Adaptive Output Regulation Of Nonlinear Feedback Systems And Its Application

The theory of nonlinear system output and feedback regulation has always been a hot spot in the field of nonlinear control.This theory is widely used in the field of aerospace and robot control,such as the application of aircraft flight attitude and suppression disturbance.The theoretical research task is: when the nonlinear system is interfered by the non-deterministic signal of the external system,in order to make the control system move towards a steady state gradually within limited time,and make the control system track the desired reference output effectively,Therefore,the closed loop feedback method is used to achieve the goal of control.If the excitation signal of the system and the external system model that generates the disturbance signal belong to the category of nonlinear output regulation problems,which can be described by differential equations,such nonlinear problems can be converted into output feedback adjustment problems with relative orders equal to two.The system has a minimum phase system and has global structural stability.Because the assumptions of the non-minimum phase are more complex,as well as the conditions of the nonlinear external system are also more tedious.If both are present in the system model,it will increase the difficulty of dealing with the problem greatly.In order to solve this kind of problem,firstly we should study the concept of the extended regulator equation,and assume that the equation is solvable,and then use the knowledge of the internal model principle to build the internal model system,while the external disturbance which has the characteristics of non-linear is generally unknown,so the designed internal model can be used to estimate the nonlinear output and the feedback adjustment problem effectively,thus,it can be converted into a calm issue that we can easily handle.The adaptive control strategy is used and The Lyapunov function is called to constructs the feedback controller so that the output and regulation problems of a given nonlinear system are solved effectively.Finally,the MATLAB is used to make simulation by which we can found that the actual output of the system can track the expected output effectively,and it proved that the constructed feedback controller can meet the expectations.The application of the nonlinear system's output and feedback regulation theory in the aerospace field is typical in terms of aircraft attitude and suppression of disturbances.For the flight attitude of an aircraft,firstly,this paper uses the quaternion method to describe it,and its disturbance signal is more complex which has a certain non-linear characteristics came from the external system mainly.Firstly,we solve the regulator equation.For the nonlinear disturbance signal generated outside the system,it can be estimated by the constructed nonlinear internal model system.Then the coordinate system of the internal model system should be transformed.For the tracking error,the same method is used.Then we transform the relevant formula,according to the relevant concepts of the Lyapunov function,we can construct an effective function and propose an effective control law so that the aircraft attitude has a global sense of stability,the results of MATLAB simulation prove the feedback controller can meet our expectations.