Model Reference Tracking Control Of Quasi-linear Systems And Its Applications

Many practical models is nonlinear in production activities of human actually.It is more accurately to describe the motion by nonlinear system,nonlinear system controller design and closed-loop system stability are the difficulties in nonlinear control theory,and also the research focus,it has important theoretical value.The quasi-linear systems studied in this paper is a kind of nonlinear system that can be rewritten into the form of linear systems.Quasi-linear systems are different from linear systems,the coefficient matrix of quasi-linear systems contains state variables.Quasi-linear system are widely used in spacecraft control,missile control,robot control,etc.In the past decade,research on quasi-linear system control methods are launching gradually,it has achieved a few theoretical and application results,but currently the research results mainly aim at stabilizing the quasi-linear system,and less research on model reference tracking control.In the field of spacecraft control,many practical control tasks can be formulated as the model reference tracking control problem of quasi-linear systems.The main research contents include the following three aspects.The general first-order quasi-linear system and the quasi-linear reference model are given.Based on the quasi-linear system direct parametric method,a model reference output tracking control law for quasi-linear system is proposed.The designed controller consists of the feed-forward compensation controller and the feedback stabilization controller.The feed-forward compensator is designed to guarantee the output of the closedloop system to track the output of the reference model asymptotically.Based on the idea of model reference tracking control,the existence condition equations of quasi-linear model reference tracking controller are established.Based on the generalized inverse theory,the parameterized feed-forward compensation controller is obtained,which contains free parameters to be designed.The feedback stabilization controller is designed based on the direct parametric method of quasi-linear system,it makes the closed-loop system is asymptotically stable under the action of feedback stabilization controller only.Although the open-loop system is quasi-linear,i.e.non-linear,the closed-loop system is linear.There are also free parameters in the feedback stabilization controller,and the poles of the closed-loop system can be allocated to adjust the dynamic performance.The effectiveness of the proposed quasi-linear model reference tracking method is verified.Twodifferent numerical examples are used for simulation analysis.The quasi-linear system model reference output tracking control law is proposed and applied to the design of integrated attitude and orbit controller for spacecraft.Aiming at the target spacecraft in circular orbit,one side of the serving spacecraft with on-board equipment always points to the target spacecraft,and its fly-around motion is carried out to observe the target in an all-round way.To solve this problem,firstly,a 5-DOF integrated attitude and orbit control model is established in the framework of two-dimensional line of sight coordinate system combined with Euler angle,and the reference model is established according to the characteristics of the fly-around mission,then a quasi-linear model reference tracking control method is applied to design the controller in the framework of the second-order system,so that the attitude and orbit state of the controlled spacecraft can be asymptotically tracked to the system state of the reference model,thus completing the fixed attitude-oriented fly-around mission.Finally,the effectiveness of the method is verified by numerical simulation.The degree of freedom in the tracking parameterized controller can be used to improve the required performance of the closed system,which is reflected in the design of a integrated attitude and orbit controller for flying around the spacecraft in elliptic orbit with fixed attitude direction.Based on the spacecraft relative motion T-H equation and attitude Euler angle,a quasi-linear 6-DOF integrated attitude and orbit control model without small angle approximation is established.The model contains bounded unknown parameters.According to the requirements and characteristics of flying around the elliptical orbit spacecraft with fixed attitude direction,a second-order quasi-linear integrated attitude and orbit control reference model is established.A robust quasi-linear model reference tracking controller is designed by using quasi-linear model reference tracking control law.In order to reduce the eigenvalue sensitivity of the closed-loop system,the optimization problem of reducing the eigenvalue sensitivity of the closed-loop system is solved.The simulation results show that the closed-loop system can asymptotically track the output of the reference model in the presence of uncertainties.The mission of fixed attitude pointing flying around the spacecraft in elliptical orbit is completed.