Robust H_∞ Control Of Inverted Pendulum Systems Based On LMI Algorithm

The inverted pendulum system is a typical uncertainty system of multi-variable, non-linear, natural unstable and strong-coupling. During the control process, it can effectively reflect many key issues of control, such as nonlinear, robustness, as well as stabilization problems. The robust H∞, control method is mostly used to research systems containing uncertainty factors, and the inverted pendulum is just the simplest mathematical model abstracting from this class of systems. Researching on the control method of inverted pendulums could provide reference for effective control of the class of systems, and the correlative fruits have wide application prospects in aerospace, robotics and other fields. Accordingly, researching on robust H∞control of the inverted pendulum system bears important theoretical significance and practical value.In the past, referring to stability control studies on the inverted pendulum system, most of controller design didn't consider the existence of many uncertainties while the system was working. In the light of this reason, the thesis put forward the robust H∞control strategy, which was applied to research the controller design method for inverted pendulum systems with uncertainties. Also, robust H∞state feedback controllers were solved with the linear matrix inequalities (LMI) algorithm instead of Riccati equation method. On the basis of introducing structures of the single, double and triple inverted pendulums, the mathe-matical models of systems were developed through the Newton kinetic and Lagrange equation methods, and state space representations were presented. And then, the paper employed the LMI-based robust H∞control method to stabilize systems, designed H∞state feedback controllers for all level inverted pendulums, and discussed robust performance of systems under uncertain factors.H∞state feedback controllers were solved with the LMI algorithm, which regards iterative times as binding conditions.This approach got a group of controllers to meet design requirements, effectively dealt with the problem that the original Riccati equation method only acquired the optimal solution satisfying a single performance indicator and achieved the multi-objective control. In the process of designing H∞state feedback controllers, the thesis summed up the selection method for the weighting matrix and proposed a basic rule:Firstly, the controller designed satisfies system performance indexes of disturbance constraint and builds up robustness of uncertainty systems. Secondly, we should try our best to make the controller simple and advance its real-time capability. Considering the characteristic that uncertainty diversification of inverted pendulum systems, the single level inverted pendulum was targeted to study system dynamic response perform-ance under cart disturbance and pendulum disturbance. In order to compare with other methods, PID approach was used for the single inverted pendulum, and LQR method was applied for the double level pendulum. As can be seen by comparing control performance, the system constructed with LMI-based robust H∞control method has better robust stability and anti-jamming, besides, controllers designed with the method further optimize system performance.