Modeling and control of greenhouse temperature-humidity system based on grey prediction model

Abstract: Greenhouse temperature-humidity system can be regarded as a hybrid system, where the discrete variables, i.e. the switching states of environmental control devices, e.g. ventilation window, wet curtain-fan, sunshade nets and et al, and the continuous variables, i.e. greenhouse temperature, humidity, and measurable but uncontrollable disturbance inputs consisting of outside temperature, outside humidity, solar radiation, wind direction, wind speed and et al interact. Besides, what makes the greenhouse temperature-humidity system difficult to control is the existence of the outside measurable but uncontrollable disturbance inputs. As a result, some conventional methods like feedback, feedforward are not applicable to the greenhouse temperature-humidity system. In this paper, according to the hybrid characteristic of greenhouse temperature-humidity system, a method based on switched models was proposed for modelling and predictive control of greenhouse temperature-humidity system. The data sampling experiment was carried out under the open ventilation window condition and closed ventilation window condition, respectively. Firstly, by correlation analysis, outside temperature, outside humidity and solar radiation, which had obviously strong correlation with inside temperature and humidity, were chosen as three disturbance inputs of extended auto-regressive (ARX) models of the greenhouse temperature-humidity system, which could simplify model structure to some extent. Then model parameters of two subsystems were obtained by forgetting factor recursive least squares (FFRLS) under open ventilation window condition and closed ventilation window condition, respectively. Secondly, predictive control problem of greenhouse temperature-humidity system was transformed into mixed integer quadratic problem (MIQP), which was solved by branch and bound algorithm. In addition, grey prediction method GM(1,1) was adopted to predict the measurable but uncontrollable disturbance inputs appearing in this system. Furthermore, due to limitations of the physical properties of the environmental control devices, the upper/lower amplitude constraints of inputs should also be taken into consideration. If the inside temperature was above the upper constraint or the inside humidity was below the lower constraint, switching state of ventilation window was open at the next step, if the inside temperature was below the lower constraint or the inside humidity was above the upper constraint, switching state of ventilation window was closed at the next step. After both solving mixed integer quadratic problem and upper/lower amplitude constraints analysis, optimal switching signal was obtained. In what followed, we considered the stability problem of the achieved switching model. Traditional stability analysis mainly focused on asymptotical stability when time approached infinity based on the Lyapunov stability theory, but there could be such a case that the system is asymptotically stable but at some finite time points the system has bad performance which may lead to uncertain results or system halting. Therefore, Finite-time stability of greenhouse temperature-humidity switched system is nontrivial for practical control case. Finite-time stability of two subsystems and switched system was illustrated by simulation results. At last, the simulation study was carried out, and inside temperature and humidity could be controlled within the setting range basically, and inside temperature and inside humidity could approach setting final goal in the end of control time, which showed the effectiveness of the modeling and control method achieved in this paper.