Rotary inverted pendulum (RIP) system is an under-actuated system. The RIP system consists of a pendulum, which is rotating freely in the vertical plane. A swing-up action using a pivot arm in the horizontal plane would then result in the pendulum to achieve upright equilibrium point. This paper describes the design of double proportional-integral-derivative (PID) controls with a linear quadratic regulator (LQR) controller for the stabilisation control of a RIP system. Besides, the dynamic model of the RIP system is described too. The LQR controller was tuned using Taguchi method of design of experiments (DoE). The double-PID controller was designed using Ziegler-Nichols second method, which the LQR controller is embedded in the RIP system to improve the stabilisation performance. The effectiveness of the double-PID and LQR controller is clarified with a RIP experimentally. The proposed controller has demonstrated succeed stable the pendulum within 0.5 degrees in three seconds and the rotary arm within 22.5 degrees.

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