Tiểu luận Lý thuyết điều khiển nâng cao - Nguyễn Thanh Bình

BÁO CÁO TIỂU LUẬNLÝ THUYẾT ĐIỀU KHIỂN NÂNG CAO10/24/20211Backstepping Based Flight Control 	NHÓM 1Nguyễn Thanh BìnhLê Văn Khang HuyTrần Nhật TrườngOverviewModern Aircraft ConfigurationAircraft DynamicsForce, Moment and Attitude EquationsBackstepping Approaches to Flight Control DesignBackstepping Backstepping Design for Flight ControlFlight Control LawsSimulation10/24/20212Modern Aircraft Configuration10/24/20213Aircraft Dynamics 	, Aircraft position expressed in an Earth-fixed coordinate system; 	, The velocity vector expressed in the body-axis coordinate system; 	, The Euler angles describing the orientation of the aircraft relative to the Earth-fixed coordinate system; 	, The angular velocity of the aircraft expressed in the body axes coordinate system;10/24/20214Aerodynamics Forces and Moments10/24/20215	Body axis coordinate systemForce Equations (Body-axes)10/24/20216Rewrite the force equations in terms of Force Equations (wind-axes)10/24/20217Where the contributions due to gravity are given by, Moment and Attitude EquationsMoment Equations:Attitude Equations:10/24/20218Backstepping based flight control designConstructive (systematic) control design for nonlinear systems. Lyapunov based control design methodAvoid cancellation of “useful nonlinearities” (unlike feedback linearization). Stability is guaranteed for all angles of attack (unlike gain scheduling).Different flavors: Adaptive, robust and observer backstepping. 10/24/20219BacksteppingConsider the systemWhere 	 are state variables and is	 thecontrol input. Assume a virtual control law 	 is known such that 0is GAS equilibrium of the system. 10/24/202110BacksteppingLet,	 be a clf for the subsystem	 such thatThen, the clf for the augmented system is given by Moreover, a globally stabilizing control law, satisfying is given by	10/24/20211110/24/2021Backstepping design for flight control10/24/202112Controlled variables: General maneuveringControl Objectives10/24/202113Assumptions: Control surface deflections only produce aerodynamic moments, and not forces. The speed, altitude and orientation of the aircraft vary slowly compared to the controlled variables. Therefore, their time derivatives can be neglected. Longitudinal and lateral commands are assumed not to be applied simultaneously.The control surface actuator dynamics are assumed to be fast enough to be disregarded. 10/24/202114Backstepping design for flight controlThe roll rate to be controlled,	 , is expressed in the stability axes coordinate system. The stability axes angular velocity, 	 ,is related to the body axes angular velocity, 	 , through the transformation:	whereNote that the transformation matrixIntroducing: 10/24/202115Aircraft Dynamics Revisited10/24/20211612345Roll rate dynamics: Equation 1Angle of attack dynamics: Equation 2-3Sideslip dynamics: Equation 4-5The nonlinear control problem The angle of attack dynamics and the sideslip dynamics can be written as For notational convenience it is favorable to make the origin the desired equilibrium. Let, 	 is the desired equilibrium. 10/24/202117The nonlinear control problemThe dynamics becomeWe will use backstepping to construct a globally stabilizing feedback control laws for the system assuming general nonlinearity	.10/24/202118The nonlinear control problemAssume there exists a constant, , such thatThen a globally stabilizing control law can be given by	 where,	 and	10/24/202119Block Diagram10/24/202120The nonlinear system is globally stabilized through a cascaded control structureAircraft Application10/24/202121Flight Control LawsAngle of attack control	Sideslip regulation	Stability axis roll control	10/24/202122Gain Selection, How should the control law parameters be selected?For control, linearize the angle of attack dynamics around a suitable operating point and then select to achieve some desired linear closed behavior locally around the operating point. For regulation, can be selected by choosing some desired closed loop behavior using linearization of the sideslip dynamics. 10/24/202123