Uniform ultimate bounded robust model reference adaptive PID control scheme for visual servoing

This paper proposes a uniform ultimate bounded (UUB) controller framework using model reference adaptive control for visual servoing of the ball on plate system. To address the major challenges in designing a control scheme for visual servoing applications including inter-axis coupling, exogenous disturbances, and plant perturbations due to modelling errors, a robust model reference adaptive PID control scheme using e ₁ modification method is put forward. The key advantage of this methodology is its ability to yield asymptotic stability of the closed loop system without prior information on the plant perturbations. Moreover, exploiting the Erzberger's perfect model following condition, the algorithm obtains the pseudo inverse of the system to make the system track different test trajectories. The stability and convergence of the proposed scheme are proved using Schwarz's inequality condition and Frobenius norms. To evaluate the tracking performance, two test cases namely reference following during exogenous disturbance and tracking under plant perturbations are validated. Simulation results accentuate that the proposed scheme yields satisfactory tracking response even during plant perturbation and exogenous disturbances.