Abstract
ABSTRACTThis paper proposes a new control strategy to the position control of the ball in the ball and beam system by adopting an active disturbance rejection control (ADRC). ADRC is composed of a tracking differentiator (TD), an extended state observer (ESO), a nonlinear state error feedback control law (NLSEF), and a disturbance compensation device (DCD). The ESO observes and tracks the position of the ball and the direct current (DC) servomotor in real time. The total disturbance of the system can be expanded and amplified, and can also be effectively compensated in real time to suppress interferences by the ESO. The procedures of research are as follows. First, the model of the ball and beam system, including the motion equation of the system and the DC servomotor, is established. Second, ADRC is designed and applied to the ball and beam system and the DC servomotor. Third, the control model of the ball and beam system is built on the basis of ADRC. Finally, the ball position of ADRC is simulated and verified. The results show that the ball and beam system based on ADRC exhibits better performance than the proportion integration differentiation controller.
Highlights
The ball and beam system is regarded as a typical nonlinear system
In studying the balance of goods carried by mobile robots, performing attitude control of space vehicles, nonlinear control of actuators, and position control of spacecraft in space engineering can all use the model of the ball and beam system as the control object
disturbance compensation device (DCD) is used to compensate the total disturbance of the position angle of the direct current (DC) servomotor controlled by the inner loop and the total disturbance of the ball and beam system controlled by the outer loop
Summary
The ball and beam system is regarded as a typical nonlinear system. Its nonlinearity is mainly manifested in: 1, Dead zone and saturation characteristic. 2, DC servomotor and pulley drive non-linearity. 3, Discontinuity of position measurement. 4, Nonlinear resistance. Various intelligent control methods, such as adaptive and feedback control of fuzzy dynamic systems (Amjad, Kashif, Abdullah, & Shareef, 2010; Chang, Chan, Chang, & Tao, 2011), were applied to the ball and beam system These studies elaborated the procedures that involved certain inhibitory effects on the external interference of the system, but the influence of internal interference was not fully discussed. The position angles of the DC motor of the inner loop and the ball of the outer loop are used as controls This scheme can help solve the contradiction between overshoot and speed, and it can suppress the influence of interference on the control of the ball and beam system. The final conclusion is obtained by comparing the simulation results
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