Adaptive Fuzzy Control of a Class of MIMO Nonlinear System With Actuator Saturation for Greenhouse Climate Control Problem

This paper presents an indirect adaptive fuzzy control scheme for a class of MIMO non-affine nonlinear systems with unknown dynamics and actuator saturation for greenhouse climate control problems. The objective is to implement output tracking control on nonlinear systems. Using feedback linearization, control inputs with known control gains are first synthesized by well-modeled dynamics of the system, and Taylor series expansion is used to transform unknown non-affine dynamics into the corresponding affine forms. Fuzzy logic systems (FLS) are introduced to estimate the unknown nonlinearity of the transformed affine system and the saturation nonlinearity due to the actuator constraint. The control inputs corresponding to nonlinearity are constructed based on the estimations. By introducing a robust control term, estimation errors and external disturbances are well handled, so as to guarantee the stability when tracking the control process. The control gain estimation obtained by FLS is modified to avoid singularity. Lyapunov stability analysis is performed to derive the adaptive law. To validate the effectiveness of the proposed control scheme, we apply it to a greenhouse climate control problem. The ventilation rate in the greenhouse model is unknown; therefore, it is estimated by FLS. The simulation exhibits satisfactory results, in which the temperature and humidity inside the greenhouse are well tracked. Note to Practitioners-Control design for complex system is still a challenging task in many engineering problems due to the uncertainties such as model inaccuracy and unmodeled dynamics. Adaptive robust control is an effective method to handle the uncertainties and external disturbances. Although it is usually impossible to derive the complete model of a complex system, a part of unmodeled dynamics can still be estimated by approximation technologies such as FLS and neural network. Based on the background of greenhouse climate control, we propose a scheme to solve a class of control problems in which the system model contains unknown functions that reflect relevant dynamics as well as input constraint. Feedback linearization and FLS are combined to design a climate controller. The advantage of the presented control scheme is that we can use mature methods to the largest extent in determining part of the control law. Although the motivation of this control scheme is to solve the greenhouse climate control problem, we still hope that it can be applied to similar problems in other engineering fields.