| The inverted pendulum is a typical multivariable,high-order,nonlinear,and strongly coupled absolutely unstable system.Its degree of freedom is greater than the number of drives.The under-actuated pendulum is controlled by the coupling of the pendulum rotation pair.The control of the inverted pendulum can intuitively reflect the anti-interference,follow-up,robustness and other issues in the control system,and it has become the preferred platform for research and testing of control theory and control methods.This paper studies the pendulum stabilization control method of the first and second linear inverted pendulum;researches and analyzes the nonlinear dynamic characteristics of the second-level inverted pendulum under harmonic excitation;designs and builds the inverted pendulum actual test experimental system,completes the system The hardware design realizes the effective control of the inverted stabilization of the first-stage inverted pendulum system,and compares and analyzes the experimental results.The main research content and work of this thesis are as follows:(1)Deduced the nonlinear dynamic model of the first and second linear inverted pendulum system.After linearization,the transfer function model and state space model of the first linear inverted pendulum system are deduced.The two-level linear inverted pendulum system The state-space model of,and the quantitative method is used to analyze the open-loop stability and controllability and observability of the first and second linear inverted pendulum systems.(2)Two controllers,PID and LQR,are designed for the stable pendulum control of the first-stage linear inverted pendulum system,and the effectiveness of the designed controller is verified through simulation.At the same time,the relationship between the changes in the value of the weighting matrix Q and R and the dynamic characteristics of the first-stage linear inverted pendulum system in the performance indicators of the LQR control strategy is studied.After that,the LQR stabilization control controller of the two-stage linear inverted pendulum was designed,and the effectiveness of the designed controller was verified through simulation.(3)The bifurcation and chaotic motion of the harmonic motion of the double inverted pendulum system are studied and analyzed,and the phenomenon of the inverted pendulum system entering chaos and bifurcation is visually studied by using analog numerical methods.From the time response diagram,phase diagram,bifurcation diagram and Lyapunov exponent diagram of the system,the influence of the system dynamics under a single parameter change is analyzed.The dynamic characteristics of the dual-parameter matching of the system are analyzed,and the dualparameter matching phase diagram of the system is obtained.(4)With the computer+motion controller+AC servo motor as the control core,the inverted pendulum physical experiment system was designed and built,the realtime human-computer interaction program was developed on the computer,and the inverted pendulum control algorithm was written in the motion controller.Finally,after debugging,the two controller algorithms of PID and LQR are successfully implemented to control the first-stage linear inverted pendulum system. |
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