Fuzzy Gain-scheduling Control And Its Application To Hypersonic Vehicle

The robust gain-scheduling control theory,originating from classical gain-scheduling control which is the most widely used control scheme in practical engineering,provides a systematic approach for nonlinear control design.Its main idea is to utilize widelyavailable linear controller design tools to address nonlinear problems,while provide guaranteed stability and performance properties for the closed-loop systems.So far,the framework of robust gain-scheduling control theory has been established and the key issues have been well addressed based on the robust control theory.The main problem,which remains difficult to apply the robust gain-scheduling control theory to the practical engineering,is the modeling of linear parameter varying(LPV)model.To overcome this issue,the relation between LPV models and T-S fuzzy models,which have been proved as universal approximations of nonlinear dynamics,has been studied in the research.Moreover,several fuzzy gain-scheduling controller design methods are proposed based on the combination of T-S fuzzy model and robust gain-scheduling control techniques.Based on the relation between T-S fuzzy model and LPV model,a novel transformation method,converting T-S fuzzy model into linear fractional transformation(LFT)structured LPV model,is given.Then,a design method of dynamic output feedback LFT controller,in which the fuzzy weighting functions are treated as the scheduling parameter,is proposed based on quadratic Lyapunov functions.Compared with the existing T-S fuzzy control method,the presented method has less conservatism and can guarantee a better induced L2 norm performance.Besides,the control design method has been strengthened to cope with the T-S fuzzy plant with saturated actuator.To reduce conservativeness of the control design method,fuzzy Lyapunov functions are introduced to replace common Lyapunov functions.The full block S-procedure is employed to deal with the quadratic terms of fuzzy weighting functions in the analysis and synthesis conditions.Moreover,some slack matrices are also utilized to handle the derivative terms of fuzzy weighting functions.As a result,a fuzzy gain-scheduled dynamic output feedback controller design method is proposed based on fuzzy Lyapunov function,while its extension to saturated plant is also given.To perform the proposed fuzzy gain-scheduling control methods,design of flight control system for the hypersonic vehicle is conducted.The model of the hypersonic vehicle’s longitudinal dynamics is given,followed by its curve-fitting model obtained by replacing forces and moment by their curve fit approximations.The T-S fuzzy modeling method is employed to obtain T-S fuzzy models both the attitude dynamics and the trajectory dynamics of hypersonic vehicle,then the generalized T-S fuzzy models can be established by introducing some weighting functions.The generalized T-S fuzzy model serves as the controlled plant for control design,while the nonlinear model is used in simulation to demonstrate effectiveness of proposed control methods.Finally,the proposed anti-windup fuzzy gain-scheduling control methods are used to design the hypersonic vehicle’s flight control system,including an attitude stabilizing controller and a trajectory tracking controller.Simulation results,performed on the nonlinear model of hypersonic vehicle,are presented to show the effectiveness of the proposed control design method.