Research And Application Of Model Predictive Control For A Class Of Lagrange Systems

In the field of Industrial Control,Lagrange Mechanics method has the excellent model description and system adaptability,while the emerging Model Predictive Control(MPC)theory has the distinct control effect and robust performance,therefore,the combined design of them has gradually become a research hotspot in academia.But most of the relevant theoretical studies are in the initial stage,and many research results are not mature.Accordingly,this paper presents the MPC schemes for two Lagrangian systems,which are practical and typical in modern industry,furthermore,the feasibility and stability of the MPC scheme have been verified through the simulation experiment.In this paper,the Lagrange Mechanics method is firstly introduced by comparing the traditional Newtonian Mechanics method,which illustrates the superiority of the Lagrange Mechanics method in the modern industrial machinery system.From the cartesian coordinate system to the generalized coordinate system,the general expression form of the Lagrange mechanical function is deduced on account of the motion particle system.Based on this,by way of the analysis of the fractional viscoelastic properties of Magnetorheological Damper(MRD),this paper establishes a Lagrange dynamic model with fractional characteristics for MRD.In addition,by means of the study of the flexible structural characteristics,a Lagrange dynamic state-space model with flexible features is designed for the flexible manipulator system,which can validate the universality and practicability of Lagrange Mechanics method.As for the design features of the fractional Lagrangian dynamic model,the basic concepts and related characteristics of fractional calculus are introduced,and by considering two common types of fractional numerical approximation strategies,this paper employs the Oustraloup filtering algorithm to achieve the rational function approximation to the MRD's fractional model.Based on the fractional Lagrange approximation model of MRD,the vibration prediction control scheme and numerical simulation experimen t of MRD are implemented in the paper.Moreover,through the comparison of unconstrained and input/output constrained experimental results,this paper analyzes the feasibility and control effect of the proposed MPC scheme.On account of the sampling discretization theorem,the discre-time prediction controller and the stability derivation of the MPC scheme for the flexible manipulator system are completed.What's more,the simulation results are designed and analyzed by comparison with PID and LQR methods,which can testify the stability and feasibility of the application of MPC scheme in Lagrangian system.In summary,the idea of combining MPC scheme and Lagrange Mechanics method is definitely feasible.Moreover,the design proposal of this paper can dealt with the uncertainty and randomness accompanied by the process of industrial control timely,which significantly improves the robustness and dynamics of the controlled system.Consequently,while improving the control effect,the Lagrangian system's online optimization ability and anti-interference ability can be ameliorated remarkably by means of the application of MPC scheme.