Constrained Control For Nonlinear Systems And Its Applications

Because of the physical constraints,external interference and security,the constraints such as the input,output or state constraints inevitably exist in the real control systems.These fac-tors make the controller design of nonlinear system more complex and difficult.Therefore,based on an asymmetric barrier Lyapunov function(ABLF),the control problems with output constraints for nonlinear systems are discussed in this dissertation.Firstly,a class of nonlinear system with time-varying output constraints is addressed.Secondly,the control problem for a class of uncertain nonlinear systems with output constraints is considered.Thirdly,a new load torque observer is designed via fractional calculus against the complex nonlinearity and uncer-tainty for brushless DC motor,hence,an improved constrained control strategy is developed.Finally,considering the anti-skid braking system(ABS)of aircraft,stability region is taken into account directly,the constrained control problem of wheel slip ratio is discussed;meanwhile,for the uncertainty of adhesion coefficient,an adaptive wheel slip ratio controller is designed to improve the efficiency of braking and the robustness of ABS.The main research results can be summarized in the following parts:1.A brief review of the background of this paper is introduced,an overview of nonlinear control methods is given.Then,the research status and development trend of brushless DC motor and ABS are summarized.2.A constrained control scheme based on the ABLF and DSC technique is developed to address time-varying output constraints for a class of nonlinear system.The proposed control scheme can avoid the proliferation and singularity of repeated differentiation.As a conse-quence,it can relax the requirements of high order differentiability for stabilizing functions and high power of output tracking error transformation involved in ABLF synthesis.The new controller can be proved to guarantee that all the closed-loop signals remain bounded,and to ensure output constraints never violated.Comparison studies with previous work validate that DSC incorporated with ABLF can achieve favorable performance bounded within constraints,and it can also ensure fast and stable tracking convergence in the presence of disturbance.3.The control problem for a class of uncertain nonlinear system with output constraints is addressed.An adaptive constrained control scheme based on DSC in conjunction with ABLF has been developed,the scheme can be adjusted by estimating and correcting those unknown parameters on-line.A detailed method of choosing control parameters is also given during the process of controller design.Moreover,the structure of this controller is simple by employing DSC technique.The proposed controller guarantees the boundedness of output constraints and the asymptotic stability in the closed loop.Simulation results further illustrate that the proposed method under estimated the unknown parameters not only quickly tracks the desired trajectory with great accuracy and robustness against uncertainties but successfully ensures the output constraints never violated.4.The position constrained control for brushless DC motors with strong nonlinearity and uncertainty is focused.Firstly,we use horsepower dynamometer platform to demonstrate the efficiency of DSC constraint control scheme,which is investigated in chapter two.In addition,a new load torque observer is designed via fractional calculus to observe the load torque,which is the main uncertainty in DC motor.Moreover,its convergence with zero steady error has guaranteed by the Mittag-Leffler stability theorem.Finally,experiments are conducted to illus-trate the advantage of the proposed method in the real control system.The results illustrate that the fractional load torque observer achieves fast performance with great control accuracy and a better ability of noise rejection,and the constrained controller has a favorable performance bounded within constraints.It can be concluded the proposed controller with the fractional observer has a valuable application in engineering field.5.The constrained control of wheel slip ratio for ABS of aircraft is discussed.An approach that combines DSC technique and an ABLF is presented by considering the stable region and unstable region of wheel slip ratio directly.In addition,an adaptive constrained control scheme is developed to address both the constraints on the wheel slip ratio and the online estimation of the unknown friction coefficient,which can quickly estimate the friction coefficient with great accuracy and robustness against uncertainties in tyre-road friction.Finally,a series of simulation results are shown to verify the efficiency of the proposed schemes.Simulation study illustrates that both the proposed methods successfully ensure the wheel slip ratio remains in the stable region,thus avoid self-locking.