Research On The Control System For Multistage-Planar Inverted Pendulum

Inverted pendulum system is a typical example of nonlinear unstable system. Except for the feature of nonlinear, it has the characteristics of high-order, multivariable, close coupling, underdrive etc. By inverted pendulum control systems, many abstract concepts in control the-ory could be shown intuitively.The research on inverted pendulum systems could be widely used in the field of biped robot walking, semiconductor, the gesture control in the rocket lau-nching process, missile intercept con-trol system and so on.The main works of this paper are as following:1.It firstly introduces the background, significance and classification of inverted pendu-lum, and analyzes its research status.Then, the paper briefly introduces present status of opti-mal control theory.2.On the basis of in-depth research on existing achievements of inverted pendulum cont-rol system at home and abroad, this paper derives the model of n-order planar inverted pendu-lum and the uniform dynamic equation through adopting the methods of Lagrange Equation and Holistic modeling. Upon that, we study the single and double planar inverted pendulum intensively. In the neighborhood of balance point, nonlinear model of system is linearized and state-space equation is achieved.Besides,the controllability and observability is analyzed in this paper.3.As is known to us, the bigger is the initial angle of rocker which the inverted pendulu-m system can control,the better is the performance of the controller. So, this paper gives a re-ference index by which we can distinguish the superior inverted pendulum control system. On this basis, this paper adopts closed loop program in place of Simulink simulation using Matla-b tool to find out the optimal solution of parameters of LQR algorithm applied in the linear d-ouble inverted pendulum.