Analysis and Control of Ball Displacement in Air Levitation Experiment by Using a Disturbance Rejection-Based Technique

This work describes the application of a disturbance rejection technique for controlling ball position in an air levitation experiment. The prototype consists of a light-mass ball that moves freely inside a vertical transparent cylindrical tube. The control objective is to force the ball position to track a desired vertical trajectory by defining a voltage control law for an air blower actuator. The system’s nonlinear mathematical model is presented and discussed. To deal with model uncertainties, nonlinearities and non measurable states, the design and the analysis of a Modified-Plant Active Disturbance Rejection Controller (MP-ADRC) are performed. ADRC-based controllers have been studied for decades, and their main characteristics are the use of an extended state observer (ESO) to estimate the non-measurable signals of the plant and a state-feedback control law in standard form fed by that observer. The key advantage of the adopted variant MP-ADRC, which contrasts with the basic methodology, is that it only requires knowledge of the sign $(+/-)$ of plant’s control coefficient, rather than its exact value. This improves the well-known robustness property of the method, allowing its application to a general class of dynamical systems with uncertain parameters. By adopting and using such a control methodology, the resulting closed-loop scheme exhibits several advantageous characteristics: (i) it is robust to parametric uncertainties; (ii) it can compensate for external disturbances and unmodeled dynamics; (iii) it can deal with plants with slowly time-varying control coefficient; (iv) even for nonlinear plants, mathematical analysis using Laplace transform can always be performed. This work also presents and discusses simulation and experimental results obtained with the proposed control strategy applied to a real air levitation prototype.