Linear Quadratic Regulator Control of Greenhouse Indoor Climate Incorporating Feedback Linearization

Abstract

Greenhouses are highly vulnerable to internal and external climate factors like sunlight, temperature, humidity, and carbon dioxide. An appropriate control mechanism of the greenhouse environment is required to maximize the growth and quality of the plants. Even though controlling the indoor climate of a greenhouse is difficult due to the system nonlinearity and existence of coupling relation among system parameters, the designed controller should have good tracking and rejection performances. With this as a starting point, feedback linearization linear quadratic regulator (LQR) control of greenhouse indoor climate is implemented in this thesis. The nonlinear multi-input multi-output (MIMO) dynamic model of greenhouse climate is obtained and transformed to its equivalent linear model using input-output feedback linearization. Then, a proportional-integral (PI)-type LQR controller is designed based on the linearized model to obtain a fast response with less overshoot. In addition, a genetic algorithm (GA)-based practical proportional integral derivative (PID) controller that minimizes the performance indices such as integral absolute error (IAE) and integral square error (ISE) is implemented for comparison purposes. The setpoint tracking and disturbance rejection performance tests are performed by considering different psychrometric processes for the daytime summer season operations. The performance of these controllers is evaluated using performance measures such as overshoot, settling time, recovery time, and perturbance peak values. In the tracking test, the closed-loop response of indoor temperature at 28℃ and 20g [water]/kg [dry air] using the LQR temperature controller gives 1.6369min, 3.0330min, 0, and 1.8523 of rise time, settling time, overshoot, and IAE, which is very small as compared to the PID, respectively. Also, the LQR humidity controller gives a 0 overshoot with 0.5814 of IAE even though the settling time (3.8772min) is slightly greater than the PID. In the rejection test, when both the intercepted solar radiant energy and outside temperature are increased while setpoints are fixed at 28℃ and 18g [water]/kg [dry air], the LQR recovers the output responses of temperature and humidity quickly with a recovery time of 4.2819min and 3.7231min, respectively. These values are very small compared to the PID controller. In general, the performance measures of the implemented controllers in both performance tests informed that the LQR indoor temperature and humidity controller is better than the PID controller for this designed system.