Research On LPV-PID Control With Its Application To Flight Control

With the development of the aviation industry and its increasing impor-tance in technology innovation,more attention has been paid to the research of flight control methods to improve aircraft performance.At present,most real flight control systems adopt the proportional-integral-derivative（PID）control combined with the traditional gain-scheduling control method.Be-cause it provides a flexible design framework and a simple control structure,this method is widely used in flight control system design.But the traditional gain-scheduling control cannot guarantee the system performance theoreti-cally,so a large amount of experiments are required to verify effectiveness of the control system.Linear parameter varying（LPV）control is presented to solve the prob-lem.The LPV control method that extends the robust control of the linear system to the nonlinear system.This kind of the nonlinear system has a lin-ear system structure and the system matrices depend on real-time measur-able parameters.The LPV control can ensure the stability of the system in the designed parameter space,and the parameter-dependent controller can be adjusted according to the system parameters,instead of interpolation.How-ever,the application of this method in real systems still faces many chal-lenges.Firstly,most LPV controllers are based on state feedback or dy-namic output feedback control,which need to feedback all system states or construct complex dynamic output feedback controllers online.In addition,because the physical meaning of the controller gains cannot be explained directly,it is difficult to tune the gains online.Based on the above background,this paper studies the gain-scheduling PID control design of LPV systems,aiming to combine the advantages of LPV and PID control.This method makes the control system not only have the simple structure as PID control but also can guarantee the performance of the system in a wide parameter space theoretically.The main content of this paper can be summarized as the following three aspects:（1）In this paper,the gain scheduling PID control design for LPV sys-tems is studied,and some novel synthesis conditions in linear matrix inequal-ities（LMI）are presented.Firstly,the state feedback based gain-scheduling proportional-integral（PI）control is studied.The nonconvex optimization problem is transformed into a convex optimization problem using the ex-tended LMI approach.Compared with the traditional methods,this method decouples the Lyapunov matrix from the system matrices and has lower con-servatism.Considering the limitation of state feedback,this paper further studies the output feedback LPV-PID control.In order to solve the non-convex optimization problem,the PID controller is transformed into a static output feedback controller.Then,the control synthesis conditions with LMI constraints are proposed by using elimination lemma and matrix transforma-tion,and the bounded induced₂norm and₂norm of the system can be guaranteed.Compared with the existing methods,the method in this paper has fewer constraints and expands the feasible solution space.（2）This paper studies the smooth switching LPV-PID control method.Firstly,according to the average dwell time switching logic,the synthesis condition of switching LPV-PID control is proposed.In order to ensure the system performance on the switching surface,a smooth switching LPV-PID control algorithm is proposed.This method can have the control gains change continuously with the Lyapunov function switching,to avoid the per-formance degradation caused by the sudden changes of control input in the traditional switching control.Compared with the existing methods,tt can guarantee that every subspace of the LPV system has an independent Lya-punov function,and improve design flexibility.（3）In order to reduce the influence of actuator saturation,this paper studies the control method for the system with saturations based on the LPV PID control.An anti-windup compensator is added to reduce the influence of the windup caused by the integral term of the PID control.The system regional stability is proved according to the saturation control theory,and the synthesis conditions of the controller are proposed.The method can design the gains of the controller and compensator at the same time.In conclusion,this thesis studies the gain-scheduling PID control of the LPV systems and proposes the synthesis conditions of the controller with less conservatism.At the same time,it also considers the switching control problem and saturation control problem encountered in the real applications,to solve the problem of the sudden change of control input in the switching control,and the system performance degradation caused by saturation.It reduces the application difficulties of LPV control.