State feedback gain tuning for inverted pendulum in frequency domain using one-shot closed-loop transient response data

In this paper, a method to tune state feedback gain for single-input multivariable systems is proposed. The method uses only a single set of closed-loop transient plant I/O data. The I/O data in the closed-loop system are filtered by a simple high pass filter, and the frequency response of the plant is obtained with the Discrete Fourier Transforms of the filtered data. The state feedback gain is determined to stabilize the closed-loop system and to improve the control performance based on the point of view of loop shaping using the estimated frequency response of the plant. The validity of the proposed method is illustrated through an experiment on a state feedback control of an inverted pendulum with an inertia rotor.