Application of the PID controller for objects with a dual integrator

Currently, traffic management of autonomous transport systems requires precise and stable regulation of objects, the dynamics of which can be represented by a second-order model with acceleration integration. The dual integrator is considered as such an object, describing the relationship between the control action (acceleration) and the position of the platform. Despite the simplicity of the structure, the synthesis of a regulator for such an object remains a non-trivial task due to marginal stability, accumulation of errors, and high sensitivity to external disturbances. The paper shows the use of a classical PID controller to control an object with dynamics, discusses the features of its tuning, the limitations of Ziegler-Nichols type methods, and the need for manual or adaptive adjustment of coefficients. An example of practical implementation on a two-wheeled self-balancing robot using an inertial sensor and a microcontroller is given. The results obtained demonstrate the effectiveness of the PID controller for stabilizing an unstable object, ensuring a reduction in static error, resistance to external disturbances, and the correct formation of transients. This work can serve as a basis for further improvement of control systems and the development of intelligent control algorithms.