Linear Quadratic Optimal Control Applied to the Greenhouse Temperature Hierarchal System

Abstract

Optimal greenhouse temperature management systems as hierarchical systems have been employed to achieve suitable conditions for crop growth. The system is generally decomposed into upper and lower layers. The lower layer usually includes online controllers that try to cancel tracking errors of temperature set points obtained from the upper layer. However, as the greenhouse temperature is highly non-linear, the problem of lower layer controller design becomes very complex and the online computational demands are great, which limit the practical applications of hierarchical systems. This paper presents the design of a practical greenhouse temperature hierarchical control approach. In lower layer, a linear quadratic optimal controller with heater inputs is used. The strategy is based on a linearised model achieved by using an accurate linearisation method for an inside temperature non-linear physical model which can be described as an affine non-linear one. The controller is designed by means of finding a tradeoff between set point tracking and cost requirements reduction. The upper layer calculates optimal temperature trajectories by minimising net costs. Performance of the hierarchical control system is studied in simulation. The results show that the upper layer controller can effectively achieve the set point and that the lower layer controller can contribute to a good control performance with a minor cost increment.