MODELLING AND CONTROL OF A GLASSHOUSE MICRO-CLIMATE

Transcription

1 MODELLING AND CONTROL OF A GLASSHOUSE MICRO-CLIMATE Matthew Lees Centre for Research on Environmental Systems and Statistics Lancaster University, Lancaster LA1 4YQ Introduction Most climate control systems in glasshouses are based on single variable regulation using manually tuned two and three term (PI and PID) controllers. Current research on carbon dioxide (CO 2 ) enrichment and optimal growth strategies suggests that such controllers no longer provide sufficiently tight control over the climate variables and there is a need for superior multivariable control using modern model-based design methods. CRES has developed powerful new approaches to multivariable modelling and control and has used these for the successful implementation of what is believed to be the first multivariable control system for a glasshouse micro-climate. A commercially sized Venlo glasshouse at Silsoe Research Institute (SRI), shown in Figure 1, has been used to evaluate the proposed modelling and control methodologies. Figure 1: Internal view of the Venlo greenhouse with tomato crop Sensor box CO 2 sampling tube Development of an iconographic simulation model of glasshouse micro-climate In the initial phases of the project, the non-linear dynamic glasshouse climate model, originally developed at the SRI, was re-written in a form suitable for the multivariable control research. In particular, various additional sub-systems had to be introduced into the model, including CO 2 mass balance equations, involving both photosynthesis and respiration effects,

2 as well as models for the various actuators used in the control of temperature, humidity and CO 2. This new version of the model, shown in Figure 2, was developed at CRES using Simulink, a novel iconographic computer simulation program. This is the first time such an advanced computer simulation program has been applied to glasshouse systems (or, indeed, to any other horticultural and agricultural systems) and it yields a number of distinct advantages in research and development terms. These include: the pictorial representation of the model, which enhances its visualisation and practical utility; the ability to both change model parameters interactively during simulation runs and to easily change or expand the model as additional research results are obtained; and direct access to the associated Matlab program, where advanced techniques developed in CRES for data analysis, model identification, optimisation, model order reduction and linearisation are available. Figure 2: Simulink representation of the greenhouse climate model u1 u2 CO2 u3 u4 Humidity u5 u7 Thermal Rad Temperature u8 Weather Inputs u9 Thermal Cond x1 x2 Control Inputs Stomatal Res x3 x4 x1 x2 x3 x4 x5 x5 x6 x7 Mux Demux x6 x7 En Ex x8 x8 x9 x10 x11 Derivatives x9 x10 x11 Latent Heat En Ex CO2 model Extensive practical evaluation of the model using continuously recorded glasshouse climate and external meteorological data has established that it satisfactorily simulates the system behaviour over extended periods of time. For example, over a typical eleven day interval, the simulated glasshouse air temperature had a root mean squared error of just 1.69 ºC and the major aspects of the dynamic behaviour over this period were reproduced satisfactorily. These results confirmed the utility of the simulation model as a suitable surrogate for the real system

3 in the subsequent control system design and optimisation studies, prior to the further practical development of the designs on the Venlo glasshouse at SRI. They also opened up the possibility of many other uses for the simulation model, such as greenhouse design and operator training. For example, a variant of the Simulink model developed in the project is currently being used by SRI to help design a rather novel coastal glasshouse system (New Scientist, 29/05/1993). Novel methods for linearisation and reduction of the nonlinear simulation models While it is essential for the initial evaluation and development of control systems, the large nonlinear Simulink model is not in a suitable form for analytical control system design. The control model has to be a much smaller, linearised representation of the dominant dynamic modes that characterise the behaviour of the nonlinear model about its major operating points. The conventional method of linearising models described by nonlinear differential equations, is based on the calculation of the first term of the Taylor series for small perturbations in the states and inputs around a steady state operating point. This linearisation stage is followed by model reduction; a procedure which requires the subjective selection of states to be removed. CRES has developed an alternative and more flexible, one step, statistical approach which has been utilised in all the subsequent design studies. In this new approach (Young and Lees, 1995), the Simulink model is perturbed around an operating point (e.g. an equilibrium state) and statistical identification and estimation procedures are then applied to the resulting input-output data to yield a minimal order, transfer function matrix (TFM) representation of the dominant mode dynamics. This combination of model linearisation and reduction into a single operation is a major advance on existing analytical linearisation techniques based on Taylor series approximation and it represents a significant achievement of this research project which will prove useful in many other applications. For instance it has been used recently to show how a 26 th order, nonlinear, global carbon cycle model used in the Inter-governmental Panel on Climatic Change (IPCC) studies can be approximated almost perfectly for quite large perturbations by a 4 th order linear model (see Young, in this Workshop). In the glasshouse example, the reduced order TFM model has three control inputs (boiler valve position; CO 2 injection rate; and water spray injection rate) and three outputs (air temperature; CO 2 concentration; and relative humidity). This TFM model, which is characterised by 4 first order, discrete-time transfer functions and 5 simple gain elements, approximates the high order nonlinear model dynamics very well over a wide range of environmental conditions (e.g. different set points over the whole envelope of operating conditions) and is an ideal form for initial multivariable control system design. Planned experiments on a Venlo glasshouse at Silsoe Although the reduced order control model allows for initial control system studies, modern model-based predictive control system design methods require the control model to be validated fully on the basis of planned experimental data obtained from the real system. To this end, two experimental periods in the Winter of 1992 and Spring of 1993 have been used to carry out numerous open-loop experiments on the Venlo glasshouse at SRI. As expected, the identification and estimation results confirm the earlier simulation-based studies but show that the control model parameters change as a function of meteorological conditions: for example, the CO 2 model gain is found to be related to the long term changes in solar

4 radiation. These results have confirmed the need for a control system design that is robust to model uncertainty, with adaptive gain adjustment over the longer term. The meteorological data collected from the experiments also provided realistic disturbance inputs to the simulation model during final control system testing, prior to its implementation on the real system. For example, relationships between the measured outside air temperature and the control variables have enabled extremely effective feed forward control elements to be incorporated into the multivariable control system design. Multivariable control system design Various important advances in TDC design theory have been made within CRES during the project (see Chotai, in this Workshop, for details). Of particular relevance to this project, multivariable extensions of the single input, single-output design procedures have been developed (Young et al, 1994): here, the TFM control model is converted to a left matrix fraction description which then facilitates the formulation of the multivariable, non-minimal state space (NMSS) representation required for Proportional Integral Plus (PIP) control system design. This PIP controller can be based on either state variable feedback pole assignment or optimal Linear Quadratic Gaussian control. In both cases, however, the nonminimal state depends only on sampled input and output measurements, so that the power of state feedback can be exploited fully without the need for the complexity of state estimation and loop transfer recovery (Bitmead et al, 1990). The resultant PIP control law is also inherently in an incremental form which avoids integral windup, a major problem in conventional PI and PID controllers. Originally, it was intended to apply multivariable dynamic decoupling control to the glasshouse micro-climate. In this very advanced type of design, one controlled variable (e.g. temperature) can be changed without any effect on other associated variables (e.g. humidity). Two different analytical approaches to the multivariable decoupling problem have been developed during the project and applied successfully to the multivariable glasshouse control problem. However, the research has also established that such high performance decoupling design is not necessarily desirable for the ordinary grower, since the extra control input energy required would not be cost effective. The steady state decoupling provided by the lower power, standard, multivariable PIP controller ensures excellent set-point tracking and the associated dynamic coupling effects are acceptably small. However, other agricultural and industrial controllers that require tighter control (e.g. in robotic applications; scientific research etc.) will benefit from the more advanced decoupling design techniques developed in the project, which represent a considerable advance in multivariable control systems design theory. Another important part of the control systems research has been concerned with investigating the importance of the control system structure on regulatory performance and has led to the development of a new forward path structure which is particular well suited for agricultural applications. This structure minimises the effect of large disturbances (e.g. weather conditions) on the control input, resulting in a controller which has much smoother actuator movements. This latter feature is particularly important where the control actuator is a costly mechanical unit, such as a mass-flow valve or motor. For example, practical evaluation of the forward path PIP temperature controller at SRI has shown that the control valve activity can be reduced significantly, with consequent reductions in both valve wear and energy utilisation. In particular, although it provides much tighter control, the valve movement per hour of the PIP controller is only 15% of that required by the commercial PI controller operating at the same mean pipe temperature.

5 Control system implementation The multivariable PIP controller design was evaluated first on the full nonlinear Simulink simulation model with high level disturbances based on the meteorological data collected during the planned experiments at SRI. The controller was then implemented in the Venlo glasshouse at SRI over a three month period during the 1993/94 growing season with a tomato crop in the glasshouse. In these important validation experiments, the control software was written in standard ANSI C to ensure portability to other hardware platforms and applications typical of those available in large horticultural glasshouses. Comparisons of control performance between the conventional PI controller currently used at SRI and this PIP controller show that the latter has quite similar total energy utilisation but much superior tracking of climate set-points and reduced actuator wear. Figure 3 shows the control performance of each climate variable over the entire validation period. Each plot shows the percentage of the time that a control variable remained inside a certain control limit: for example, air temperature was never more than 1.5 ºC away from the desired level; it was less than 1 ºC away from the set-point for 98% of the time; and less than 0.5 ºC away for 85% of the time. The controller has also proved very efficient in following optimal micro-climate trajectories computed at SRI to optimise plant growth and productivity. In addition, it was more robust than anticipated to extreme events not investigated in the design studies, as exemplified on the night of 24 th January 1994, when a wind gust of 20m/s smashed several panes of glass resulting in large wind incursions. After an initial drop in temperature the controller responded quickly, controlling the temperature to within 1 ºC for the rest of an extremely stormy night. Figure 4 shows some sample implementation results from the 23 rd to the th of February 1994: tight control to the setpoints is achieved in each case, with smooth actuator movements. Note that humidity and CO 2 are only controlled during daylight hours. Figure 3: Controller performance for all implementation results 100 Temperature 100 Humidity 100 Carbon Dioxide [% time] [% time] [% time] [ C] [% RH] [ppm] Conclusions This article has shown how the approach to TDC system design developed in CRES can be applied to the multivariable modelling and control of a glasshouse micro-climate. The resultant PIP controller has been implemented on the Venlo glasshouse at SRI. The controller gives excellent results, following the desired setpoints tightly during the whole of a 3 month evaluation period. This ability to accurately follow the desired setpoints allows optimally determined control strategies to be realised and extreme conditions, which could damage the crop, to be avoided, so resulting in reduced production costs for the glasshouse industry.

6 Moreover, the potential for the wider application of the modelling and control system design methods developed in the project is demonstrated by other successful applications in horticulture and industry including, most recently, the design and successful implementation of a PIP control system for the regulation of CO 2 in an Open Top Chamber used in climate change research (Norris et al, 1995), and also the control of climate in plant physiology experiments (e.g. Taylor et al, 1995). Figure 4: Implementation results from the Venlo glasshouse Venlo temperature control results (23 /02/94) 20 [ C] 15 VP :00 13:00 19:00 1:00 7:00 13:00 19:00 1:00 Venlo relative humidity control results (23 /02/94) 70 [%] MIST 7:00 13:00 19:00 1:00 7:00 13:00 19:00 1:00 Venlo carbon dioxide control results (23 /02/94) 5 [ppm] CO2E 7:00 13:00 19:00 1:00 7:00 13:00 19:00 1:00 Time

7 References Bitmead, R.R., M. Gevers and V. Wertz (1990), Adaptive Optimal Control: The Thinking Man s GPC, Prentice Hall, New York. Chotai, A. (1995), Latest automatic control research in CRES, CRES workshop, Lancaster University. Norris, T.S., Bailey, B.J., Lees, M.J. and Young, P.C. (1995), Design of a controlled-ventilation open-top chamber for climate change research, accepted for publication in, Journal of Agricultural Engineering Research. Taylor, C.J., Lees, M.J., Young, P.C. and Minchin, P.E.H. (1995), True Digital Control of carbon dioxide in agricultural crop growth experiments, accepted for publication in, Proceedings of 13 th IFAC World Congress. Young, P.C. (1995), Uncertainty in global carbon cycle models, CRES workshop, Lancaster University. Young, P.C. and Lees, M.J. (1995), Linearisation and reduction of glasshouse climate models for control system design, accepted for publication in, Acta Horticulturae, 404. Young, P.C., Lees, M.J., Chotai, A., Tych, W. and Chalabi, Z.S. (1994), Modelling and PIP Control of a Glasshouse Micro-Climate, Control Engineering Practice, 2(4),