Research On Stability Control Of Inverted Pendulum Systems

The inverted pendulum is a typical high order systems, with multivariable, nonlinear, strong coupling, fleet and absolutely instable. It has been idiomatic method that testing the processing capabilities of control methods for instability, nonlinear, and fast systems based on inverted pendulum to scholars of control domain. In the controlling process, it can effectively reflect many key problems such as robustness and tracking in control. The control methods of pairs of inverted pendulum are also widely used in military, aerospace, robotics and other areas at the same time.In the beginning, this paper elaborates the background and development of the inverted pendulum control systems, then introduces the structure of the inverted pendulum systems, and deduces and sets up the mathematical model(state space equation) by means of dynamics and Lagrange function, analyses the controllability, observability and stability of the inverted pendulum systems through modern control theory subsequently.In order to achieve stability control of the inverted pendulum, several methods are designed. At first, PID control and fuzzy logical control are raised. Comparing with the merit and demerit of conventional PID controller based on inverted pendulum, we design a new PID controller, which obtains a PID controller for controlling the cart’s displacement and a PD controller to control the pivot angle, achieving stability control of the inverted pendulum systems. This method has a good robustness on stability control of the pivot angle. In the fuzzy control system, the dimension of input varieties of fuzzy controller is depressed by designing a fusion function using optimization control theory, and the function can reduce the rules of fuzzy sharply and solve the "rule explosion" problem effectually. The simulation result shows that the LQR-Fuzzy logical controller not only has quite good stability, but also is able to make the cart of pendulum moving to designed in advance place along orbit easily.After that, we design different variable structure control systems for the inverted pendulum with mismatched norm bounded uncertainties and matched uncertainties consisting of internal disturbance and external disturbance based on LMI. In this part, the concept of stability is introduced to ensure that all the eigenvalues of closed-loop system locating in the left of one set point, and performance index of the closed-loop system is guaranteed. Then, we design different simulation models of above-mentioned systems using Simulink toolbox in Matlab, and the simulation result show that the designed control strategy has apparent superiority.At the end of the paper, we summarize the significance of the research, the purpose of the paper and the work task. At the same time, some new methods will be raised in controlling the inverted pendulum systems to be stable.