This thesis work explores the control of inverted-pendulum-type robotic systems using Lagrange dynamics, focusing on improving stability and response through advanced control strategies. Initially, a PID controller is utilized to analyze the system’s step response and disturbance reactions. Subsequently, a pole placement approach with full-state feedback is proposed, using Ackermann's formula to optimize the feedback gain matrix. Enhancements include refining the PID controller and applying state-space design techniques to better handle system uncertainties and disturbances. Practical simulations demonstrate that these methods significantly enhance system stability and response, affirming the superiority of the closed-loop state-space model over traditional control techniques.