Double Inverted Pendulum Simulink Simulation Model Using LQR Control Algorithm

This Simulink simulation model implements a double inverted pendulum system controlled using the Linear Quadratic Regulator (LQR) algorithm, providing a computational framework for simulating and studying complex balancing systems. The LQR controller design involves solving the algebraic Riccati equation to obtain optimal gain matrices that minimize a quadratic cost function, balancing system performance and control effort. The model incorporates state-space representation where system dynamics are defined through matrices A (system matrix), B (input matrix), Q (state weighting matrix), and R (control weighting matrix). The Simulink environment offers an intuitive graphical interface enabling users to easily configure model parameters, adjust weight matrices, and simulate various scenarios through drag-and-drop block connections. Key functional blocks include state feedback controllers, integrators, and system plant models with real-time visualization tools for monitoring pendulum angles and cart positions. This educational and research-oriented model demonstrates practical implementation of optimal control theory, allowing users to analyze system stability margins, response characteristics, and robustness through parameter variation studies. The simulation supports both academic learning and engineering applications in control systems design, particularly for understanding LQR's role in stabilizing multivariable systems with competing performance objectives.