introduction
The inverted pendulum system is a nonlinear, strongly coupled, multivariable, and naturally unstable system. In control processes, it effectively addresses issues in control theory such as system stability, controllability, robustness, convergence speed, servo characteristics, and tracking, making it an ideal model for testing various control theories. The Linear Quadratic Regulator (LQR) problem holds a crucial position in modern control theory. Its advantages lie in its simple control scheme, small overshoot, and fast response speed. This method can effectively control not only single-stage inverted pendulum systems but has also been successfully applied to the control of linear double inverted pendulums and bipedal robots.
This paper focuses on a single-stage inverted pendulum system, completing specific system modeling and MATLAB simulation of LQR control. By increasing the system's own disturbance and changing the weighting matrix R in the LQR controller, the simulation results show good control performance.
1. Modeling a single-stage inverted pendulum
2. Controllability Analysis of the Inverted Pendulum System
3. Single-stage inverted pendulum system LQR control
4. Simulation of LQR control for a single-stage inverted pendulum system in MATLAB environment
5. The impact of the weighting matrix on the dynamic performance of the system
The simulation results show that the settling time and overshoot have decreased, as have the rise time and steady-state error. However, the system stability is very poor, and the timing process is very noisy.
6. Conclusion
This paper presents a mathematical model of an inverted pendulum system and employs the LQR control method in optimal control to locally linearize the system. Simulation experiments demonstrate that this method is feasible and effective for the inverted pendulum system. The influence of the weighting matrices Q and R on the system performance indicators is also analyzed.
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