Investigation of the stability of the control system of a self-balanced two-wheeled robot

The main characteristics of the control system are the stability and quality of regulation. A stable system always returns to the equilibrium position after the external perturbation ceases to act. An unstable system goes into overdrive after the slightest push.

A self-balancing robot has many different sensors. To maintain balance, a rotational motion sensor and an angular velocity sensor will be used. The speed of the motors can be controlled by changing the duty cycle of the pulse-width modulation. The robot model takes a voltage value as input and outputs the state of the system. At the output of the function, the value from the encoders and the gyroscope is given. The robot will stand only if a controller is developed that makes the whole system stable. The controller must ensure the stability of the robot. Since the position of the robot is unstable, in order to maintain balance, the movement of the robot must be in the same direction as the angle of the body. In modern control theory, there are many methods for stabilizing an unstable system.

This paper presents a universal approach to constructing the Lyapunov vector function, based on the geometric interpretation of the theorem on the asymptotic stability of the direct Lyapunov method and the concepts of stability. This approach allows us to represent the Lyapunov function as a potential function, and the control system as gradient systems from catastrophe theory.

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