Linear Active Disturbance Rejection Control Design And Application On Two-mass-spring System

The actual mechanical vibration system is often complex and nonlinear,so in order to better analyze,calculate and control,it is often necessary to simplify and the actual system.The two-mass-spring system is a common mechanical vibration system,and it is the simplest multi-degree-of-freedom system,which contains a rigid mode and a flexible mode,and the flexible mode frequency changes with the change of the mass block and the spring coefficient,which on the one hand has uncertainty,and on the other hand is very close to the bandwidth of the controller,so it is difficult to handle.In addition,the two-mass-spring system benchmark problem can be said to be both an anti-disturbance problem and a robust control problem.In general,the study of this system has certain theoretical value and practical significance.Disturbance and uncertainty exist in almost all systems,and the handling of disturbance and uncertainty is not easy,that is,it requires strong anti-disturbance ability and certain robust performance.Active Disturbance Rejection Controller is exactly such a control technology that can deal with disturbances and has robust performance at the same time.The state observer method in the theory realizes the estimation of this expansion state,and the function of real-time estimation and compensation of disturbance is the core function of the active disturbance rejection control technology.In this paper,the linear active disturbance rejection control research is carried out for the two-mass spring system.The main research results are as follows:1)Active disturbance rejection control via modified bandwidth tuningImpulse signal disturbance rejection is the core of the benchmark problem for two-mass spring systems,and it is also the most common control problem.In order to improve the control performance and reduce the control gain,the model-aided ADRC can be used,but the ADRC usually uses high gain to achieve control,which needs to be avoided in this benchmark problem.It is found that the pole of an observer of the traditional ADRC can be placed at the origin,thereby eliminating the integral link and greatly reducing the gain of the controller.On this basis,the damping coefficient is introduced to modify the bandwidth method,so as to ensure that the system can meet other requirements while achieving fast stability.At the same time,it can be found that the amplitude margin and phase angle margin cannot fully reflect the robust performance of the system,and the relationship between the corresponding crossover frequency and cutoff frequency and the natural frequency of the system should be considered at the same time.2)Active disturbance rejection control with observer bandwidthIt is very convenient to use the bandwidth method to tune the parameters of the ADRC,and it can be found that it is equivalent to many control methods.However,from the control of the two-mass spring system,it can be seen that the introduction of the damping coefficient to adjust the bandwidth method can improve the control.In addition,when the dynamics of the controlled object is not equal to the integral series type,the parameters obtained by using the bandwidth method can not guarantee the stability of the closed-loop system.Therefore,from the perspectives of control performance and the number of parameters that need to be tuned,a new method for parameter tuning of the ADRC controller is considered,that is,the extended state observer is tuned by the bandwidth method,and the controller gain is fed back through the static output.method is designed.The two-mass spring system is studied by using the ADRC with the bandwidth of the observer parameters,and the second-order and third-order ADRCs are used for control simulation.The results show that the second-order ADRC can also It can achieve interference suppression,but cannot meet the robust performance requirements,while the third-order ADRC can meet the design requirements.3)Active disturbance rejection control for sinusoidal signal disturbance suppressionAiming at the problem of sinusoidal signal interference suppression,two control schemes are proposed:when the frequency of the sinusoidal signal is known,the frequency information obtained in advance can be introduced into the design of the active disturbance rejection controller,and the interference signal can be controlled by using two expansion states.inhibition.When the frequency of the sinusoidal signal is unknown,an additional extended Kalman filter is introduced,the disturbance frequency is estimated by expanding the signal through the Kalman filter,and then the frequency information in the active disturbance rejection controller is modified accordingly,so as to achieve the final control effect..