Recent Developments in the Modelling and Control of Climate and Ventilation in Agricultural Buildings

Copyright IC IFAC Control Applications and Ergonomics in Agriculture, Athens, Greece, 1998

RECENT DEVELOPMENTS IN THE MODELLING AND CONTROL OF CLIMATE AND VENTILATION IN AGRICULTURAL BUILDINGS Peter Youngt, Laura Price t , Daniel Berckmans* and Karl Janssens*

t Centre for

Research on Environmental Systems and Statistics (CRES), Lancaster University, U.K.; E-mail:[email protected] *Laboratory for Agricultural Buildings Research, Katholieke Universiteit Leuven, Belgium

Abstract: This paper discusses the Data-Based Mechanistic (DBM) approach to modelling the micro-climate in agricultural buildings. Here, the imperfect mixing processes that dominate the system behaviour during forced ventilation are first modelled objectively, in purely data-based terms, by continuous-time transfer function relationships. In their equivalent differential equation form, however, these models can be interpreted in terms of the Active Mixing Volume (AMV) concept, developed previously at Lancaster in connection with pollution transport in rivers and soils and. latterly, in modelling the microclimate of horticultural glasshouses. This can be compared with the incomplete mixing and control volume concepts that have been investigated previously at Leuven. The data used in the initial stages of the research project. as described in the paper, have been obtained from a series of planned ventilation experiments carried out in a large instrumented chamber at Leuven. The overall objectives of this collaborative study are two-fold: first, to gain a better understanding of the heat transfer and micro-climate dynamics in the chamber; and second, to develop models that can form the basis for the design of optimal ProportionalIntegral-Plus (PIP-LQ) climate control systems for livestock buildings of a kind used previously for controlling the micro-climate in horticultural glasshouses. :Copyright © 1998 IFAC Keywords: Data-based modelling; imperfect mixing; forced ventilation; micro-climate; heat and mass transfer; active mixing volume; control volume; optimal control.

1. INTRODUCTION

Within the agricultural engineering literature, the Control Volume (CV) concept of Barber and Ogilvie (1982) has received considerable attention in recent years. For example, the CV approach of Berckmans et al (1992) models the dynamic response of the imperfectly mixed 3D airspace to non-linear variations of the ventilation rate and heat supply using time series methods. Daskalov (1997) also exploits time series analysis, using discrete-time 'black-box' transfer function models to characterise the measured temperature and humidity variations in a naturally ventilated pig building.

It is now widely recognised that the ventilated airspace in agricultural buildings is imperfectly mixed: see Barber and Ogilvie (1982) and the references therein. Such imperfect mixing leads to gradients in variables such as temperature. humidity, gas, dust and air velocity, all of which affect the micro-environment around the animal or plant (e.g. Berckmans and De Moor, 1993). Barber and Ogilvie (1982) suggest that multiple flow regions, stagnant zones and the short-circuiting of air to the exhaust outlet are the major causes of incomplete mixing. It is clear, therefore, that the development of models for advanced control system design must account adequately for these imperfect mixing processes.

In the present paper, the Data-Based Mechanistic (DB M) approach to modelling (e.g. Young and Lees. 1994, Young et al, 1996; and the references therein) is applied to the problem of modelling imperfect mixing in the forced ventilation of buildings, based

..,

inputs, ventilation V (l20-300m3/h) and heating element Q (0-400 Watt) determine the dominant airflow pattern within the chamber, as indicated in Figure 2. An envelope chamber or 'buffer zone' is constructed around the test-room in order to minimise the disturbance of the airflow by heat conduction from the laboratory. A series of aluminium conductor heat sinks and steam generation from a water reservoir provide the internal heat and moisture production to simulate animal occupants. To gain information about the distribution of mass and energy in a quantitative manner, 36 temperature sensors and 24 humidity sensors are positioned in a 3D array within the chamber.

on previous research concerned with the modelling and control of environmental systems. In DBM models, the model structure is first identified using objective methods of time series analysis based on a given, general class oftime series model (here linear, continuous-time transfer functions or the equivalent ordinary differential equations). But the resulting model is only considered fully acceptable if, in addition to explaining the data well , it also provides a description that has relevance to the physical reality of the system under study. In the present paper, DBM modelling is applied to data obtained from ventilation experiments carried out on a large instrumented chamber designed to represent a scale model of a livestock building or glasshouse. The model is in the form of a continuoustime transfer function , the differential equation form of which can be interpreted in terms of both to the classical theory of heat transfer and the Active Mixing Volume (AMY) models of imperfect mixing, developed previously within the context of solute transport in rivers and soils and, latterly, in modelling the micro-climate of horticultural glasshouses (e.g. Young and Lees, 1993). One advantage of the DBM model is its simplicity and ability to characterise the dominant modal behaviour of a dynamic system. This makes such a model an ideal basis for model-based control system design. In the present study, it is proposed that the model will be used in the design of an advanced Proportional-Integral-Plus (PIP) control system of a kind used previously for the multi variable control of the micro-climate in a glasshouse (e.g. Young et aI, 1994). Recent developments of the PIP design methods will, however, allow this ventilation control system to exploit the advantages of delta operator implementation optimised in terms of Linear Quadratic (PIP-LQ) and multi-objective cost functions (e.g. Young et aI, 1998; Chotai et ai, 1998).

Fig.l Experimental forced ventilation chamber. The main kinds of flow pattern are shown in Fig. 2. At high ventilation rates above 250-300m3/h, the cooler, incoming air maintains high momentum and so remains at inlet level, moving rapidly across the chamber before mixing, following collision with the end wall. It then descends and moves in a clockwise direction (left hand plot). Conversely, at low ventilation rates (80m 3/h-220m3/h) thermal forces cause incoming jets to fall and, therefore, drastically modifies the airflow pattern established at high ventilation rates (middle plot). At intermediate ventilation rates (circa 240 m3/h) the airflow (right hand plot) tends to go directly from inlet to outlet but may be considered as unstable (De Moor, 1996).

2. TEST INSTALLATION AT LEUVEN. The research described in this paper is based on the analysis of data from planned experiments in a large instrumented chamber in the Laboratory for Agricultural Buildings Research at the Katholieke Universiteit Leuven (for details see De Moor, 1996, Berckmans et al. . 1992). This chamber, which has been designed to represent a scale model of a livestock building or glasshouse and so facilitate experimental research on forced ventilation and heating in agricultural buildings, takes on board the experience of other research in this area (e.g. Leonard & McQuitty, 1985). As shown in Fig. 1, the testroom is constructed of Plexiglas, with length=3m, width=1.5m, height=2m, and is designed to create stable airflow patterns by changing the ratio between buoyancy and inertial forces . The two variable

lnlcrmedlatc Flow -240 m3Ih

Fig.2 Main airflow patterns in the chamber During the course of the initial research reported in this paper, experiments have been carried out with step increases in ventilation rate over the range 120300 m3/h, while maintaining constant input temperature. The experimental conditions were

4

chosen so that a range of airflow patterns, such as those in Fig. 2, could be simulated, with repeated runs at each rate, so ensuring the accuracy and consistency of the model parameter estimates. In these experiments, an initial working point was selected, with the initial ventilation rates set at 80m3/h for 15 minutes in order to establish steady airflow conditions (ambient temperature 24°C; internal moisture content, 0.45l/h; incoming fresh air initially at 11°C) before the required step ventilation rate change was introduced.

perturbation is currently unavailable on the test chamber system, we have considered the alternative approach using step changes in the ventilation rate, a typical example of which is shown in Fig. 3. The temperature response of the sensor closest to the inlet, for a given ventilation change, is then used as input T; to the system. The continuous-time SRIV algorithm (Young and Jakeman, 1980; Young et aI, 1992; Young, 1997; Price, 1998) is used to identify the linear TF (ordinary differential equation) model between T; and T , with the Coefficient of Determination R; and the YIC identification criterion employed as model structure identification criteria (see e.g. Young, 1989). The results of this exercise, as presented in Table l(a), show that a second order model yields an excellent explanation of the data in all the experiments, with high near to unity and large negative YIC values, reflecting the well defined parameter estimates with small relative standard errors on the estimated model parameters (shown in parentheses).

For each experiment, the time-series of input temperature, ventilation rate, and temperature/ humidity for each sensor were recorded every second. A typical example of these experimental data are given in Fig. 3, which shows the outlet temperature response (middle graph) during an experiment with an inlet step ventilation increase (upper graph) from 80 m3/h to 300m3/h; initial incoming air temperature 11.5 °C; initial installation temperature 24 °C; aluminium heater 300 watt (total); and inlet heat (Q) =0 watt. The temperature in the buffer zone between the main chamber and outer shell during the ventilation change is shown in the lower graph of Fig. 3.

R;

Table l(a) Ventilation Data File

Ventilation Rate

kjl91lb

0

SO

lOO

ISO 200 2S0 300 SampHna Internl (Ien seconds)

300

R2T

0.992

kjl507b

280

0.989

kjl510a

260

0.9907

Second Order [2,2.0) Model Parameter Estimates A(s)

B(s)

2.962 (0.175)

1.9598(0.112)

0.1113(0.012)

0.0890(0.009)

2.2728(0.146)

1.3328(0.082)

0.0987(0.011)

0.0722(0.008)

2.2597(0.122)

1.4815.(0.077)

0.0749(0.010)

0.0579(0.007)

In the case of the first experiment in Table I (kjI911b), namely the response to a step increase of the ventilation rate from 80-300 m3/h, the estimated model for the changes in temperature !J.T and I:!.Tj from the initial steady levels, takes the form,

i"'~ ;!.

Rate (m31h)

)SO

I:!.T(t) = Fig.3 Experimental results from the test chamber.

1.9598s+0.0890 !J.Tj(t) s 2 + 2.9620s + 0.1113

(1)

Fig. 4 compares the output of this model ' with the measured change in the outlet temperature and the associated model error (residual) is plotted in the lower graph. This unexplained residual series has a zero mean value and very low variance (0.021 Compared with 2.619 for the output !J.T series). There is a little serial correlation in this residual series but the variance is so low that it can be ignored in the present context.

3. DATA-BASED IDENTIFICATION AND ESTIMATION

In order to identify and model the temperature dynamics in the test chamber, it would be preferable to perform experiments in which the inlet temperature T; is changed sharply in a 'sufficiently exciting' manner (e.g. Young, 1984). In other words, the input should be chosen to induce changes in the outlet temperature T that are sufficiently informative to allow for the unambiguous estimation of the dominant dynamic characteristics. However, since the mechanism for generating such an input

5

OUllel Temperature Ruponle and Reliduah

4. MECHANISTIC INTERPRETATION: THE ACTIVE MIXING VOLUME (AMV) MODEL

.10

100

lOO

300

400

SOO

600

700

.~~ o

100

lOO

300 400 SOO Tim e (tenl or second.)

600

700

Having objectively identified and estimated a model from the experimental data, the next stage in DBM modelling is to interpret the model in physically meaningful terms. In the present context, the obvious approach is to invoke the classical theory of heat transfer and formulate the differential equations of dynamic heat transfer, bearing in mind the need to arrive at a second order, lumped, differential equation of the type identified in the first data-based phase of the modelling process, as described above.

100

800

FigA Comparison of the model estimated temperature

and the measured temperature at the chamber outlet for experiment kj 1911 b. The TF in (1 ) can be decomposed into a parallel or feedback connection of first order processes but, as we shall see in the next section, the feedback form shown in Fig. 5 has the most obvious physical interpretation. The estimates of the parameters Bo , Aa , BI and Al in Fig.5 are given under kj1911b in Table I(b), where 'FWP' denotes 'Forward Path' and FBP denotes 'Feedback Path' . The associated time constants (residence times) Tcl and Tc2 ' respectively, are given in Table I(c). The estimated parameters for the feedback decompositions in the other two experiments are given under kj 1507b and kj1510a in the same Tables.

.

+

4. J Main Chamber Equations

Consider the complete chamber-buffer zone system, shown diagrammatically in Fig.6,

T...,

T...

-t--

T

Fig.6. Schematic of the test installation, main chamber and surrounding insulating chamber (buffer zone) and key physical parameters.

T

~

vol,

s+Ao

'!l-

B)

Assume now that the imperfect mixing processes can be approximated by complete mixing within an AMV, of volume vol l (m 3 ), which is less than the volume, vol (m 3 ) , of the whole chamber. Then, standard heat transfer theory, applied between the input and output of the chamber, suggests a dynamic heat balance differential equation of the form,

.....

s+A)

Fig.5 Feedback decomposition of the TF model (l)

Data File

Table l~b! FWP Transfer Function FBP Transfer Function

Bo

Aa

BI

Al

kjl911b

1.9598

2.9151

-0.0107

0.0458

kj1507b

1.3328 1.4815

2.2186 2.2207

-0.0161

0.0541 0.0391

kjl510a

-0.008

(2)

where T is the temperature (0 C) measured at the outlet port but assumed to be representative of the temperature in the AMV; 1'; is the temperature (0 C ) measured at the chamber inlet; V is the ventilation rate (m 3s -I ); 11 is the air density of the incoming air (kgm- J ) ; CPI is the specific heat capacity of the incoming air (J I kg UC); 12 is the air density of the main chamber air (kgmcP2 is the specific heat capacity of the main chamber air (J I kgUC) ; k) is the thermal conduction coefficient through the first wall (Wm- 2 °C- I ) ; Hv is the constant heat input from the animal occupant's simulation; sfl is the

Table l(e) Data File

kj1911b

FB Decomposition

Tcl

Tc2

minutes 0.343

minutes 22.02

Main Chamber Parameters SSG

P

AMV

(m3/sec.)

(m3)

0.8

0.06

2.94

kjl507b

0.4507

18.47

0.73

0.077

4.19

kj1510a

0.4503

25 .58

0.77

0.065

3.70

J

);

6

surface area of the AMV for imperfect mixing (m2); and 1 buff is the temperature in the outer buffer zone CC)

(7)

If it is assumed that YI ~ Y2 and CPI ~ CP2 then, dividing equation (2) by vollYlcPI' rearranging and considering only temperature deviations flT, flTi and D.1buff about the initial steady state, we obtain,

4.3 Continuous-Time Transfer Functions

The differential equations (4) and (7) may be expressed in TF form by introduction of the time derivative operator s = dldt (effectively the Laplace transform for zero initial conditions)

(3)

Main chamber: flT = since

Hv is constant. This can be written as,

1 (s+al)

(/31 flTi + K IflTbuff )

Buffer zone: d(flT)

- - = /31 flTi + K IflTbuff dt

where, /31 =

-

al flT

(4)

Combining these two TF's, we obtain the following second order TF model for the complete chamberbuffer zone system:

_V_ , al = (_V_ + _k..:..1s.:;.if1:..1_) voll

vol l

volYlc pI

(8)

and where, bo =/31 ;bl =/3I(K 2 +K 3 );al =(K2 +K3 +al );

4.2 Buffer Zone Equations

a2 = (K 2 + K 3 )al - KI K 3

The following, additional set of dynamic energy balance equations may be constructed for the buffer zone or outer chamber,

Clearly, the TF model (8) is in exactly the same structural form as the estimated TF (1) and so, in DBM modelling terms, it can be considered as one particular physical interpretation of the data-based model that has scientific credibility.

4.4 Feedback Decomposition where vol2 is the volume of the AMV associated with the buffer zone (m3); k2 is the thermal conduction coefficient through the buffer zone (outer chamber) wall (Wm- 2 ·C-I ); kl is the thermal conduction coefficient through the main chamber wall (Wm -2. C- I ); sh is the surface area of the buffer zone AMV for imperfect mixing (m2); and T lab is the temperature in the outside Laboratory (·C).

The parameters Bo, Ao, BI and AI in the feedback decomposition shown in Fig.5, can now be calculated as follows:

Rearranging as in equation (2) and considering deviations from the initial steady state, this becomes, The two first-order TF's have very different time constants: TcI which reflects the fast response within the main chamber, i.e.,

which can be written as,

7

and Tc2 which is associated with the much slower temperature effect due to feedback conduction from the buffer zone, i.e.,

These contour plots illustrate rather well how, in this particular situation of high ventilation flow rate (280 m31hr.) and low in-flow temperature (l1°C), some of the in-flowing air, which enters (top centre) at the left of the chamber, flows rapidly, with very low residence time, along the top of the chamber and then descends to the exit (bottom centre) at the right of the chamber. Other air, meanwhile, circulates much more slowly below this top layer, some of it remaining in the chamber for a considerable time, particularly towards lower left hand corner at the rear of the chamber. Quite different behaviour occurs at low ventilation rates, as shown in Fig. 7(b). Here, with a ventilation flow rate of 180 m31hr. and low in-flow temperature of 11°C, the rapid time constants and low temperatures at the base of the chamber show how the cool air tends to sink to the bottom and then moves across the chamber to the outlet at the lower right centre, leaving more stagnant air above this.

1

Tc2

=-:4 ]

Finally, from the above definition of TeI , a meaningful estimate of the AMV, vol], and Dispersive Fraction, DF (the ratio of vol] to the total volume vol: Wallis et ai, 1989) in the main chamber can be obtained by reference to the estimate of TeI provided the 'flow rate' parameter p = k] sf] / r] cp] can be estimated in some manner. This is possible by reference to the steady state equilibrium conditions at the end of the experiment: the associated steady state temperatures at the inlet, outlet and insulating chamber, together with the ventilation rate V , can be introduced into the equilibrium solution of equation (2), which can then be solved for p. The resulting values of p and vol] for the 3 experiments are given in Table l(c).

funp.ane

4.5 The DBM Model and Classical Heat Transfer Theory It is clear from the relationships between the parameters in the TF model (8) and the equivalent parameters in the estimated TF model (1) that the classical heat transfer coefficients are not uniquely 'identifiable' from the experimental data. On the other hand, the heat transfer dynamics of the chamber are completely specified by the DBM parameters, which can be interpreted as specific combinations of these classical parameters. Consequently, this DBM model represents an alternative approach to modelling the system in physically meaningful, albeit not the classical, terms. And the model, in this identifiable form, is entirely adequate for both understanding the heat transfer dynamics of the chamber and designing a ventilation control system. It provides, in other words, an alternative way of presenting heat transfer theory within the context on imperfectly mixed flow processes, such as those encountered in forced ventilation systems.

ro

100

120

140

100

1ro :;re

140

100

1ro :;re

rearp.ane 51.7

ro

100

120

(a) 12OF-""4----r.---r-.,....-"'....I±l:::::>'""'-~.2..L...__._ .S 100

80

.S

20

5. AMV MODEL-INFERRED SPATIOTEMPORAL DYNAMICS OF THE CHAMBER By modelling the responses of temperature and humidity at each of the sensor locations in the experimental chamber in a similar manner to that described in previous sections, it is possible to infer the nature of the airflow patterns within the chamber. For example, the 36 transfer function models identified for a high ventilation rate experiment have time constants ranging from 20-100 seconds and Fig. 7(a) shows the time constant contours at both the front (upper plot) and rear (lower plot) of the chamber.

40

60

SO

140

160

1~0

200

160

ISO

200

OS.3 20

40

60

SO

100

120

140

(b)

Fig. 7 Time constant (in seconds) contours for experiments with (a) a high ventilation rate of 300m31h.; and (b) a low ventilation rate of l80m31h

8

The characteristics of flow in the chamber under these flow conditions are confinned by the flow visualisation techniques. It is clear, therefore, that the statistical AMV model underlying these plots is characterising the flow behaviour quite wel1 and the research programme will seek to explore this approach to spatio-temporal modelling, and other possibilities, in more detail. Initial results obtained from ful1 multi variable time series model1ing, for example, have been promising. However, this aspect of the research is in its early stages and the best methodological approach is still unclear.

available from the system, avoiding the need for complex techniques such as state reconstruction and loop transfer recovery. This considerably enhances the robustness of the resultant control system to uncertainties in the model parameters and disturbance inputs. 7. CONCLUSIONS This paper has reported recent developments in the model1ing and control of the forced ventilation in agricultural buildings. It has concentrated on the Data-Based Mechanistic (DB M) approach to model1ing applied to data obtained from initial planned experiments in a large instrumented chamber. Here, in contrast to the nonnal hypotheticodeductive procedures that are most popular in this area of research, a minimally parameterised transfer function model is first identified and estimated from the experimental data without any prior assumptions about the physical nature of the system. Having objectively identified the dominant modes of dynamic behaviour in this manner, however, the model is then interpreted in physical1y meaningful terms that relate both to the classical theory of heat transfer and the Active Mixing Volume (AMV) models of imperfect mixing, developed previously within the context of natural environmental systems. This model not only explains the data very wel1, with the minimum number of identifiable parameters, but it is also in a fonn that can provide the basis for the design of advanced Proportional-Integral-Plus (PIP) control systems optimised in tenns of Linear Quadratic (PIPLQ) and multi-objective cost functions.

6. MULTIVARIABLE CONTROL So far, the project has been concerned primarily with model1ing. However, since the experimental chamber at Leuven has been constructed with research on automatic ventilation control in mind, one major objective of these modelling studies is the control of the forced ventilation system. The proposed study will seek to design and implement advanced multi variable (i.e. multi-input, multi-output) Proportional-Integral-Plus (PIP) control algorithms based on the Non-Minimum State Space (NMSS) methods of control system design developed at Lancaster. Such PIP control systems have been used successful1y in many real agricultural and other applications, including previous research on the control of a glasshouse micro-climate (e.g. Young et al, 1994) as wel1 as open top and free air carbon enrichment (FACE) systems (e.g. Norris et al, 1996). It is planned that the PIP control system in the present project will be based on the latest adaptive PIPLinear Quadratic (PIP-LQ) optimal approach to PIP control system design using delta operator methods (Young et ai, 1992; Young et ai, 1998; Chotai et ai, 1998). These designs take maximum advantage of modern, multi variable control theory yet remain straightforward to implement in practical terms.

The present paper has reported only the initial results obtained in a col1aborative study that wil1 continue over the next three years. This wil1 include: a ful1 programme of planned experiments aimed at the comprehensive evaluation of the mass and energy flow dynamics of the test chamber over a complete range of ventilation control inputs; the use of these experimental data in the development of input-output and spatio-temporal DBM models that describe the dynamics in a fonn required for PIP-LQ control system design; and, final1y the implementation and evaluation of this control system.

There are numerous advantages to this more advanced NMSS approach to control system design. First, the vagaries of manual tuning used in more conventional two and three tenn (PIIPID) control1ers are replaced by model-based computation of the control gains. Second, the control system structure always exploits ful1y the power of state variable feedback methods, thus allowing for the implementation of optimal control strategies, such as the PIP-LQ control1er. Third, it has been shown (Taylor et aI., 1994) that NMSS design incorporates inherent predictive control action and so anticipates the need for changes in control actions. Fourth, using multi-objective optimisation methods (see e.g. Chotai et ai, 1998), it should be possible to achieve optimal regulation of the ventilation system taking into account other relevant factors. Final1y, NMSS design makes efficient use of al1 the useful measurements

The objectives of the control system design wil1 be to regulate the forced ventilation system so that it ensures the comfort and welfare of the animals, whilst minimising the costs to the farmer. To this end, the physical nature of the wel1 mixed region in the chamber needs to be control1ed by continual adjustment of the two control inputs (in-flow air temperature and flow rate). In the first instance, this wil1 be achieved in an aggregate manner by modelling the overal1 input-output AMV dynamics, as discussed in this paper, and designing an adaptive

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Norris, T.S., B. J. Bailey, M. Lees and P. C. Young (1996). Design of a controlled ventilation opentop chamber for climate change research, Journal Agric. Eng. Res., 64, 279-288. Price, L. (1998). Ph.D Thesis , Systems and Control Group, CRES, Institute of Environmental and Natural Sciences, Lancaster University. Taylor, C .J., P. C. Young and A. Chotai (1994). On the relationship between GPC and PIP control. In: Advances in Model-Based Predictive Control (D.W. Clarke, Bd.), pp. 53-68. Oxford University Press, Oxford. Wallis, S. G. , P. C. Young and K. J. Beven (1989) Experimental investigation of the aggregated dead zone model for longitudinal solute transport in stream channels, Proc. Inst. of Civil Engrs, Part 2, 87, 1-22. Young, P. C. (1984). Recursive Estimation and Time Series Analysis. Springer-Verlag: Berlin. Young, P.C. (1989). Recursive estimation, forecasting and adaptive control. In: Control and Dynamic Systems: Advances in Theory and Applications (C.T. Leondes, Ed.), Vol. 30, Academic Press: San Diego, 119-166 Young, P.e. and M. J. Lees (1993). The Active Mixing Volume (AMV): a new concept in modelling environmental systems, Chapter 1 in: V. Barnett and K.F. Turkman (eds.), Statistics for the Environment. J. Wiley: Chichester, 3-44. Young, P. C. and A. J. Jakeman (1980). Refined instrumental variable methods of recursive timeseries analysis: part Ill, extensions, Int. Jnl. of Control, 31, 741-764. Young, P. e., M. J. Lees, A. Chotai, W. Tych and Z. Chalabi (1994). Modelling and PIP control of a glasshouse microclimate, Control Eng. Practice, 2,591 -604. Young, P.C., S. Parkinson. and M. J. Lees (1996). Simplicity out of complexity: Occam' s Razor revisited, Journal of Applied Statistics , 23, 165210. Young, P. e., A. Chotai, P. McKenna and W. Tych (1998). PIP design for 0 operator systems: Part I , SISO systems, Int. Jnl. Control,70, 123-147. Young, P. C. (1997) Identification, estimation and control of continuous-time and delta operator systems. In: Identification in Engineering Systems (M. I. Friswell and J. E. Mottershead. Eds.), Univ. of Wales: Swansea, 1-17. Young, P. C., A. Chotai and W . Tych (1992). Identification, estimation and control of continuous-time systems described by delta operator models. In: Identification of ContinuousTime Systems, (N.K. Sinha and G.P. Rao. Eds.) Kluwer: Dordrecht , 363-418 .

PIP controller, using a fuzzy scheduling system, so that the temperature, humidity and size of the well mixed zone are all maintained at desirable levels or within desirable bounds. If a suitable spatio-temporal model can be developed, however, it may be possible to control the size and local climate of the well ventilated zone, and attempt to move it around the chamber to desirable locations. Initial experimental work at Leuven using flow visualisation techniques has shown the initial feasibility of such an advanced control system. Finally, since the commercial application of these techniques will have obvious cost implications, it is hoped to introduce economic factors and animal welfare parameters into the design via the multiobjective approach to the optimisation of the PIP control gains mentioned above.

ACKNOWLEDGEMENTS The authors are grateful to the U.K Biotechnology and Biological Sciences Research Council for support under grant no . 891MMI09731 ; and to the U.K Natural Environmental Research Council for a Ph.D. research studentship under grant no. GT4/951129. The research at Leuven is supported by the Belgian National Fundfor Scientific Research. REFERENCES Barber E. M. and J. R. Ogilvie (1984). Incomplete mixing in ventilated spaces. part l.Theoretical Considerations, Canadian Agric. Eng., 24, 25-29; part 2. Scale Model Study' , ibid, 26, 189-196. Berckmans, D., M. De Moor and B. De Moor. (1992). Test installation to develop a new model concept to model and control the energy and mass transfer in a three dimensional imperfectly mixed space, Proceedings of Roomvent '92: Air Distribution in rooms, Aalborg, Denmark. Berckmans, D. and M. De Moor (1993). Analysis of the control of livestock environment by mathematical identification on measured data, International Winter Meeting A.S.A.E. , Chicago, Illinois, USA. Chotai, A., P. C. Young, P. McKenna and W . Tych, (1998). PIP design for 0 operator systems: Part 2, MIMO systems, Int. Jnl. Control, 70 , 149-168. Daskalov, P. I. (1997). Prediction of temperature and humidity in a naturally ventilated pig building, Journal Agric. Eng. Res., 68, 329-339. De Moor, M. (1996). Modelling and control of energy and mass transfer in imperfectly mixed fluids, PhD Thesis, Faculeit Landbouwkundige en Toegepaste, Katholieke Universiteit, Leuven. Leonard, J. J. and J. B. McQuitty (1985). Criteria for the control of cold ventilation air jets, A.S.A.E. 85, 4014-19.

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