902 Cupyrighl@ 1996IFAC 4a-Ol 5 131h Triennial World Congre ss , San USA PREDICTIVE CONTROL OF AIR TEMPERATURE IN GREENHOUSES Bjarne Nielsen* and Henrik Madsen** ·Dept, of Ornamentais, The Danish Institute of Plant and Soil Science Kirstinebjergvej 10, DK-5792 Aarslev, Denmark. e-mail: bn@dina.kvl.dk **Institute of MathemtJJical Modelling, The Technical University of Denmark DK-2800 Lyngby, Denmark, .·mail: hm@imm.dlu.dk Abstract: This paper describes a new method for improving the control of air temperature in greenhouses. The proposed controller is an extended version of the generalized predictive controller (GPC). The prediction of air temperature is facilitated by • continuous time stochastic state space model identified for the heat dynamics of the greenhouse. A simulation study illustrates that the proposed GPC gives a more active controller with less control error than the implemented PID controller. Key words: Horticulture; Feedforward Control; Generalized Predictive Controller; Multi- variable Control; State Space Models; Stochastic Linear Differential Equation. 1. INTRODUCTION The energy consumption in greenhouses in a temperate climate zone as in Denmark is nonnally large. especially during winter time, One way to save energy is to improve the system for controlling the heat supply. An improved control gives smaller variation in the air temperature. In situations of high heat demand this leads to the possibility of decreasing the setpoint temperature closer to the lower limit of the plants. Today, the heat supply is typically controlled by a proportional integral (PI) or a proportional integral differential (PlO) controller. In this paper an improved method for controlling the air temperature in greenhouses is proposed. The energy supply is controlled by a prediction of temperature states in the greenhouse. Controllers of this type are the minimum variance controller (Astrom. 1970) and the generalized predictive controller (Clarke and Gawthrop, 1975). Such prediction based controllers have proved to be powerful et al., 1994). Model based control of horticultural glasshouse systems has previously been considered by Udink ten Cate (1983), Davis and Hooper (1991) and Young el al. (1994). The perfonnance of prediction based control systems depends on the possibility of obtaining good predictions of the temperature states in the greenhouse. Stochastic stale space models for predicting the air tempera- ture in a greenhouse have earlier heen considered by Nielsen and Madsen (1995, 1994). The present paper describes how the continuous time model is used for fomulating a GPc. Simulation experiments are used to find optimal values of the tuning parameter of the OPC. 2. PREDICTIONS OF THE AIR TEMPERATURE It is shown in Nielsen and Madsen (1995) that the air temperature in a greenhouse can be described by the linear stochastic differential equation in state space fonn: A Tdl+B,u,dt+B,u,dl+dw(l) (1)