Balancing Control of Two-Wheeled Robot by Using Linear Quadratic Gaussian (LQG)

Abstract

The Optimal Control method such as Linear Quadratic Regulator (LQR) deals with both the qualities of the response and its consumed power. In such a system, LQR faces a problem with the feedback sensor, which contains a lot of noise. Therefore, this issue can be solved by combining it with the Kalman filter, called the Linear Quadratic Gaussian (LQG). This research investigated the LQG applied in the Two-Wheeled Balancing Robot. According to the obtained data from MPU6050 (Accelero-Gyro sensor), Kalman Filter was firstly designed by adjusting the matrix R and Q. In the same way, LQR was also designed by manually tuning the matrix Q(1,1), Q(2,2) and R. The results of Kalman Filter showed that while Qacc, Qgyro, and R are 0.001, 0.003, and 1, respectively, the noise of the sensor can be successfully decreased. At the same time, while Q(1,1), Q(2,2), R of LQR are set to 1650, 25, and 3, respectively, the Two-Wheeled Robot can be stabilized in the set-point with the lowest J-function (1365.86). The verification experiment indicates that the controller can maintain the system stability even when the external disturbance is present.