Synthesis of stable control law for ball and beam system robust to disturbances based on synergetic control theory

In the article, a method of synthesizing stable control laws for ball and beam system in the presence of disturbances is presented based on synergetic control theory. The ball and beam system is a short mechanical system, has large nonlinear properties, and is easily affected by external noise. This new approach to the design of system stabilizers is based on the synergetic control theory. When synthesizing control laws based on this theory, the desired ball position is considered invariant. With the synthetic control law, only the necessary invariant is achieved but also the asymptotic stability of the entire system is guaranteed. In addition, the control law also ensures the system is robust against external disturbances and model parameter uncertainties. Analyze the stability of the system in the presence of noise through the Lyapunov function. Simulation results with different scenarios demonstrate the correctness and effectiveness of the proposed controller.