State Space Model of a Single Inverted Pendulum with LQR Control Implementation
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We have successfully established a state-space model for a single inverted pendulum system and implemented stable control using the Linear Quadratic Regulator (LQR) algorithm. Specifically, we applied the control strategy within this algorithm by adjusting the control input through feedback of system states, enabling the system to maintain balance during motion. In the implementation process, we conducted further optimizations to the algorithm to enhance both the system's response speed and stability. The control logic is typically implemented through a feedback gain matrix K calculated using MATLAB's lqr() function, which minimizes a quadratic cost function accounting for state deviations and control effort. This successful implementation provides new insights and methodologies for inverted pendulum control research, demonstrating practical application of modern control theory with code-based solutions for real-time stabilization.
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