Design of controllers for non-linear systems has long drawn the attention of researchers especially in the fields of robotics, aerospace engineering and marine engineering. A classic example of a non-linear under-actuated control system is the balance control for a rotary inverted pendulum. Basically, the control approach for such system focusses on torque control of the servo-motor for the purpose of rotating the arm and stabilising the pendulum in its upright position at the shortest possible time. The aim of this research is to supplement and further enhance the control performance of a linear quadratic regulator (LQR) controller with focus on reduced response time and degree of oscillation of the pendulum with added robustness against input disturbance applied to the pendulum position and voltage to the motor. Initially, this thesis comprehensively analysed the LQR controller parameters based on minimal balance time of the pendulum. The LQR controller by itself produced high degree of oscillations, long balance time and poor robustness against input disturbance. As an enhancement over this approach, an adjustable gain was added to the existing LQR control structure. The results showed that for a 30° balancing control, the LQR controller with adjustable gain managed to reduce as much as 70% in the balance time and 98% in the degree of oscillation, while improved its robustness by producing faster balance time and lower oscillation upon excitation by input disturbance forces. In conclusion, the LQR controller with adjustable gain has significantly improved the control performance of the rotary inverted pendulum system
