Linear Flexible Two Inverted Pendulum Optimal Control Study

Inverted pendulum is an ideal experimental platform for the automatic control theory, and many abstract concepts such as the stability, controllability and anti-jamming capability of the control system, are available through an intuitive inverted pendulum. Therefore, since the 20th century,50 years the inverted pendulum has become a classic tool in a control laboratory.Inverted pendulum is a typical non-linear, high-order, strong coupling, instability and under-actuated system, to study the precise control of an inverted pendulum is of great value on the complex objects in industrial production, so simulation or physical control of inverted pendulum experiment is a typical program to test a control theory or method in the control field.Flexible connections inverted pendulum is a typical nonlinear self-unstable system, it is more complex and difficult to control than the linear inverted pendulum. It introduces a new free-running link in the linear inverted pendulum system:free spring system. As the frequency response of the closed-loop system is constrained by the oscillation frequency of the spring system, the design limitations of the system controller are increased.In this paper introduced briefly the inverted pendulum system and robust control theory. Then explain in detail the H∞control theory. The GUGAO GLIP2011 Linear flexible inverted pendulum is studied by using Lagrange's equation to establish a mathematical model of planar inverted pendulum, by expanding and linearization the model at its vicinity of equilibrium position following the Taylor series, the linear model in two orthogonal directions of the system has been obtained. Both the system's H∞state feedback controller are established based on the linear inverted pendulum model, and the MATLAB simulation is conducted. The compared simulation results of the LQR (Linear Quadratic Regulator) control and an actual control curve of the flexible inverted pendulum is also given. In the physical control of the experiment, the balance control of one-level and the two-level flexible inverted pendulum, and achieved satisfactory results. Then in-depth study of the working principle, the external interface, instruction programs and program design methods of GUGAO four-axis motion controller works GT-400,which has laid a good foundation for the further development and research of flexible inverted pendulum.