<![CDATA[The paper focuses on the study of the Pendubot system, a classic system widely used in control research, particularly the 2-link Pendubot. This system is nonlinear with a single input and multiple outputs (SIMO) and is under-actuated. The paper addresses the challenges of applying optimal Linear Quadratic Regulator (LQR) control to Pendubot, requiring an accurate model without noise. The author proposes using a Kalman filter to estimate the system's state variables and mitigate the impact of noise. Subsequently, the LQR controller is applied based on the estimated state variables. Thus, the study suggests an integrated approach combining Kalman filtering and LQR control to enhance Pendubot's performance under real-world conditions. The combination of LQR and Kalman forms a new controller called LQG, which addresses issues encountered by standalone LQR and improves the system's optimal performance. The paper focuses on evaluating the performance of LQR and LQG controllers through system simulations with the input being the motor force applied to the first bar of the Pendubot system in MATLAB Simulink software.]]>
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