Comparison study of PID controller tuning for greenhouse climate with feedback-feedforward linearization and decoupling
The interest in ensuring optimal growth climate conditions is sustained by the increasing demand in greenhouse products, which in turn, leads to an increasing demand of high efficiency greenhouse control systems. The greenhouse climate control is complex due to the high nonlinear interaction between the biological subsystem and the physical subsystem, and due to strong coupling of the two main controlled variables: temperature and humidity. In this context, the paper presents an equivalent greenhouse climate model based on feedback-feedforward compensation technique responsible for linearization, decoupling and disturbance compensation of the greenhouse complex model. Based on this equivalent model reduced to integral plus dead time decoupled processes, a comparison study of associated PI/PID controllers employing different tuning techniques is performed by simulation.
We consider the following dynamic tax-rebate program. In each period, a (fixed) quantity tax is imposed on each unit of the good consumed and the tax revenue is rebated back to the consumer in the next period. The program lasts for infinite number of periods. We consider consumer's dynamic consumption behavior, the consumption behavior in the long-run steady state, and the welfare effects of the program. Under the standard continuity and strict convexity assumption on consumer preference, we show that the tax will strictly reduce the consumption of the good being taxed in each period as well as in the steady state, and consumer is strictly worse off. We also provide analytical solutions when consumer has quasilinear or Cobb-Douglas utility function.