Model-based quantitative analysis in two-time-scale decomposed on–off optimal control of greenhouse cultivation

Greenhouse climate is crucial for crop growth. Traditional climate control techniques are carried out through on–off actuators based on growers’ experience. Advanced control algorithms usually track setpoints through continuous control inputs. These setpoints cannot guarantee maximum profit, which can be treated as the control objective of the optimal control algorithm. This paper investigated on–off optimal control algorithms based on two-time-scale decomposition. Mixed-integer nonlinear dynamic programming is used in the fast subproblem to quantify the influence of restricting different control inputs to be integers on the control objective and the CPU time. Results show that compared with continuous control inputs, a decrease of 2.21 ¥·m⁻² in the control objective and an increase of 7.84·10³ s in the CPU time can be found when defining all control inputs to be integers with 12 collocation points in one day. The methods of sorting and pulse width modulation are used to simulate the receding horizon optimal control in the whole growing period. Results show that compared with continuous control inputs, decreases of 83.54 ¥·m⁻² and 4.45 ¥·m⁻² can be found with the methods of sorting and pulse width modulation. Moreover, the method of pulse width modulation cannot guarantee state constraint satisfaction. This paper suggests modifying actuators to supply continuous control inputs before implementing optimal control algorithms for maximum profit.