Attitude Control Method And Application Of Aircrafts Based On Nonlinear Observer

With the progress of economy and science and technology,aerospace industry has undergone an unprecedented development,and aircraft assume more complex and di-versified tasks,which also put forward higher requirements for aircraft control.The attitude tracking control is the foundation and key of aircraft control,and it has been a hotspot issues of control field.Most existing controller assume that the angular velocity of aircraft is measurable and available for controller implementation.However,angu-lar velocity measurements are not always available in fact due to some reasons,such as limited by sensors,costs,energy,etc.To handle this situation,an angular velocity observer is developed in this dissertation,and then the attitude tracking controller is designed based on this observer.This dissertation first gives the basic theory and knowledge used.We establish the inertial coordinate system and body coordinate system,and then set up the gen-eral attitude model of aircraft based on Euler's second law of motion respectively in unit quaternion and rotation matrix.After that,angular velocity observers and attitude tracking controllers are presented.The design of angular velocity observer is mainly based on contraction analysis.The key of contraction-based design is to find an auxiliary system called virtual system,which has the angular velocity's actual value and observed value as two particular solutions.Then the observed value will converge to the actual values exponentially if the virtual system is contract.We first introduce the contract angular velocity observer,which was proposed in quaternion for the attitude system of small satellites,into the attitude system of aircraft.Next,the external disturbance is considered as the extension of the original observer.For the disturbance composed of multiple sinusoidal signals with known frequencies,unknown amplitudes and phase angles,we draws from the method of internal model design in output regulation problem:first,give the steady state generator of the attitude system,and use a new state variable which is defined according to the form of the steady-state generator into the design of observer.Then find out the second-order virtual system for the steady-state generator,attitude dynamic equation and the newly defined state variable,observer dynamic equation.By proving the virtual system contracting,the exponential convergence of the observed value to the actual value can be guaranteed,and the contraction region of the observer can be given meanwhile.Considering th e ambiguity of quaternion,we develop a contract angular velocity observer in rotation matrix.Similarly,we also consider the absence or presence of the disturbance,and use the newly defined state variable to deal with the disturbance.For the matrixed kinematics equation,we define a middle variables about the rotation matrix,which is in the form of vector and can be directly used in the vectorial definition of the observer.This ensures that the actual value of angular velocity can be substituted into the dynamic equation of the observer through the derivation operation under the premise that the actual value does not appear in the observer definition,which ensures the existence of the virtual system.By comparing the contraction region of the angular velocity observer in quaternion with that in rotation matrix,we can see that the range of the latter is larger than the former with the same parameter selection,and it has a faster contraction speed meanwhile.Respectively under the quaternion and rotation matrix expression of attitude,we develop attitude tracking controller of aircraft based on the given angular velocity ob-server in the absence and presence of disturbances severally.The attitude tracking is always accompanied by the angular velocity tracking,which requires the attitude and angular velocity tracking errors approach zero at the same time.In this dissertation,the angular velocity's actual value in the angular velocity error is replaced by the ob-served value because the angular velocity is unmeasurable.The redefined error is used in the attitude tracking controllers design.Then the real angular velocity error defined by the actual value will approach zero if the angular velocity observation error and the redefined angular velocity error approach zero simultaneously.To verify the effectiveness of each observer and controller,we carry out some nu-merical simulations with MATLAB/Simulink software in different conditions.At last,we take the quadrotor UAV as an actual control object,and modify the angular velocity observer and attitude tracking controller according to the dynamic model of the quadro-tor,which verifies the practical availability of the proposed controller preliminarily.