The Robust Tracking Design For Second-Order Dynamical Systems

Second-order dynamical systems exist widely in robot, aerospace, and many other fields. And a lot of robot’s work can be described as a model tracking problem, so the study of model tracking control for second-order dynamical systems has certain theoretical and practical value. Due to the simplification, interference from outside and the uncertainty of the controlled object during the modeling process, it is necessary to discuss the robustness of model tracking control.The basic knowledge for robust model tracking based on a parametric approach is introduced in the paper. The parametric solutions for the second-order Sylvester matrix equations are given, then these parametric solutions are used for eigen-structure assignment of the second-order dynamical systems based on PD state feedback controllers, and all of controllers are provided, then the robustness of eigen-structure assignment can be realized by selecting proper free parameters.This thesis mainly focuses on the study of the robust tracking design problem for second-order dynamical systems based on a parametric appproach. Concerned with a second order dynamic system with disturbance, firstly, the researcher puts forward the robust model tracking problem, then based on the parametric PD state feedback controller form, existence conditions and the complete parametrical solutions of gain matrix for second-order dynamical systems are given, finally, disturbance attenuation of closed loop control system is realized by minimizing H 2 norm of the transfer function from disturbance to the tracking error.In order to further facilitate the model tracking design for second-order dynamical systems using a parametric approach, a simulation platform which can be used for various model parameterss is constructed; this can help to realize the interactive object parameter setting between the user and the computer. In this paper, the author firstly presents the system structure and design idea of simulation platform, then establishes simulation modules in MATLAB simulink 7.1, which is based on the theory of second- order dynamical system model tracking, finally, based on MATLAB GUI and MATLAB simulink, this simulation interface is implemented.In the end, the researcher studies the tracking control for two degrees of freedom manipulator. Firstly, the nonlinear dynamic model of the two-degree of freedom manipulator is established, then a dynamic model is piecewise linear into second-order dynamic system on the seven selected feature points, finally the model tracking controller of two-degree of freedom manipulator is provided, simulation results show the validity of the proposed method.