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.

This paper presents a practical control strategy for motion control of a pneumatic muscle actuated the system. Pneumatic artificial muscle (PAM) exhibits strong nonlinear characteristics which are difficult to be modeled precisely, and these characteristics have led to low controllability and difficult to achieve high precision control performance. This paper aims to propose nominal characteristic trajectory following (NCTF) control system, which emphasizes simple design procedure without the need of exact model parameters, and yet is able to demonstrate high performance in both point-to-point and continuous motions. However, the conventional NCTF controller does not offer a promising positioning performance with the PAM mechanisms, where it exhibits large vibration in the steady state before the mechanism stopping and tends to reduce the motion accuracy. Therefore, the objective of this study is to improve the conventional NCTF controller by removing the actual velocity feedback to eliminate vibration problem, added an acceleration feedback compensator to the plant model, and a reference rate feedforward to solve low damping characteristic of the PAM mechanism simultaneously improve tracking following characteristic. The design procedure of the improved NCTF controller remains easy and straightforward. The effectiveness of the proposed controller is verified experimentally and compared with the conventional NCTF and classical PI controllers in the performances of positioning and continuous motion. The improved NCTF controller reduces the positioning error up to 90% and 63% as benchmarked to the PI and conventional NCTF controllers, respectively, while it reduces up to 92% (PI) and 95% (NCTF) in the tracking error. INDEX TERMS Motion control, NCTF control, nonlinear system, pneumatic artificial muscle, practical controller.

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