Prescribed performance motion control: A control barrier function approach

Prescribed performance control (PPC) has been widely applied in motion control systems due to its ability to regulate both transient and steady-state performance through well-defined performance functions. However, its core design ideas, involving error state transformation or reciprocal nonlinear gain, can lead to invalid results under certain initial conditions, significantly restricting its practical application. To address these issues, a new motion control approach with prescribed performance is investigated using the control barrier function (CBF) technique. The tracking control problem is formulated as a quadratic programming by modifying a baseline controller subject to the proposed PP-CBF constraints, where the disturbance observer technique is employed to handle lumped disturbances, such as unknown friction and load torque. Unlike conventional PPC methods, this framework allows for initial states outside the performance envelope and mitigates potential singularity issues near the boundary. The stability of the optimization-based control policy is rigorously analyzed. Comparative experimental tests conducted on a permanent magnet synchronous motor platform illustrate the effectiveness of the proposed method in achieving the prescribed performance specifications and its adaptability to nonlocal initial conditions and suddenly added loads.