remains in the ducts once the system is turned off. So, it was also impossible to mathematically model the warming behavior of the fluid in OFF condi-tion. To overwhelm these problems, it was registered, with a thermal sensor (details in section 4.1.1), the temperature behavior of the duct at the inlet, which is quite similar to the fluid temperature behavior due to low thermal inertia of the duct; indeed the small section of duct, where sensor is placed, has a small mass so that it can be assumed that the duct temperature follows almost instantly the fluid temperature. The cooling times and warming times of the duct were then used in the mathematical model to represent the fluid that enters the duct instead of modeling the whole cooling system of the re-frigerant. Actually, the duct warming depends on the baseplate temperature and presents two inflection points (see figure 2.14) that slightly move up or down if the baseplate temperature is higher or lower. To avoid the difficulty to model this behavior it was preferred to remove the two inflections and use a modified function to describe the warming of the fluid (2.15) where no dependency on the baseplate temperature is presented. Obviously, this is an important difference from the real model, anyway it alters just the length of the overshoots but not the fact that their duration depends on the baseplate temperature: this behavior is catched by the model and, for its purposes, it was retained sufficient. In this way, when the system is turned on, the inlet temperature in the model is not constant but follows the modified registered path; when the system is turned off the fluid, that remains in the ducts, starts to warm according to the warming path registered (2.15). When a transition from OFF to ON or vice versa occurs the temperature of the fluid will start from the last value it had reached on the warming/cooling path (figure 2.16).

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Figure 2.14: the black dots are the inflection points, connected by the dashed lines, to highlight how they depend on the baseplate temperature. It can be also appreciated the different thermal inertia depending on the baseplate temperature.

Figure 2.16: it is shown the behavior of the modeled fluid in time and as function of control action. As usual the control action (red line here) has two values: the higher represents when the cooling system is turned on and the lower when it is turned off.

The modelled fluid temperature at regime was considered of -90°C as can be seen in figure 2.15 so, lower than the duct temperature at regime; this is a

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Figure 2.15: the blue line represents the measured temperature behavior of the ducts; from this path, it was modeled the fluid temperature behavior (used in simulations) represented by the red line.

realistic assumption because fluid is certainly colder than ducts and in some system identification tests, where serpentines had been unbolted from plates (so that there was not conduction with any other bodies), it resulted that a temperature about -90°C were reachable by them.

As a recap, the main assumptions on the fluid temperature model are: 1. When a transition from OFF to ON occurs, the fluid entering has

the same temperature of the last value reached during the warming: actually, it should be some degrees higher cause the fluid entering was warming outside the chamber, so it warms faster than the fluid inside 2. It is assumed that the cooling and warming path of the fluid in the ducts is independent from the temperature inside the chamber; actually it is not in the warming phase, where can be observed dependence from the temperature of the baseplate as shown in figure 2.15. This does not alter the kinds of dynamics but just the speeds of them. No dependence from baseplate was observed in the cooling phase because the time to cool the refrigerant depends only on the behavior of the cooling system that is always the same.

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2.5 Cooling modeling in ducts

During the running of the simulation it must be computed the amount of cooling power delivered by the refrigerant in the duct at each step of integra-tion, the ˙Qref rigerant in figure 2.10. To do so a code that works together with

the Simulink model was developed, using as inlet refrigerant temperature in the duct, the temperature that is described by the function of figures 2.15 and 2.16, to compute the evolution of the fluid temperature from inlet to outlet. Instead, in the Simulink model, duct is considered as a lumped mass so that all the body has a single value of temperature: this is a realistic assumption because it was experimentally tested, placing many sensors along the path of the serpentine that, except for a small initial transient when the cooling system is turned on, the duct temperature is more less constant from inlet to outlet. This phenomenon is explainable by the fact that as soon as the fluid enters the duct it cools the first small piece of duct to almost the same temperature and than refrigerant warms; the new upcoming fluid from the inlet finds the first part of duct already cold so that it goes to cool the next segment and so on; thus the duct in few minutes reaches a homogeneous temperature so that it is reasonable to model it as a lumped mass in the Simulink model. For the same reason it can be assumed that the baseplate cools uniformly along its surface being in contact with a body (the duct) that has a constant temperature. This last behavior too was experimentally validated showing that different zones of baseplate cool together though with some differences in temperature values (figure 2.17). In the model, when the cooling system is turned on, the refrigerant enters the duct at the value it had reached during its warming (cooling system at rest) or at ambient tempera-ture if it is at the beginning of the simulation, then its temperatempera-ture decreases in time as explained above (figure 2.16).

Pressure at inlet Pin was assumed to be 40kP a: the compressor gives to

the fluid a pressure of 3MP a but it is not possible to estimate correctly the value it enters the ducts due to the large number of pressure drops in the cooling system components; 40kP a is just a value that, between others, gave good results in the simulations in terms of time of cooling but it is probably not the real value of pressure; anyway three corrective factors were used, described in below, to regulate the behavior of the refrigerant due to lack of information about it so that many of the assumptions will become not quite relevant. It was assumed that the fluid is completely vaporized by the expansion valve so that it enters the duct in gas phase, in accord with the inlet pressure value; from the measurement of the duct temperature (green line of figure 2.14) it can not be observed a behavior that let suppose that a phase

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Figure 2.17: five different points of the baseplate cool together but with an increasing difference of temperature at lower values. The central point is the one used as TRP meanwhile the other four are located at the four corners of the baseplate. The near ones are those of the side closer to the door of the TVC.

transition of the refrigerant occurs inside the serpentine: the only behavior experimented is that of the inflections but it is a temperature dependent phenomenon meanwhile phase transition is not, thus this let suppose that fluid is vaporized by the lamination valve before the inlet in chamber. The volumetric flow rate at duct inlet ˙Vin was assumed as a fraction of the

volumetric flow rate worked by the compressor ˙Vc= 27.3m3/h, this because,

along the duct, pressure drops and so volumetric flow rate increases thus, at the inlet, it must be lower than at the outlet:

˙

Vin= ˙VcK

The coefficient K is one of the main coefficients used to model the cooling in order to find a behavior similar to the real cooling system and was finally chosen as K = 0.6 .

Inlet density ρin, thermal conductivity λin, specific heat cp,in and dynamic

viscosity coefficient µin, were computed from interpolation of tables of R23

(references[3] and [4]) knowing inlet temperature and pressure; inlet mass flow rate was then computed as min = ρinV˙in.

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they are assumed of the same length L and it is computed the cooling power provided by just one of them, then it is doubled.

The amount of cooling power provided by the fluid to the single serpentine is computed dividing it in N segments each of length ∆x = L

N (it was used

N = 1000), then at each iteration of the simulation the code computes the heat exchanged between each segment and the fluid. This occurs in series i.e. one segment after another, to take into account the thermal properties variation. Properties are considered uniform inside a segment and equal to inlet values.

The procedure used for the ith _{segment is as follows, according to figure 2.18:}

Figure 2.18: in each section of the duct the thermal-physical properties of the fluid are assumed constant and are computed using the inlet values of pressure and temperature.

1. Inlet thermal-physical properties ρi, λi, cp,i and µi are computed from

previous segment outlet pressure and temperature (see point 6)

2. The speed of fluid inside segment is computed as: vi = min_Aρ_csi ,where

Acs is cross sectional area of duct, equal for each segment

3. Dimensionless numbers are computed inside the ith _segment:

• Reynolds number: Rei = ρivi_µD_i (D is the diameter of the duct)

• Prandtl number: P ri = µi c_pi

λi

• Nusselt number: for Rei >= 2300 it was used the Gnielinski’s

correlation according to references [25] and [33] that is N ui =

(f /8)(Rei− 1000)P ri

1 + 12.7pf/8(P r2/3 i − 1)

where the friction factor f is computed as f = (1.82 log10Rei −

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Instead, when Rei < 2300, assuming constant heat flow rate in

the duct segment, and assuming fully developed flow, according to reference [25] it was used Nui = 4.36

4. Convective coefficient is computed as: hi = N uiλ_Di

5. For the computation of the heat exchanged with the ith duct segment

the following two equations were used: (

˙

dQi = mincpi(Touti− Tini)

˙

dQi = hiAlat(Tduct− Tavi)

Lateral area across which heat is exchanged with duct is Alat = πD∆x

and Tavi =

(T_ini+T_outi)

2 . From the system above, it can be computed

first Touti as:

Touti = ˙ mincpiTini+ AhTduct− Ah T_ini 2 ˙ mincpi + Ah 2

then dQi using one of the equations of the same system. The Tduct,

temperature of the duct, is the value of the lumped mass of the duct that comes from the Simulink model.

6. Finally, the inlet values of pressure and temperature, used to compute the thermophysical properties of next segment, are Tini+1 = Touti and

Pini+1 = Pini− 1 2ρiv 2 i ∆x

D ff, where ff is the friction factor computed from

Rei:

fF =

(

64/Rei, if Rei < 2300

0.124Re−2_i , if Re >= 2300

More details about friction factor and pressure drops in references [5] and [6].

Once dQi is computed, in series, for each of the N segments of the duct,

the cooling power provided to the Simuink model during each iteration is ob-tained as: ˙Qref rigerant = 2

N

P

i=1

dQi, assuming that the two serpentines subtract

the same amount of heat.

When the cooling system is turned off the temperature of the fluid starts to raise automatically in the model according to fig 2.17. However, the fluid is still cold and until the duct temperature does not reach a value higher than the baseplate one, this latter keeps cooling: in this case heat exchange occurs by free convection. In the modeling of the free convection inside

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ducts, the fluid temperature is dictated by the imposed path (2.17); it was assumed a constant fluid pressure of 10kP a inside the duct and the fluid volume is obviously the free volume inside the duct. No duct segmentation is needed in this case, assuming constant temperature and pressure in the whole volume; Thermal physical properties are computed from pressure and temperature as before from tables interpolation. The Nusselt number was assumed Nu = 4.36 just for simplicity, but a corrective factor was added in the convective coefficient computation: h = Nuλ

Dkh, where kh is the

coefficient to regulate the natural convection to be similar to real system dynamics; it was selected as 7 after some trials.

As a resume,two tunable parameters are inserted in the equations in order to overcome the many uncertainties on the system and to find the configuration that best fits the real system:

• K to regulate the mass flow rate, the higher the value the lower the temperature value the baseplate can reach

• kh, fundamental during the free warming of the fluid and so, in

regu-lating the thermal inertia

Another parameter was added to the simulation that is an additional amount of mass of the baseplate: from simulations, baseplate cooled too fast with respect real system and to render the dynamics more similar, the simplest solution was to increase its mass of a value dM; again after some trials, it was chosen dM = 70kg.

After all these assumptions and approximations, it is important to highlight again the fact that the model has not the aim to be a perfect copy of the real system but only to be able to simulate the same kind of dynamics de-scribed in section 2.2 and this objective was well accomplished. The three corrective factors K, kh and dM were fundamental to obtain cooling times

of the same magnitude of the real system; without them the cooling was too fast and overshoot too short; anyway the kinds of dynamics (overshoot and retarded cooling respect to switch on) are present in the construction of the Simulink model that remains quite detailed and correct in his assumptions. The limitation as already explained, and that rendered the introduction of the three constants necessary, is the lack of information on the fluid pres-sure and mass flow rate but if these properties could be estimated correctly, the system model should become quite more accurate without any particular modification.

Finally it must be pointed out that, having registered the temperature of the ducts from real tests, another approach could have been to impose the

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temperature of the ducts in Simulink without need to compute the cooling power: this was tried but failed completely because due to lumped mass modeling, with an imposed temperature, no thermal inertia is present and the baseplate follows the ducts behavior in cooling and warming without delays. The correct approach instead is to impose the amount of heat subtracted by the system at each iteration, as it was done in the model, allowing the main bodies to respect the cooling times that depend on the thermal properties of the fluid to cool the ducts, and to warm in off condition.

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Chapter 3 Development of the ANN

configuration and training

procedure

In this chapter all the work that led to the final training procedure to be used for the experimental tests is described: most of this part obviously relied on simulations but a small part of experimentation too is included. Indeed it occurred that the standard training procedure for the controller (used also in [29]) revealed the incapacity to counteract the overshoot behavior of excessive cooling of the baseplate during the first experimentation test performed, though from simulations it resulted very effective. So a deeper analysis of the phenomenon was done identifying the reasons of it (section 3.3.6) and developing an original solution for this problem (section 3.3.7). The training procedure, i.e. - the kind of ANN architecture, - the data sets required and - the training configuration (with identification of the inputs necessary to develop a controller with prediction capabilities), are deeply analyzed and described in the respective sections, however only a contained analysis was paid to the number of neurons, layers and delays because in a simulation environment, with data sets numerically obtained, the system identification resulted quite easy. The proper selection of number of neurons, layers and delays was more crucial in the training of the real system so this aspect is deeper analyzed in chapter 4.

In the first two sections that follow a brief and simple introduction to ANN is presented and is described the neural model reference control that is the architecture used for the controller generation.

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3.1 Intuitive introduction to ANN system for

plant identification and control

This section describes qualitatively what is an artificial neural network (ANN), to introduce the concept of training though it does not have any presumption to be explanatory and sufficient to a complete comprehension of the next sec-tions for which references [11][12][13][17][18][28] and [34] should be enough; in particular, for a good introduction to use of ANN, reference [34] is highly recommended.

An ANN used to identify a system, roughly speaking, is a combination of the system inputs through some coefficients called weights that, after an iterative procedure called training used to find the best values for the weights, is capable to reproduce the input-output relation of the system to be identified. The ANN needs to know how the system behaves in order to tune its weights to be able to reproduce the behavior of that system or to be able to control it. It needs examples, called data sets, that are temporal histories of the inputs and outputs of the system. During each iteration of the training, the ANN selects the weights (according to specific criterions of the training[7][30]) and checks the error between the outputs obtained from the combination of the inputs using the weights and the real outputs that should be obtained according to data sets then, depending on the error, weights are recomputed in order to find better values to reduce the error itself; figure 3.1 shows the general procedure of training. The structure of the ANN, i.e. how the inputs are combined, can be built as much elaborated as desired though there are already many approaches well validated for control architectures (a wide description of control architectures is available in[19][22][23][24][28]).

3.2 Neural model reference control

In this thesis it was selected the neural model reference control architecture, between the main ones, because though the controller training is computa-tionally quite expensive respect to many other approaches, since it requires the use of dynamic backpropagation[11][21], on the positive side the neural model reference control applies to a very large class of plants [34]. Another important reason why it was chosen is the specific type of control action that can be executed on the TVC: the only control action with which the cool-ing system can be controlled is its switchcool-ing ON and OFF; this information is provided from the data sets to the ANN respectively with the values +1 (ON) and −1 (OFF) as the output of the controller. This is just a

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CON-Figure 3.1: the neural network has the goal to generate the same outputs of an unknown function given the same inputs. The ANN compute the predicted outputs combining the inputs through the weights; from the error with the real outputs, weights are then updated (adaptation) iteratively to reduce the error.

VENTION, that is necessary, to associate to the control action a number during the training though the real control action is not a value but the ON or OFF state of the system. Due to this, all the kinds of controllers that are trained using as output of the net the control action would be constricted to be able to generate only ±1 and to be trained checking the error on this parameter; this was done but it gave problems to the optimization algorithm as will be explained in section 3.3.4. Moreover the error would not be very representative because measured on a quantity that does not exist in the real real system (the control action value is a dummy variable). With the neural model reference control instead this does not occur because the per-formance with which the neural network is trained is the error between the real temperature obtained with a certain control action (values provided by data sets) and the temperature obtained in the plant model using as input the same control action; so the value of the control action does not take part to the optimization, instead, as output, it is used the baseplate temperature value that is the real important parameter to control.

Neural model Reference control consists of two neural networks as shown in figure 3.2. One neural network is used to model the system and one neural network is used to control the system. Using the data sets (measured inputs and outputs of the system), the ANN plant model is trained offline. This block estimates the plant behavior, and the output of this block is used to

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calculate the training error. After this, the controller is trained such that plant response follows a reference model. Controller parameters (weights) are updated based on the error signal computed from the system output and the neural network model of the plant. Figure 3.3 shows the details of the

Figure 3.2: In neural model reference control architecture the NN plant model is trained first; NN controller is then trained offline checking the error between the reference model (data sets) and the NN plant model outputs obtained with the control action.

neural network plant model and the neural network controller. There are three sets of controller inputs: delayed reference inputs, delayed controller outputs (plant inputs), and delayed plant outputs. For each of these inputs, the number of delayed values to use are selected. There are two sets of inputs to the neural network plant model: delayed controller outputs and delayed plant outputs. In practice, for the training of the TVC plant model, the controller output is the control action (represented by the values ±1 as already explained) and the plant output is the baseplate temperature. In the plant identification process for neural model reference control, although there are delays, they occur only at the network input, and the network contains no feedback loops. For these reasons, the neural network plant model can be trained using the backpropagation methods for feedforward networks[34]. The training of the neural network controller, however, is more complex: as can be observed in figures 3.2 and 3.3 the model reference control structure is a recurrent (feedback) network[34]. This type of network is more difficult to train than the feedforward networks used for plant identification and requires dynamic backpropagation (the reader is referred to [12] and [13] for various forms of dynamic backpropagation algorithms). In this thesis algorithm implementation is not discussed because for the neural network

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Figure 3.3: The structure of the neural model reference control is divided in NN plant model and NN controller; the NN plant model weights (IW,LW) and biases (b) are trained apart with the plant (or using data sets) and are frozen during the controller weights training. Here both NN controller and NN plant model have a hidden layer and an output layer.

design it was used the neural network toolbox of MatLab [18] that provides all the codes once the network is built.

3.3 Numerical validation

The fundamental problem of controller development with ANN is how to train the ANN controller and in this, the model of the real system, becomes of fundamental importance because the TVC has very slow dynamics and an approach of trial and error with the real system would be infeasible. Instead, the model allows to test many configurations in extremely less time and to generate as many data sets as desired, to find the best ones for the correct training. Obviously, this suppose a correct modeling of the system that includes the same dynamics (see 2.2) to be sure that a training procedure for the controller that works in the model will work for the real system too. The work done in the first phase of the simulations was to select the right data sets and the training parameters: many data sets were generated, it was necessary to test the controller generated with a lot of different

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com-binations of them and then select the number of delays for each input and the number of neurons for each layer. This procedure was followed both for plant training and controller training. Work was long and hard but finally many fundamental observations for obtain a good training of the controller were identified: these are divided in three sections about the data sets 3.3.2, the training of the ANN plant model 3.3.3 and the training of the controller 3.3.4; but before to move to them some practical important considerations on the control action have to be discussed.

3.3.1 General considerations on the control action

The controller needs to be able to keep the TVC temperature at a fixed value: actually, this is impossible due to fact that the only possible control action is the ON or OFF state of the chamber and this will imply oscillations of the temperature about the target value to maintain; no real asymptotically-stable regime can be reached. Obviously if the continuous switching from ON to OFF and vice versa of the system could be as frequent as desired, oscillations, in theory, could be mitigated as much as wanted but practically this would lead to a continuous switching on and off of the compressors that is certainly not a desirable thing for a good maintenance of the system, so for avoid these kind of problems the fastest control switching from one state to another was restrained to occur only at a distance of a minute. In practice the controller is set to generate a control action each minute and keeps it for sixty seconds, then it recomputes the best output, ON or OFF state, to control the system.

The controller, according to its inputs that are the past values of its output (ON/OFF) and the past values of the baseplate temperature (the tempera-ture to control), generates the control action; however it needs a third input that is the reference i.e. the temperature value to which it must bring the baseplate temperature. The difficult part, during the training, is to teach to the controller that it must make sure that the baseplate temperature follows the reference. To explain this, figure 3.4 can be of help: the inputs allow the controller to generate a control action that acts on the system, under this action the system undergoes a variation of its state, in practice its temper-ature changes: controller must learn that this new state of tempertemper-ature has to be the same value it had received as input. So, from this point of view it becomes easy to understand that, during the training, the reference inputs must be the same values that are used also as output of the training i.e. the baseplate temperature values that from data sets we know will be obtained. In this way, the controller learns that the reference is the value that must be

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reached with the control action to generate. Once the controller is trained it

Figure 3.4: NN controller receives past values of baseplate temperature (Tb) and of the control action (inpB) plus a reference that represents the desired temperature in the TVC (plant). In this way it generates the new control action that acts on the system producing a change of its state.

is tested on the TVC simulator in Simulink and, in input as target, now it receives the temperature that is desired inside the chamber; actually, instead of a constant reference, it is better to use a negative slope line (for example in figure 3.6 is -1°C/5min) that goes from the initial temperature value of the baseplate to the desired value and only once this value is reached, the reference remains constant. This is done because the ramp is a bit similar to the natural behavior of the TVC temperature, in the sense that it takes some time to decrease, otherwise the controller could have troubles in computing the correct control action in the case of a reference that from the beginning has a constant value; it would be like to say to the controller that the base-plate is at ambient temperature and that at the next instant it must be at a completely different value: this is a behavior never seen in the data sets and the controller works well with references similar to the ones of the data sets.

3.3.2 Data sets generation and selection

The data sets are temporal histories of the inputs and outputs of the system we want to represent with the ANN: in our case a data set is obtained in the simulation, or in the real system, by switching on or off the cooling system different times and registering the values of the baseplate temperature and the state of the control action (1 for ON and -1 for OFF).

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The types of data sets used are of fundamental importance: data sets must contain as many information as possible on the behavior of the system; they must be representative of all the scenarios in which to work. The first idea was to register the cooling of the model up to a certain temperature, then to switch off until temperature starts to rise, then to start the cooling again up to another temperature and so on (an example in figure 3.5) covering with the data sets all the temperatures the TVC can reach. The controller obtained however was not able to control the temperature satisfactorily, pre-senting very big oscillations about the target values as can be observed in figure 3.6. These results, together with previous considerations, brought to

Figure 3.5: a data set, obtained from simulation, that ranges from few degrees below 300K down to 240K. It was generated, together with others, with the aim to train a controller capable to control temperature in all the ranges but this approach was not successfull.

understanding that to control the temperature with small oscillations about a constant value, in the training there must be some data sets that can be representative of this specific behavior. So, the idea was to generate data sets that presents small oscillations of the temperature about a certain value and this was obtained switching on and off the cooling system, in the model, at small intervals of time. As example in figure 3.7, the upper left data set shows the temperature of the TVC simulator where, after an intermittent cooling to about -12°C, an intermittent warming is performed with ON pe-riods (dton) of 2 minutes and OFF periods (dtof f) of 10 minutes: during this

warming the temperature reaches an equilibrium, more less, about -1°C with small amplitude oscillations; changing the couple dton/dtof f a new value of

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val-Figure 3.6: simulation of the controller trained to work in all ranges of tem-peratures. Here the targets are, in order, 0°C, -10°C and -30°C. The baseplate temperature (blue line) follows the reference (red line) but with big oscilla-tions that reduce in reducing the temperature target.

ues ranges between ambient temperature to -20°C about, so data sets of this kind will teach to the controller to control the temperature in this range of values, but for lower temperatures other data sets are necessary. This led to the conclusion that for a system of this kind the training of the controller requires data sets of many hours representative of many different ranges of temperature. A training of this kind not only would require a very long time but may also have problems of underfitting and would not be able to gen-erate a controller capable of working in all these different conditions. The solution was to train different controllers, each for a specific range of tem-perature avoiding to the single net the difficult objective of a too much wide generalization.

From simulations another important aspect was observed: it is much easier to control low temperatures with respect to high temperatures. This is intuitive because the difficulty in control the temperature lies in the ability of the controller to predict and counteract the overshoot before it occurs: in other words the controller must avoid to keep the cooling system turned on too much, otherwise after the switching off it continues to cool excessively, so it must be able to predict how much earlier to switch off the system, knowing that the cooling will continue for a while.

It should be evident that the lower the temperature the smaller the overshoot after the switch off because, as explained in 2.2, the overshoot depends on

Control design of a thermal vacuum chamber cooling system based on artificial neural network

Scuola di Ingegneria Industriale e dell’Informazione

Master’s degree in Space Engineering