Renaud-Pierre Martin
email: renaud-pierre.martin@lcpc.fr

François Toutlemonde

Design of a heat treatment representative of the curing conditions of a massive concrete structure ■ ABSTRACT delayed Ettringite Formation (dEF) is a concrete pathology that affects certain materials, depending on their composition, previously exposed at early age to a significant temperature rise (with a threshold of about 65 °C). During the casting of massive elements in particular, the combined effects of weak heat transfers and of the heat of hydration can lead to a significant temperature increase in the core of the structure inducing a major risk of DEF. In order to investigate the mechanical effects of this reaction to improve the management of the affected structures, studies are ongoing at the French Public Works Research (LCPC).

This article describes the design of a heat treatment process that simulates the setting conditions in the core of a massive structure to induce DEF. The design concepts are presented in a first part, and describes in details the use of the QAB test to determine the heating phase. Then a numerical and experimental validation of this heat treatment is proposed in a second part.

Mise au point d'une cure thermique représentative de l'échauffement d'une pièce massive de béton

■ RéSumé

La réaction sulfatique interne (RSI) est une pathologie du béton qui affecte, suivant leur composition, certains matériaux ayant subi au jeune âge une élévation conséquente de leur température (seuil de l'ordre de 65 °C). Lors du coulage de pièces massives notamment, sous les effets combinés de transferts thermiques faibles et de l'exothermie de la réaction d'hydratation du ciment, la température à coeur peut augmenter de manière significative et induire des risques de RSI importants. Afin d'étudier les effets mécaniques de cette pathologie pour mieux gérer les ouvrages qui en sont atteints, des études sont en cours au LCPC. Cet article décrit la mise au point d'un procédé de cure thermique permettant de simuler les conditions de prise au coeur d'une structure massive afin d'induire des effets de RSI. Il présente dans un premier temps les concepts de dimensionnement considérés et notamment l'utilisation de l'essai QAB pour la détermination de la phase de chauffe. Ensuite, une validation numérique et expérimentale de la cure thermique est proposée.

INTRODuCTION

Delayed Ettringite Formation (DEF) is an endogenous reaction capable of damaging concrete structures: this pathology is characterized by material swelling, which in turn induces cracking as well as a deterioration in mechanical performance. In France, several tens of structures are presently affected by this reaction [1]. Materials subjected to a significant temperature rise, beyond a threshold on the order of 65°C, at the early age are prone to this reaction [2]. As such, massive structures are found to be heavily exposed to this risk, with the combined effects of an exothermic cement hydration reaction and weak heat transfers leading to high and extended temperature rises at the core. These internal temperature variations cause ettringite dissolution-recrystallization mechanisms in the hardened material [3, 4], thereby generating the disorders indicated above and providing the reason for serious issues encountered with physical integrity at the structural scale.

In order to develop a set of tools dedicated to reassessing impaired structures [5], the French Public Works Laboratory (LCPC) is currently conducting an experimental study [6] intended to improve understanding of DEF mechanical effects at both the material scale (specimen testing) and structural scale (tests on beams) and thus further the work previously completed on the alkali-aggregate reaction [7]. To generate a "DEF potential", this experimental study proposes submitting materials after casting to a thermal treatment representative of the thermal and hydrological conditions under which setting takes place at the core of a massive concrete specimen. To apply a comparable thermal history for these various types of test samples, a specific approach has been adopted that incorporates the entire range of thermal mechanisms involved. This article will present the methodology developed to achieve such a thermal treatment process.

The next section will outline the methodological scope, with emphasis on the benefits of the QAB test in defining the heating phase. Afterwards, the components of a numerical validation exercise will be discussed, along with a thermal treatment model derived by implementing the CESAR-LCPC finite element computation code (TEXO module). The last section will describe an experimental validation of this treatment process.

THEORETICAL DEFINITION OF THE HEAT TREATmENT

Specifications ■

After casting, a heat treatment (also called thermal treatment) is to be applied to the test sample in an effort to recreate the maturation conditions that exist at the core of a massive element, including the temperature conditions capable of prevailing as a result of an exothermic cement hydration reaction. To facilitate a laboratory-based thermal treatment (via a considerable decrease in material cooling time compared with times experienced in situ), the actual temperature profile of the massive specimen has been simplified into a trapezoidal shape. The process then involves determining the various phases of: heating, constant temperature step, and the cooling necessary for completion of treatment.

The primary objective inherent in this thermal treatment is to apply a repeatable thermal history on the entire set of samples, for the purpose of producing materials with comparable "DEF potential": it has been possible to demonstrate [8, 11] that both the maximum temperature reached and the high temperature holding period exert influence on the potential DEF magnitude. The goal here consists of producing temperature deviations between the various specimens of less than ±1°C during the period of constant temperature. Moreover, application of a homogeneous temperature field to each specimen throughout this phase allows considering all parts of the structure to react identically, regardless of specimen size: temperature differences inside the same specimen must not exceed ±1°C, and the ultimate process be reproducible: any discrepancies in repeatability between two successive thermal treatments must remain below ±1°C during the constant temperature period. As a final constraint, the cooling phase must not cause cracking due to thermal shock.

Humidity ■

During production of a concrete element, cement hydration only uses a portion of the mixing water to form hydrates. Besides the porosity it generates after material drying, this excess water induces high relative humidity in the material at an early age. Experimental results [9] indicate that the relative humidity in small concrete prisms (measuring 76 × 76 × 280 mm 3 ) remains above 90% for more than 7 days, and this holds true even for specimens dried with a relative humidity equal to 50%.

In light of these findings, it was decided to conduct the thermal treatment in water, which not only provides for realistic application conditions given the humidity conditions prevailing at the core of a massive sample after casting, but also maintains specimens in a saturated state, which acts to promote DEF development. In addition, the creation of an actual thermal treatment device is facilitated when using water instead of humid air. Water also brings thermal inertia to the treatment system, which in turn allows for stricter temperature control with respect to external disturbances.

Heating phase ■

Given research program choices in terms of specimen size, the objective of this treatment consists of applying the same thermal history to both a set of beams (0.25 × 0.50 × 3.00 m 3 ) and cylindrical specimens (on the order of 0.1 m in diameter by a height of between 0.2 and 0.3 m), so as to generate an equivalent swelling potential from one specimen to another, as well as within the same specimen.

Due to the dimensions involved, temperature control at the beam core by means of applying a surface temperature boundary condition is difficult to implement, even more so at an early age when the predominant thermal mechanism is cement hydration. Furthermore, the thermal inertia of beams raises concerns over exceeding the temperature order during the heating phase -constant temperature step transition, i.e. the core of a beam only "feels" this change in heating mode belatedly relative to the beam surface. In contrast, the temperature of small-sized cylindrical specimens is easily controlled by the temperature setting in the treatment tank, thanks for the most part in this case to the abundance of thermal exchange phenomena (due to a greater exchange surface area / volume ratio for a given specimen, a low thermal inertia and a high heat transfer coefficient in water). These phenomena have been illustrated in Figure 1: for this particular example, temperature at the beam core displays deviations with respect to the treatment protocol that are much more pronounced than for a cylindrical specimen, which leads to substantial temperature variations between differentlysized specimens.

As a means of avoiding these scale effects, it was decided to simulate adiabatic conditions during the initial phase of temperature increase (Fig. 3): temperature history during the heating phase is tied to temperature evolution, as determined by a QAB test, for the concrete mix under study. By limiting thermal transfers with the outside, this approach is able to ensure homogeneous temperature inside the specimen regardless of its size: this assurance offers control (from a theoretical standpoint) of treatment temperature as the temperature rises during cement hydration under adiabatic conditions. Moreover, this configuration enables recreating a temperature history resembling that of a massive element after casting, wherein the very weak exchange conditions lead to significant temperature increases at the time of cement hydration. 2 simulates temperature changes at the core of a massive element 2 × 2 × 8 m 3 in size (these material characteristics are identical to those presented in the "Modeling set-up" section below, with an exchange coefficient on the side and bottom faces equal to 2.55 W/m 2  °C -representative of a wooden formwork 20 mm thick -and an exchange coefficient on the exposed upper face equal to 10 W/m 2  °C, under conditions of a constant 20°C outdoor temperature): in this case, the temperature exceeds 70°C for more than 3 days.

Constant temperature plateau ■

In light of these findings, a 3-day threshold duration was established, as a compromise between the swelling potential provided by the thermal treatment and the organizational constraints associated with treatment duration.

Temperature ›

The heating phase simulates adiabatic conditions by adapting treatment temperature to the heat release, as determined while the QAB test is being run (see section entitled "Heating phase"). The temperature reached at the end of this phase can then be evaluated by calculating the rise in material temperature under adiabatic conditions. Waller proposed an approach to derive the value of this heat of hydration [13]; the present article will concentrate on the concrete mix design provided in According to this relation, Δ T(∞) is the temperature rise experienced under adiabatic conditions at the end of cement hydration (expressed in K), Q(∞) the cement hydration heat at infinite time (in J/m 3 of concrete), and C th the average calorific capacity of concrete (in J/K/m 3 ) evaluated on the basis of fresh concrete and the specific heat capacities of mix components at 20°C.

Cement hydration heat may be determined without any other information once the cement chemical composition is known [13]. Table 2 lists the chemical composition of cement used in these study specimens. Waller [13] also suggested the specific hydration heat values given in Table 3 for each cement phase. Cement heat of hydration can then be calculated by applying Equation (2), where q c is the specific heat of cement hydration (in J/g), q i the heat of hydration of Phase i (in J/g), and φ i the mass proportion of Phase i in the cement (in g/g). The numerical application of Equation ( 2) yields a specific heat of cement hydration equal to 384 J/g. (2)

The cement heat of hydration at infinite time Q(∞) is to be calculated using Equation (3), in which α(∞) is the final degree of hydration, c the cement concentration in the studied concrete mix (in g/ m 3 ) and q c the specific heat of cement hydration (in J/g):

(3)

Based on a bibliographical review and from his own research results, Waller proposed Equation In [13], Waller provided a specific heat at 20°C of 0.73 J/K/g for siliceous aggregates and 4.19 J/K/g for water. To incorporate the drop in specific heat induced by the mobilization of water in a hydrate formation, AFNOR [14] suggested using a reduced specific heat of water set equal to 3.80 J/K/g, while Jolicoeur [15] proposed decreasing specific heat as a function of bound water quantity, as per Equation (6):

(6)

In this relation, the mass of bound water is evaluated by assuming it equal to 23% of the cement hydrate mass. Moreover, Waller introduced a fixed decrease in calorific capacity, in accordance with Equation (7), making it possible to incorporate the change in concrete heat capacity under the hydration effect of the various cement phases. c is the cement content in the concrete composition (in kg/m 3 ) and α the degree of cement hydration.

(

) 7
Table 5 summarizes results of the specific heat calculation for concrete as a function of the adopted approach. The accuracy and precision of these volumetric specific heat values are not easy to measure: the cement hydration reaction proves, in reality, to be highly complex and leads to the formation of hydrates, each possessing its own specific heat. Furthermore, these specific heats actually vary with temperature. This approach however offers the double advantage of simplicity and ability to obtain estimations of the material calorific capacity without the need to run complex tests.

Lastly, depending on the approach adopted for evaluating the material specific heat, Table 5 offers an evaluation of concrete temperature rise under adiabatic conditions, on the basis of Equation (1).

Since the specimens were produced at an average temperature of 20-25°C, the final temperature under adiabatic conditions will be in the range of 75-80°C. At this stage of the thermal treatment design, a threshold temperature of 80 ± 1°C has been selected.

Cooling ■

The thermal treatment for application to specimens concludes with a cooling phase. In order to both avoid specimen cracking due to thermal shock and ensure representativeness of the phenomena observed during fabrication of massive specimens, cooling speed has been set at -1°C/h. This phase also allows limiting total process duration in order to simplify laboratory procedures.

Treatment temperature profile ■

Based on the set of criteria defined above, the corresponding thermal treatment applied to test specimens has been depicted in Figure 3. The heating phase (with a duration of 24 hours and a maximum heating speed of 10°C/h) has been determined from results of a QAB test (Fig. 3) conducted for the specific concrete mix. Given the activation of diverse reactions initiated during the hydration of a cement sample, it is difficult to theoretically predict the associated heat release or its kinetics. It would be preferable therefore to proceed with an experimental determination of these parameters by means of a QAB test. The heating phase is initialized 2 hours after the beginning of specimen casting, since this time interval corresponds to the material placement phase in the laboratory. Next, a plateau is established at a temperature of 81°C, extending 72 hours (see previous section). Moreover, specimens are cooled at a speed of -1°C/h until reaching a temperature of 25°C. This process lasts a total of 151 hours, i.e. slightly longer than six days.

NumERICAL SImuLATION OF THE THERmAL TREATmENT PROCESS

Modeling set-up ■

In order to assess the relevance of the treatment process developed in the preceding section, numerical models have been generated: through use of the TEXO module [16-18] included in the CESAR-LCPC finite element computation code [19], the thermal treatment of a beam (measuring 0.25 × 0.50 × 3.00 m 3 ) and a cylinder (diameter = 0.11 m, height = 0.22 m) have both been simulated. The primary data input consists of the temperature rise under adiabatic conditions, obtained by running a QAB test. The other main characteristics and parameters of these calculations have been listed in Table 6 and Figure 4. Both the thermal conductivity and specific heat of the material lie at orders of magnitude estimated to be representative of an ordinary concrete. The heat transfer coefficient was set at a value of 100 W/(m 2  °C), which is the order of magnitude of the exchange coefficient in water [20]. Moreover, a sensitivity analysis of results to this parameter has indicated that increasing the heat transfer coefficient by a factor of 10 only induces a slight deviation in the temperature field evaluation for specimens covered in our calculation protocol.

Theoretical thermal response of a beam ■

Figure 5 shows the evolution in temperature at both the center and edge of the common crosssection of a beam during heat treatment. These results highlight one of the benefits of a pseudo servo-control of heating speed as the material heats under adiabatic conditions: a relatively homogeneous temperature field is obtained in the specimen (Figs 5 and6) during heating, despite high heating speeds, in order to reach the thermal treatment plateau. At the heating phase-temperature plateau transition, the targeted value is only exceeded by a very slight margin at the beam core: the proposed approach thus enables considerably limiting the thermal inertia effects of a specimen of this type.

Figure 5b provides the evolution in temperature difference between the beam center and edge (Fig. 4a) over the course of the treatment process; this difference remains less than 4°C during the heating phase and narrows to around 3°C during cooling. Over the entire temperature plateau period (i.e. between t = 24 and 96 hours), this difference lies near zero. From a theoretical standpoint, the thermal treatment defined herein is able to meet the temperature field homogeneity criterion established in the protocol specifications. Dimensional influence: Theoretical evaluation ■ Figure 7 reflects the deviations in theoretical temperature between a beam core and the core of a smaller specimen (Fig. 4). These results underscore the small discrepancy existing between these two types of samples during the threshold phase (from t = 24 to t = 96 hours), in compliance with the designated protocol specifications. In the heating phase, this deviation climbs to as high as 5°C during the most intensive heating (10°C/h). This effect is primarily correlated with the differences in thermal inertia between the two elements: it winds up being easier to control the temperature at the core of a small-sized specimen, by imposing a boundary condition, rather than the temperature of a beam. The strong similarity of Figures 5b and7 is worth noting: temperature at the core of a specimen remains very close to treatment temperature throughout the process. This interpretation would also be applicable to the deviations observed during cooling.

Sensitivity study: Influence of a change in cement ■

Figure 8a compares the temperature evolution inside a QAB calorimeter and under adiabatic conditions (i.e. once thermal losses have been corrected and thermoactivation included) of both a concrete specimen chosen for these thermal treatment specifications (Concrete 1: see Section entitled "Heating phase") and a less exothermic concrete (Concrete 2). The chemical composition of the corresponding cement is listed in Table 7. In calculating the equivalent age, an average ratio of E a /R 5000 K has been assumed as part of this initial approach. Given the lack of complementary data, this value was considered as representative of the types of concretes under study. Undertaking QAB tests at different temperatures would serve to improve the accuracy of this Figure 8b displays the thermal responses of the beams built using these two concretes. In the case of Concrete 2, a QAB type approach with a "sigmoid" pattern heating phase still proves to be somewhat efficient, as the observed temperature deviations with respect to the temperature order are comparatively less than those generated under constant heating speed (see Fig. 1). On the other hand, the recommended guideline at the specimen core is greatly surpassed between t = 14 and t = 30 hours. This example reveals therefore the benefit of identifying a calibrated heating phase in the studied concrete by performing a QAB test, for the purpose of minimizing temperature deviations inside the treated specimen.

EXPERImENTAL VALIDATION OF THE THERmAL TREATmENT PROCESS

Experimental set-up ■

Practically speaking, as part of the research conducted at LCPC beginning in 2006 on the mechanical effects of DEF, thermal treatments have been conducted using a device specifically designed for this study [6]: a tank filled with water whose temperature is regulated by means of a 24-kW immersion heater guided by a programmable device (Fig. 9a), into which specimens are immersed after casting. Temperature homogeneity in this tank is maintained by stirring the water via pump action. This set-up does not include any cooling system: the temperature is lowered by natural cooling at first (through the temperature differential between the tank and the outside), then by injecting cold water into the water circuit.

Performance tests made it possible to guarantee that during a constant temperature step, temperature may be regulated to an accuracy of ±0.5°C with respect to the temperature order. This process is repeatable, also to an accuracy of ±0.5°C, in acknowledging the level of uncertainty on temperature measurements. Temperature homogeneity in the tank has been verified, yielding maximum temperature differences in the tank of 1°C during heating phases. illustrates an experimental approximation to this thermal treatment via such a device. A deviation can be observed at the end of cooling between temperature of water and the temperature order (maximum deviation found to be on the order of 2°C): at this stage of the process, reducing the temperature deviation between the tank and the outside would hinder the natural cooling capacities of the system. According to this scenario, cooling is forced by increasing the flow rate of cold water injection.

Experimentally-derived thermal response of a beam ■

With the aim of experimentally evaluating the behavior of a beam during this thermal treatment, a specimen has been instrumented along a common cross-section (located 0.6 m from the longitudinal extremity) using temperature sensors at points denoted M1, M2, M3, M4 and M5, positioned respectively at depths of 0.04 m, 0.08 m, 0.17 m, 0.27 m and 0.37 m relative to the upper beam show the temperature evolution at these specific spots during the heating phase, constant temperature step and cooling phase, respectively.

It can be noticed that experimental behaviour, on the whole, agrees with the modeling output presented in the previous section. During the heating phase, temperature deviations at the various instrumented points remain below ±2°C despite the heating speeds. This finding experimentally confirms the benefit of calibrating the heating phase on results from the QAB test, corresponding to the concrete under study, thereby ensuring the most homogeneous temperature field possible in a specimen with high thermal inertia. These temperature differences do not exceed ±0.5°C during the constant temperature step, hence in compliance with the criterion established in process specifications. During the heating phase -plateau transition however, the treatment guideline is slightly surpassed within the beam, to a level of approx. 1°C over about 10 hours. Moreover, during the cooling phase, these deviations remain less than 1°C until reaching a temperature of roughly 45°C, at which point it becomes more difficult to maintain constant cooling speed (see section above). Beyond this temperature, all differences lie below 2°C. These results have made it possible to validate the thermal treatment process with respect to the temperature field homogeneity criterion.

Figure 13 compares the evolution in temperature at point M4 during the heating phase, according to whether it has been obtained experimentally or numerically. TEXO module predictions turn out to be in agreement with the practical conception of thermal treatment. Nonetheless, it is remarked that beginning at t = 8 hours, the model shows a tendency to underestimate temperature at the beam core (with a maximum deviation of around 3°C). This observation may be explained by a difference in how fast the cement hydration reaction is progressing at this specific instant, with such a difference stemming from the discrepancy in experimental and theoretical thermal states at the time of casting.

While the model takes into account a material placed at a temperature of 20°C, the experimental protocol demonstrates that this hypothesis is difficult to accurately satisfy (see Fig. 10, t = 2 hours), due to the room temperature at the time of specimen production or to the mixing effect. Figure 14 offers the evolution in temperature differential between points M4 and M1 throughout the treatment process. These results highlight the good correlation between predicted thermal behavior and behavior observed during the experimental campaign. It has been found this time however that the model overestimates the deviation during cooling; over this treatment phase, hydration reactions only constitute a small fraction of the thermal phenomena governing specimen behavior, with exchange-induced losses becoming predominant. It is likely for the observed differences at this point to be correlated not only with an overestimation of the beam specific heat (a complicated correlation to evaluate as a result of its dependence on both temperature and degree of hydration reaction progress), but also with an underestimation of the formwork/water exchange coefficient. These deviations however remain limited.

The results presented in this section showcase the relevance of a numerical modeling set-up using the TEXO module for refining the treatment procedure prior to a full experimental campaign.

Controlling for scale effects: Experimental evaluation ■

Figure 15 presents the temperature deviation existing between the core of a cylindrical specimen (diameter = 0.11 m; height = 0.22 m) and a beam core (according to both numerical and experimental approaches). During the heating phase, a comparable thermal behavior can be observed regardless of the approach adopted. Nonetheless, the differences in initial thermal state lead to maximum deviations on the order of 3°C between model output and experimental findings. Throughout the temperature constant period, temperature differences between specimens remain below 1°C, thus satisfying the established target (see section entitled "Treatment specifications"). Moreover, during cooling, an overestimation of this deviation is once again apparent for the same reasons cited above (i.e. evaluation of specific heats and heat transfer conditions). In the end, the experimental depiction of this treatment process on a beam and a smaller specimen has served to validate the process relative to its objective, which consists of applying a similar thermal history to differently-sized specimens.

Repeatability considerations ■

In an effort to assess the repeatability of this thermal treatment process, several beams of identical composition and dimensions underwent thermal monitoring. Figure 16a gives the evolution in temperature within each specimen at a depth of 0.27 m from the upper surface (Point M4). The main differences between beams are noticeable: at the beginning of the heating phase and under the effect of variable initial thermal states (which may be ascribed to the variation in room temperatures at the time of the various casting steps, i.e. between 20°C and 25°C); and at the end of cooling, when it becomes more difficult to control treatment tank temperature due to the effect of the surrounding air temperature. Figure 16b proposes a graph to describe temperature deviations between specimens over time. Deviations are highest during roughly the first 10 hours of treatment: the influence of material placement temperature is dominant over this stretch of time. Once the intense heating phase has been completed, these deviations decrease substantially. During the temperature threshold, differences remain below the ±1°C limit stipulated in the process specifications.

CONCLuSION

This article has presented the methodology implemented in order to design a heat treatment process that generates DEF swelling. Applied to the material after casting, this process is intended to simulate concrete setting conditions at the core of a massive element. One of the main objectives assigned to this thermal process has consisted of applying a similar thermal history to specimens of all sizes.

One critical aspect of this thermal treatment lies in calibrating material heating speeds during the early age to temperature increases under adiabatic conditions, as measured by means of a QAB test. It therefore becomes possible to simulate the adiabatic conditions for concrete elements, which enables minimizing the thermal effects tied to their inertia as well as ensuring a better homogeneity of their temperature field.

A numerical study of the process has also been performed. Based on a finite element modeling set-up using the TEXO module of the CESAR-LCPC computation code, this study has provided an initial approach to estimating the relevance of a temperature profile during treatment, with respect to both the thermal field homogeneity criterion and scale effects (via a comparison of temperatures in beams and smaller specimens).

Lastly, an experimental validation of the thermal treatment was carried out. Once the performance of the customized device had been verified, we highlighted the benefits of this thermal treatment relative to the application of a homogeneous and repeatable temperature field for all types of specimens.

Such a treatment process may be introduced regardless of the specific concrete mix design; it is merely necessary to know the level of heating experienced by the material during setting under adiabatic conditions, which can be easily determined from a QAB test.

ACKNOWLEDGmENTS

The authors would like to thank LCPC's Structural Experimentation and modeling unit and in particular F.-X. Barin, C. Bazin, J. Billo, m. Estivin, L.

  Figure 1Temperature simulation at the core of concrete specimens subjected to heating (constant heating rate applied equal to 2.5°C/h)

  of the heating phase, specimens are exposed to a constant temperature step, which in addition to solubilizing the ettringite crystals previously formed during cement setting, allows adsorbing sulfates by the C-S-H structures, thus providing for a stockpile of reagents for subsequent DEF development [3, 10]. Expansion potential then increases with thermal treatment duration [4, 8, 11]. Measurements conducted on actual structures demonstrate that the temperature inside a massive element can remain above 70°C for eight full days [12].

Figure

( 4 )

 4 below to derive the final degree of concrete hydration [13], which for the concrete under study herein amounts to 0.78, for a W/C ratio of 0.46. With a cement concentration of 410 kg/m 3 , the heat release under adiabatic conditions at infinite time for the considered concrete is calculated to be:123 000 kJ/m 3 . (4)At this stage of the analysis, the specific heat of the concrete still needs to be calculated. For this purpose, Waller [13] proposed Equation (5), where m i is the quantity of component i in the mix (in g/m 3 ) and c i the specific heat of component i (in J/K/g). The specific heat of a cement can be assessed by means of a linear combination of the mass proportions of each cement phase and their corresponding specific heat, as indicated in

  Figure 3Temperature evolution over the course of the heat treatment process

  Figure 5 a) Theoretical thermal response of a beam to the treatment process; and b) deviation in the corresponding temperature between the center and edge of a section

Figure 6

 6 Figure 6 Temperature fields inside a beam at: a) t = 5.5 hours; b) t = 9 hours; c) t = 120 hours

  Figure 8 a) Heat release of concretes; and b) thermal response (temperature at the specimen core) of the corresponding beams

  Figure 10Experimental thermal response of a beam: Heating phase

  Figure 13Heating phase temperature at point m4 (at a depth of 0.27 m)

  Figure 14 Temperature deviations between points m4 (0.27 m deep) and m1 (0.04 m)

  Lauvin and J.-C. Renaud for their valuable assistance throughout the experimental phase of thermal treatment validation, as well as D. Siegert (with the Department of Measurement, Monitoring and Scientific Computations), whose participation proved determinant during development of this treatment process. The authors are also grateful for the support provided by EDF (E. Bourdarot, A. Jeanpierre) towards the research program devoted to the mechanical effects of DEF.

  Figure 16 a) Thermal monitoring of three identical beams during the treatment process (Point m4); b) corresponding temperature deviations

Table 1 .

 1 Equation (1)

	Figure 2
	Simulation of early-age
	temperature evolution
	at the core of a massive
	element (2 × 2 × 8 m 3 )	Temperature (°C)
					Time (days)
	Table 1 Concrete mix design specifications (in kg/m 3 )	Cement	Mixing water	0/2 siliceous sand	4/8 siliceous aggregate	8/12 siliceous aggregate	W/C
		410	199	854	100	829	0.46

serves to calculate this temperature rise under adiabatic conditions [13].

C 3 S C 2 S C 3 A C 4 AF CaSO 4 , 2H 2 O

	41.5%	27.2%	5.0%	11.5%	7.4%
	C 3 S	C 2 S	C 3 A		C 4 AF
	510	260	1100		410

Table 4

 4

	C 3 S	C 2 S	C 3 A	C 4 AF	CaSO 4 , 2H 2 O
	0.745	0.740	0.768	0.815	1.074

[13]. The ensuing calculation produces a specific heat of the cement at 20°C equal to 0.72 J/K/g.

(5)

Table 3

 3 Specific

heat values of cement phase hydration, according to [13] (in J/g)

Table 2

 2 Cement composition (according to Bogue's method)

Table 4 :

 4 Specific

heats of the various cement phases at 20°C [13] (in J/K/g)

Calculation method Without H 2 O reduction (i.e. free water) Fixed H 2 O reduction (according to NF EN 196-9) (Jolicoeur, 1994) (Waller, 2000)

	Specific heat (kJ/K/m 3 )	2388	2314	2240	2247
	Estimated temperature rise (°K)	51	53	55	55

estimation [21].

	C 3 S	C 2 S	C 3 A	C 4 AF	CaSO 4 , 2H 2 O
	43.2%	2.2%	2.4%	11.6%	5.6%


J Chauvin

A Albrecht

G Corde

N Petit

MODELING AND CONTROL OF A DIESEL HCCI ENGINE

Keywords: Diesel, airpath control, modeling, non minimum phase

This article focuses on the control of a Diesel engine airpath. We propose a detailed description of the airpath of a Diesel HCCI engine supported by experimental results. Moreover, we propose a simple, yet innovative, motion planning control strategy. At the light of this study, we can finally conclude, with supportive results, that motion planning is indeed an appropriate solution for controlling the airpath dynamics.

INTRODUCTION

Performance and environmental requirements of Diesel engines have steadily increased over the last thirty years, which in turn has required an increase in the sophistication of employed control strategies. Advances in model based control over this period have been one of the keys in meeting the demands placed on modern combustion technologies. Lately, the Highly Premixed Combustion mode (HPC) -including Homogeneous Charge Compression Ignition (HCCI) -has become of major interest. It requires the use of high Exhaust Gas Recirculation (EGR) rates.

The key idea is that the recirculated burned gas lower the in-cylinder temperature and dilute the air charge which reduces the emissions of nitrogen oxides. Simultaneous ignition in the whole combustion chamber is performed and controlled. Significant reduction in pollutants emission was proven in practice through numerous experiments (see [START_REF] Kahrstedt | Combustion processes to meet future emission standards[END_REF][START_REF] Amnéus | Homogeneous Charge Compression Ignition engine: experiments and detailed kinetic calculations[END_REF] for example). In that combustion mode, the core variable is the Burned Gas Rate (BGR) in the intake manifold (see Figure 1). BGR offsets may cause misfires and malicious noises. In the HCCI combustion mode it is very high (40% or more). Accurate control of BGR can be achieved by controlling the whole airpath system: intake and exhaust manifolds, EGR loop and fresh air loop. This is the subject of the paper.

As studied in [START_REF] Kolmanovsky | Issues in modelling and control of intake flow in variable geometry turbocharged engines[END_REF]Kao and Moskwa, 1995b), the airpath system of a turbocharged Diesel engine features coupled dynamics. The EGR acts as a discharge valve for the turbocharger. Most studies consider the following control setup: both intake pressure and intake air flow are closely controlled using EGR valve and Variable Geometry Turbocharger (VGT) using Gain schedulling PI controllers as in [START_REF] Stefanopoulou | Control of variable geometry turbocharged Diesel engines for reduced emissions[END_REF][START_REF] Van Nieuwstadt | Experimental comparison of EGR-VGT control schemes for a high speed Diesel engine[END_REF], using constructive Lyapunov control as in [START_REF] Janković | Constructive Lyapounov control design for turbocharged Diesel engines[END_REF] or LPV formulation as in [START_REF] Jung | Comparison of uncertainty parameterisations for H-infinity robust control of turbocharged Diesel engines[END_REF]. Controlling both intake and exhaust pressure has been exposed in [START_REF] Ammann | Model-based control of the VGT and EGR in a turbocharged commonrail Diesel engine: theory and passenger car implementation[END_REF]. All these studies prove the relevance of a multivariable control.

Fifth IFAC Symposium on Advances in Automotive Control, AAC 2007

Following a preliminary approach we presented in [START_REF] Chauvin | Experimental motion planning in air-path control for HCCI engine[END_REF], we use a motion planning strategy by expliciting a feed-forward term.

The contribution of the paper is as follows. We propose a detailed description of the airpath of a Diesel HCCI engine supported by experimental results. Moreover, we propose a simple, yet innovative, motion planning control strategy. At the light of this study, we can finally conclude, with supportive results, that motion planning is indeed an appropriate solution for controlling the airpath dynamics.

The paper is organized as follows. In Section 2, we detail the control problem. In Section 3, we detail the influence of the airpath actuators on the combustion process. Section 4 proposes a simplified model for control purpose. We explicit the control strategy and experimental results on a 4 cylinder HCCI engine in Section 6. Conclusions and future directions are given in Section 7.

CONTROL PROBLEM

Our approach to combustion control is to manage the air and burned gas masses in the cylinder. In other words, we focus on the airpath system. Figure 1 shows the flow sheet of the airpath. Flows of fresh air and the Exhaust Gas Recirculation (EGR) mix into the intake manifold and are aspirated into the cylinders. Engine control performance requirements usually include consumption, pollutants, and noise reduction. Those requirements are often incompatible. Therefore, a tradeoff is needed. This impacts the reference setpoints of air and burned gas masses in the cylinder (M air,cyl and M bg,cyl ). In practical applications, those variables can not be measured. Yet, equivalent variables can be considered. Controlling those two masses is equivalent to controlling the intake pressure P int (being an image of M air,cyl + M bg,cyl ) and the burned gas rate F int (representing

M bg,cyl
M air,cyl +M bg,cyl ). Setpoints are often chosen to maximize EGR in order to lower the NO x emissions at low load. At high load, the negative impact of EGR onto combustion stability and efficiency imposes the use of low EGR. Typically, the setpoint at 1500 rpm and high load is (P int,sp = 2bar, F int,sp = .05) using low EGR, while at 1500 rpm and low load setpoints under consideration are close to (P int,sp = 1.013bar, F int,sp = .45) using high EGR.

In this context, the control problem we need to address is a large transient problem for a two outputs, two inputs system. The control inputs are the VGT actuator position S vgt (v 1 ) (ranging from 0 to 1) and the EGR valve normalized effective area S egr (v 2 ) (ranging from 0 to 1). Both are bounded. Other external inputs include the fueling rate and the engine speed N e . The underlying dynamics is also of dimension 2. The states are the outputs: P int and F int .

INFLUENCE ON THE COMBUSTION PROCESS

The air feedback loop purpose is to control the gas mixture in the cylinder, i.e. the air and burned gas masses in this case. Unfortunately, these variables can not be measured directly on the engine. Yet, relied variables can be considered as the fresh air mass flow D air , the intake pressure P int , the intake temperature T int and the burned gas rate in the intake manifold F int . In a classical Diesel HCCI engine architecture, two actuators are available to control the air path : the EGR valve located on the EGR loop and the Variable Geometry Turbine (VGT) distributor. Since the air and EGR paths are strongly coupled, it is not possible to deal with the two actuators independently with two separated control loops :

• To vary the fresh air mass flow rate, the corresponding energy required by the turbine from the exhaust gas depends on the available mass flow, which is directly linked with the EGR flow. • To vary the EGR flow, the corresponding pressure deviation required between the exhaust and the intake manifolds is directly linked to the turbocharger operating conditions (supercharging pressure and exhaust counter-pressure).

The next subsections describe with more details the actuator influence on the air path and the intake condition impact on the combustion process.

Actuator influence on the air path

Influence of the EGR valve actuator Basically, the EGR valve regulates the mass flow rate of gas coming from the exhaust manifold to the intake manifold. At a fixed EGR valve position, the EGR flow is established according to the pressure deviation between intake and exhaust manifolds.

Opening the EGR valve increases the EGR flow but decreases the available energy for the turbine and may decrease both the intake pressure P int and the fresh air mass flow D air . The influence of the EGR valve position on the air path at fixed operating conditions is represented in Figure 2. A summary of the impact of the EGR valve on the gas aspirated in the cylinder is reported in Table 1.

Variable M asp,air M asp,bg M asp EGR valve ↑ ↓ ↑ ↓ VGT ↑, low EGR ↓ ↑ ↓ VGT ↑, high EGR ↑ ↓ *
Table 1. Summary of the impact of the actuators at fixed operating conditions. ↑ increase, ↓ decrease, * minor effect.

Influence of the turbocharger actuator Basically, the VGT regulates the supercharging pressure which is directly related to the fresh air mass flow D air and intake pressure P int . Under fixed operating conditions, closing the VGT increases the part of the energy available at the turbine housing intake that will go through the turbine wheel and, so, increase the turbocharger speed and then the compression ratio of the compressor. Therefore, it causes the increase of the intake manifold pressure. At the same time, closing the VGT increases the exhaust counter-pressure due to the turbine and so, the exhaust manifold pressure. Both intake and exhaust manifold pressures are then modified with the same trend because of the VGT modification. This potential modification of the pressure deviation between intake and exhaust manifolds may impact the EGR flow but with a variable trend. Because of this interaction with the EGR loop, the effect of the VGT on the steady state values of D air is not always monotonic. For the HCCI Diesel engine, this is especially difficulty to manage when the EGR valve is largely open. In this case, closing the VGT to increase the fresh air mass flow may lead to decrease D air . The influence of the VGT for two EGR valve positions at fixed operating conditions is presented in Figure 3. A summary of the impact of the VGT on the gas aspirated in the cylinder is reported in Table 1.

Intake condition impact on the combustion process

In the previous subsection, we described the impact of the actuators on the air path variables (intake pressure, intake temperature, . . . ). Now, we comment the impact on the combustion through the pressure curve. For that, we look at several combustion parameter:

• P cyl,max : the maximum cylinder pressure during the combustion. • CA 50 : crank Angle when 50% of the fuel has been burnt. • τ ai : auto-ignition delay.

• Noise: noise produced during the combustion (correlated to the maximum of pressure gradient). • IMEP: torque produced by the combustion.

According to the BGR level, to introduce burned gases in the combustion chamber modifies the combustion process in several ways :

• It plays the role of an inert gas that increases the cylinder gas mixture thermal inertia : this is the main effect at low BGR. • It plays the role of a third body that enhances the apparition of specific chemical reactions (catalytic effect) and slows down the reaction rates (diluting effect) : this is the main effect at high BGR.

The BGR has therefore a great impact on the combustion process. In an HCCI Diesel engine, it participates to reduce the temperature peak, to increase the global auto-ignition delay of the main combustion, to have the cold flame phenomenon, and finally to reduce the NO x production. Note that it is the total burned gas fraction in the cylinder that acts on the combustion. These burned gas are comprised of both residual gas from the previous cycle and exhaust gas cooled by the EGR cooler and recycled to the intake. Figure 4 presents the cylinder pressures obtained from an EGR valve variation at the engine testbed. A great impact can be noticed on the combustion process and on the engine response in terms of NO x emission and noise production as presented in the Figure 5. Unfortunately, this figure also shows that the BGR is not the only intake conditions that has varied during these tests and the intake pressure and temperature have also been modified. In fact, it is very difficult to obtain a single intake condition variation from experimentation. That is one of the reasons why the engine simulation support is very useful for control development [START_REF] Albrecht | Control design for hcci combustion engine based on virtual engine simulator: from control development to real-time calibration[END_REF]. In this case, a phenomenological combustion chamber model has been used to simulate the combustion process. After being validated on a wide range of operating conditions, the model has been used to perform single intake condition variations. More details about the phenomenological modelling approaches used in this study and the HCCI/conventional combustion model validation are presented in (Albrecht et al., 2006a). Based on this combustion model, single intake condition variation simulations have been per- formed for BGR, pressure intake and temperature intake around the reference operating set point of 5 bar IMEP and 1500 rpm engine speed.Increasing the BGR leads to increase the main combustion start angle by modifying the auto-ignition delay and enhancing the cold flame phenomenon. Thanks to simulation support, this BGR effect can be observed more accurately on the burned mass fraction (BMF) results which allows in particular to identify the cold flame phenomenon (linear part of the BMF curve). Moreover, the increase of the mixture thermal inertia coupled with the delayed combustion start after the top dead center angle decreases the maximum cylinder pressure.

In Figure 6, it can be observed that increasing the intake pressure leads to a higher pressure at the top dead center angle and then speeds up the ignition occurrence and increases the maximum cylinder pressure. The intake temperature variation has a lower effect on the cylinder pressure, influencing lightly the auto-ignition delay. This variable is not taken into account in this paper but can be introduced later since it can be useful in the context of the HCCI combustion high sensitivity. A summary of the impact of the air path variables is reported in Table 2.

Variable P cyl,max CA 50 τ AI Noise IMEP F int ↑ ↓ ↑ ↑ ↓ ↓ P int ↑ ↓ ↓ ↓ ↑ ↓ T int ↑ * ↓ ↓ ↑ *
Table 2. Summary of the impact of the air path elements. ↑ increase, ↓ decrease, * minor effect.

INTAKE MANIFOLD MODELLING

Flows of fresh air (measured by the Manifold Air Flow) and from the EGR come into the intake manifold to be aspirated into the cylinders.

In numerous references found in the literature (e.g. [START_REF] Tsai | Dynamic turbocharged Diesel engine model for control analysis and design[END_REF]Kao and Moskwa, 1995a)), mean value engine modelling approaches are considered. These use temporal and spatial averages of relevant temperatures, pressures and mass flow rates, and lead to a seven state reference model. The states are the intake and exhaust manifold pressure, temperature, and composition, and the turbocharger speed. Further, we propose a reduction down to 2 states. Motivations are given in the following subsection.

Modelling assumptions

First of all, as it is standard in modelling the intake manifolds in spark-ignited engines (e.g. [START_REF] Hendricks | Modelling of the intake manifold filling dynamics[END_REF]), we neglect the temperature fluctuations. Out of the seven usual state variables, two are eliminated. The already discussed common model reduction (see [START_REF] Van Nieuwstadt | Decentralized and multivariable designs for EGR-VGT control of Diesel engine[END_REF][START_REF] Stefanopoulou | Control of variable geometry turbocharged Diesel engines for reduced emissions[END_REF], [START_REF] Jung | Comparison of uncertainty parameterisations for H-infinity robust control of turbocharged Diesel engines[END_REF] and [START_REF] Janković | Constructive Lyapounov control design for turbocharged Diesel engines[END_REF]) consists of a three dimensional reference control model using the intake pressure, the exhaust pressure and the turbocharger speed as states. Composition dynamics are not taken into account because the corresponding two states (intake and exhaust composition) are difficult to measure and are only weakly observable from the remaining three states. In our case, we use the Air/Fuel Ratio sensor located downstream the turbine. It is an image of the composition in the exhaust manifold. This major difference with usually considered setups suggests us to substitute the exhaust pressure dynamics with the intake composition dynamics. Finally, we neglect the turbocharger dynamics. The reason for this simplification is that the turbocharger speed dynamics is very slow compared to the pressure and composition dynamics. Finally, the turbocharger speed is modelled as a static function of the intake pressure P int and the intake air flow D air . These hypothesis yield a reduction down to a two dimensional

State space model

Two balance equations provide the model we build our work on.

Total mass balance in the intake manifold Ideal gas law in the intake manifold leads to

P int V int = M int RT int
Assuming that variations of temperature are small, mass balance writes

Ṗint = RT int V int (D air + D egr -D asp ) (1)
Classically (see [START_REF] Heywood | Internal Combustion Engine Fundamentals[END_REF] for example), we assume that the aspirated flow can be computed as D asp = η vol (P int , N e ) Pint RTint V cyl Ne 120 where V cyl is the cylinder volume. η vol is the volumetric efficiency which is experimentally derived and, eventually, defined though a look-up table

η vol (P int , N e ).
Composition balance in the intake manifold The burned gas ratio F int is the fraction of burned gas in the intake manifold. It writes

F int 1 - M int,air M int
The composition of the EGR (F egr ) is the composition in the exhaust manifold (F exh ) delayed by the transport through the EGR pipe. We consider that this delay is negligible, i.e. F egr = F exh . Mixing dynamics is modelled as

Ḟint = RT int P int V int (D egr (F exh -F int ) -D air F int )
(2) Gathering ( 1) and (2) leads to the following ref-

erence system ẋ1 = α int (u 1 + u 2 -η vol (x 1 , N e )β int x 1 ) ẋ2 = α int x 1 (F exh u 2 -(u 1 + u 2 )x 2 ) (3)

INTAKE DYNAMICS ISSUES

As described in [START_REF] Kolmanovsky | Issues in modelling and control of intake flow in variable geometry turbocharged engines[END_REF]Kao and Moskwa, 1995b), the coupled air path dynamics features nonminimum phase dynamics on some operating points.

Step of VGT position

When applying a closing step in the VGT control signal, the exhaust manifold pressure rises. This results in a higher mass flow through the EGR and a higher intake manifold pressure. Closing the VGT also results in lower mass flows through both the turbine and the compressor. But, as a result of the increasing pressure in the exhaust manifold, these mass flows eventually increase and, after a while, reach a state where the mass flows are higher than before the step in the VGT position. This is a typical behavior for a nonminimum phase behavior. It results of zeros in the right half plane in the pole-zero map of the system.

Step in EGR position

When the EGR valve opens, first the flow through the EGR valve increases thereby increasing the intake manifold pressure. However, since a relatively smaller portion of the exhaust gas is supplied to the turbocharger, and since the exhaust manifold is emptied at a higher rate when the EGR valve opens, eventually the intake manifold pressure decreases. The latter effect is, however, delayed because of the turbocharger dynamics.

Non minimum phase behavior

Around a steady state point (x, ū) , the linearization of (3) leads to δ x = Aδx + Bδu, where δx

x -x, δu u -ū, A -α int   β int 0 0 ū1 + ū2 x2 1   and B α int   1 1 - x2 x1 F exh -x2 x1   . If we apply a step of input δu, we have δ x(0) = α int   δu 1 (0) + δu 2 (0) F exh δu 2 (0) -x2 (δu 1 (0) + δu 2 (0)) x1  
Then, asking more EGR and more pressure will lead to a high increase of δu 1 + δu 2 leading to an inverse response of the BGR.

EXPERIMENTAL RESULTS

Motion planning control strategy

Yet, using (appropriately valued) step inputs does not provide satisfactory transients. It has been impossible for us to get such a control strategy to work efficiently on our test bench. Numerical simulations through the AMESIM environment have provided us with some insights. In Figure 7, it appears that without model-based feedforward action, one is not able to take into account the apparent non-minimum phase effect of dynamics (3) (as seen in [START_REF] Kolmanovsky | Issues in modelling and control of intake flow in variable geometry turbocharged engines[END_REF] for example). There are too many oscillations and too large errors. These can not be damped before a new transient is to be achieved.

On the other hand, it also appears that interaction between air and EGR loops combined with the nonlinear nature of the system between highly varying setpoints makes the system difficult to handle using classical control design methods. We propose a motion planning control strategy which rely on the computation of transient trajectories for the airpath dynamics (3). This strategy is detailed in [START_REF] Chauvin | Estimation and Control of a Diesel HCCI engine. Estimation for time periodic systems[END_REF]. It comprises 4 sub procedures: setpoint computations through static maps, trajectory generation, model inversion, and saturation of open-loop control values. We explicit the main part, the model inversion, in the next subsection.

Model inversion

System (3) is fully actuated and invertible. Thus, an analytic expression of the input can be derived from the state variables and their first derivatives histories. In fact,

     u 1 + u 2 = η vol (x 1 , N e )β int x 1 + 1 α int ẋ1 -x 2 u 1 + (F exh -x 2 )u 2 = 1 α int ẋ2 x 1 (4)
This rewrites

u 1 = f 1 (x, ẋ) u 2 = f 2 (x, ẋ) (5)
                   f 1 (x, ẋ) = 1 F exh F exh -x 2 α int ẋ1 - 1 α int ẋ2 x 1 +(F exh -x 2 )η vol (x 1 , N e )β int x 1 f 2 (x, ẋ) = 1 F exh 1 α int x 2 ẋ1 + η vol (x 1 , N e )β int x 2 x 1 + 1 α int ẋ2 x 1 (6
) In these last expressions, F exh , α int , N e , and β int are all given by sensors measurements. The unique open-loop control law (u mp 1 , u mp 2 ) corresponding to any desired (x mp 1 , x mp 2 ) trajectory is

u mp 1 = f 1 (x mp 1 , ẋmp 1 , x mp 2 , ẋmp 2 ) u mp 2 = f 2 (x mp 1 , ẋmp 1 , x mp 2 , ẋmp 2 ) (7)

Experimental results

Figures 8 and 9 report experimental closed-loop results. The scenario is a varying torque demand at constant engine speed (1500 rpm) in both HCCI combustion mode and conventional combustion mode. We now detail these experiments.

From t = 102s to t = 112s here, we have an IMEP transient at 1500 rpm in HCCI combustion mode. The IMEP of the system starts at 2 bar and eventually reaches 5 bar. This transient aims higher intake pressure and BGR setpoints. Starting and ending operating points are both in HCCI combustion mode. Let us focus on Figure 8. By contrast with all decentralized controllers, we notice on that our controller takes into account the well known non minimum phase behavior of the system reported in [START_REF] Kolmanovsky | Issues in modelling and control of intake flow in variable geometry turbocharged engines[END_REF]. More precisely, one can check that the main contribution to this is due to the openloop controller (the closed loop control histories being very close to it). When the EGR valve opens, the flow increases leading to a pressure rise in the intake manifold. Meanwhile, the exhaust pipe acts as a discharge for the VGT. Its opening lowers the EGR supplied to the turbocharger yielding a significant drop of the exhaust manifold flow. The turbocharger slows down which eventually causes the decrease of the intake manifold pressure. This phenomenon is delayed and slowed down by the turbocharger inertia. Simple ramps and/or steps will fail to let the system reach the desired setpoint. With the proposed control strategy, the model takes into account this complex behavior. The motion planning efficiently drives the system to its setpoint.

From t = 112s to t = 122s here, we have a tip-in (high increase of torque demand) at 1500 rpm. Implicitly, it is desired to steer the system from a low load point with high EGR to a high load point with much less BGR. The proposed open loop control strategy successively closes the EGR valve and then closes the VGT with an overshoot. One can notice the resulting decrease in EGR flow and simultaneous increase of the fresh air flow. As expected from a motion planning control strategy, this does provide a soft landing for the state variables x 1 and x 2 onto their set points. During the transient, the open loop control laws are indeed saturated. This results in the temporary mismatch between the airflow and its set point. This effect is particularly noticeable on this very large pressure transient that we choose for sake of illustration.

Again, transients are smooth and present only small oscillations. It is instructive to note that, in this exact same setup, we failed to get a decentralized controller preventing both stall and noises.

The main reason for this seems the undesired overshoot of the BGR.

CONCLUSION

The presented work demonstrates the relevance of motion planning in the control of the -coupledairpath dynamics of turbocharged Diesel engines using Exhaust Gas Recirculation. For the HCCI combustion mode, very large rates of burned gas need to be considered and we have proven on a realistic test-bench cases that the proposed approach can handle such situations. Despite strong coupling, the airpath dynamics has nice properties that make it easy to steer through our control strategy. Its triangular form yields exponential convergence over a wide range of setpoints. It can also be shown, through a simple analysis, to satisfy operational constraints, provided transient are chosen sufficiently smooth.

The next step will be to adapt the strategy to other engine configurations, i.e. two turbochargers and/or two EGR pipes with various thermal conditions.

Figure 1 .

 1 Figure 1. Air path problem. The sensors used are colored in grey.

Figure 2 .

 2 Figure 2. Experimental variation of the EGR valve at fixed operating conditions (4 bar IMEP injection strategy, N e = 1500rpm, VGT = 20%). Effect on the air path.

Figure 3 .

 3 Figure 3. Experimental variation of the VGT actuator at fixed operating conditions (4 bar IMEP injection strategy, N e = 1500rpm, EGR valve = 0% and 50%). Effect on the air path.

Figure 4 .

 4 Figure 4. Experimental variation of the EGR valve at fixed operating conditions (5 bar IMEP injection strategy, N e = 1500rpm, VGT = 33%). Effect on the cylinder pressure.

Figure 5 .

 5 Figure 5. Experimental variation of the EGR valve at fixed operating conditions (5 bar IMEP injection strategy, N e = 1500rpm, VGT = 33%). Effect on the intake pressure, intake temperature, NO x and noise versus BGR.

Figure 6 .

 6 Figure 6. Numerical variation of the intake pressure at fixed in-cylinder conditions (5 bar IMEP injection strategy, Ne = 1500 rpm reference set point). Effect on the cylinder pressure.

Figure 7 .

 7 Figure 7. Tentative open loop transients with step inputs.

Figure 8 .

 8 Figure 8. Experimental results: IMEP transient from 2 to 5 bar, to 9 bar, to 5 bar, and then to 4 bar at 1500 rpm. Flow histories. Dashed : set point (u sp ), solid: closed-loop trajectory.          

Figure 9 .

 9 Figure 9. Experimental results: IMEP transient from 2 to 5 bar, to 9 bar, to 5 bar, and then to 4 bar at 1500 rpm. BGR histories. Dashed : set point, solid: closed-loop trajectory.

Acknowledgments The authors would like to thank Yann Creff for his support and Dominique Soleri for providing the experimental facilities.