Inverted Pendulum Singular Perturbation Method For Modeling And Control

In project application, because the actual system controls request more precisely, also set more and more high request in the modeling accuracy, especially some small parameter perturbation such as the small time-delay, the inertia, the capacity or the conductance and so on also received by the related researchers' attention, they no longer neglected these small parameters to reduce the order to simplify the model like formerly. The singularly perturbation model is an efficacious method to solve this problem which is widely applied in controller design of the robot, the flight vehicle and so on.As a high-order, multivariable, nonlinear system, inverted pendulum's characteristic value distribution and the frequency range characteristic are similar to the singularly perturbed system's characteristic. This paper established inverted pendulum's singularly perturbation model based on the foundation of its general linearization model, and the following work has been done:(1) Analyzed inverted pendulum's model's mechanism & characteristic, gave single inverted and double inverted pendulum's singularly perturbation model by its characteristic.(2) Applied optimal control in a quadratic form and the state feedback H_∞control method to single inverted and double inverted pendulum's general linearization model separately to carry on controller's design and the simulation.(3) Based on single inverted and double inverted singularly perturbation model which is established, applied singularly perturbation method, designed inverted pendulum's optimal control in a quadratic form and the state feedback H_∞controller.(4) Compared the above two different methods of controller design in view of control effect, may see the method which applied singularly perturbation speed decomposes, through the boundary layer revision, improved the system's slow variable control effect.(5) Carried on the substantial control according to the simulation parameter on single inverted pendulum system, the experimental result and the simulated data were consistent, proved accuracy of the simulation conclusion.