Sinusoidal Signal Tracking Control Based On Equivalent Reconstruction Method

The tracking control problem of periodic sinusoidal signals widely exists in industrial fields such as power electronics,servo drives,and precision manufacturing.The accuracy of tracking control seriously affects production performance.Since the sinusoidal signal belongs to a neutral stable system,how to ensure the stability of the system and the rapidity of tracking is an important research issue.In this paper,a sine equivalent reconstruction method is designed to realize accurate and fast tracking of periodic signals.This method analyzes the relationship between the reference signal and its frequency and system response,and uses the equivalent reconstruction method to design the controller structure and parameters.Through the analysis and adjustment of the controller parameters,the stability and convergence of the control performance are ensured.In addition,the robustness of tracking control of sinusoidal periodic signals is verified under the reference input noise environment.The specific research content is as follows:(1)A sinusoidal equivalent reconstruction method is designed to realize tracking control of periodic signals.Introduce a low-pass filter and the controlled object in series to combine them into multiple first-order inertial links to excite the sinusoidal characteristics,and obtain a set of unmeasurable sinusoidal signals with a cascade relationship;under the condition of known frequency,the special standard form of The auxiliary filter and the parameters are equivalently reconstructed,and the tracking control of the sinusoidal signal is realized by the reverse recursion.(2)For high-order systems,the use of standard auxiliary filters will increase the order of the controller,and the parameters are not easy to adjust.The relationship between the output of the auxiliary filter and the desired sinusoidal signal is converted into a diagonal form using appropriate coordinate transformation.This method increases the degree of freedom of parameter adjustment,and realizes the reduction of the order of the system,which can improve the rapidity of the tracking performance.Since the relationship between the sinusoidal frequency and the auxiliary filter is given,this method can be introduced into the design problem of time-varying frequency sinusoidal tracking control.(3)The robustness of the tracking control under the reference input noise environment is verified,the regular sinusoidal signal is tracked,and the unmodeled signal is suppressed.Using Lyapunov’s theorem,the relationship between controller parameters and system stability is given,and the condition of always final bounded characteristic is satisfied under the reference input noise environment.This design method makes full use of system information and can ensure strong robustness in the environment of uncertain reference input.