The Control Of Auto-Swing Up And Stabilizing Based On BVP Arithmetic For The Rotational Inverted Pendulum

As a typical unstable system with the characteristics of multi-variable and non-linear,inverted pendulum system is very popular in the research of control theory and applications,and proved to be a kind of classic experimental device in illustrating control theory. Controlsystem stability, controllability, convergence rate and anti-jamming capability can be shownthrough inverted pendulum system intuitively，and its control method has an important valuein the field of automation, so the research for inverted pendulum system has an importanttheoretical and practical significance.At first the background and current situation of the research of the rotational invertedpendulum system is introduced. The rotational inverted pendulum system model is based onLagrange equation, then the model is linearized at the equilibrium point and the linear modelis obtained. The state equation of the system is deduced. The property of the system isanalyzed and it is proved that the linear model is able to be controlled and observed at theequilibrium point.The swing-up problem of the rotational inverted pendulum is discussed, and theauto-swinging up control strategy based on BVP arithmetic is adopted. The swing-up controlprogramming from hanging to the upright position can be transformed into the two-pointboundary value problem (BVP) of nonlinear systems. According to the boundary conditionsof the swing-up process, the control torque function of Fouries series form with freeparameters is constructed. The BVP is solved with the bvp4c function in Matlab toolbox, andthe control torque sequence is obtained.The swing-up process is open-loop feedforward control essentially. In order to inhibitionparameters perturbation, the closed-loop stabilizing control is designed around the uprightposition for the rotational inverted double pendulum with unstable zero-dynamics. Thesimulation of swing-up, stabilizing and switching process illustrates the effectivity of thecontrol strategy.Finally the experimental of the inverted pendulum system is studied.The digital controlsystem is designed based on Infineon XC164CM microcontroller and its peripheral circuit isdesigned in order to control the rotational inverted pendulum. The control algorithm of swing-up and stabilizing of inverted pendulum is implemented by C language. The result ofthe experiment is analyzed and it demonstrates that the control method of swing-up andstabilizing is reasonable.