Output Regulation Based On BLF Technology And Its Application In MEMS Torsional Micromirrors

MEMS micromirrors are optical instruments of the order of magnitude and are widely used in image scanning,optical communication,high definition projection and medical imaging.They have attracted a lot of attention in academic research and engineering applications.Scholars are hot on research.The electromagnetically driven torsion micromirror belongs to a sub-category of MEMS micromirrors.Because of its small driving voltage,fast signal response and wide scanning range,it has good application value.Therefore,MEMS electromagnetic torsion is used in this paper.Micromirrors are the subject of research.The triangular wave signal has the characteristics of uniform scanning in each scanning process.Therefore,the triangular wave signal has good performance in the application fields such as barcode scanning,so it is of great engineering application significance to solve the tracking control problem of the triangular wave signal.In the study of modern control theory,output regulation theory has always been a hot research direction.Output regulation theory is an important and practical control method to solve the tracking control problem of servo system.Therefore,this paper uses the output regulation theory as the control method,and combined with the BLF(Barrier Lyapunov function)technology,realizes the limited tracking of the triangular wave reference signal by the MEMS electromagnetic torsion micromirror.The specific research work of this paper includes the following aspects:1.Mathematical modeling of the MEMS electromagnetic torsion micromirror in the experimental platform,establish a mathematical model of the micromirror,and then use the output adjustment theory to design the internal model and feedback controller for the micromirror system.The validity of the mathematical model of the micromirror is verified in the open state of the system.2.Study the solution to a limited output regulation problem for a class of nonlinear systems.Firstly,according to the internal model principle,the output adjustment problem of the original nonlinear system is converted into the stability problem of the augmented system after adding the internal model structure.Then,the backstepping method is used to design the feedback controller,so that the augmented system realizes Lyapunov stability,and then Solve the problem of output regulation of the original system.In order to limit the tracking error of the system,the constrained Lyapunov function(BLF technology)is introduced when designing the feedback controller,so that the tracking error of the original system to the reference signal not only gradually increases to zero,but also limits the tracking error to a set limit.Within the interval,the tracking error of the system is limited and not too large.3.Using the mathematical model of the MEMS electromagnetic torsion micromirror built before,based on the output regulation theory,design the internal model structure and feedback controller for the MEMS electromagnetic torsion micromirror,and introduce the constrained Lyapunov function to make the MEMS electromagnetic torsion micromirror achieve Limited tracking of the externally input triangular wave reference signal and preventing the micromirror tracking error from colliding with the bottom spiral coil.The tracking experiment of MEMS micromirror on triangular wave is completed on the micro-mirror experimental platform,and the output adjustment theory can be used to solve the limited tracking control problem of MEMS micromirror.