State-Constrained Adaptive Control for Precision Air-Bearing Active Vibration Isolation System

Abstract

This paper addresses the control challenges of air-bearing active vibration isolation systems with state constraints, multi-variable coupling, strong nonlinearity and parametric uncertainties. A novel adaptive control scheme based on barrier functions and state transformation is proposed. The scheme first transforms physical state constraints into mathematical constraints by using a constructed barrier function to ensure the system operates within safe boundaries. Combined with a dynamic surface control (DSC) architecture and a single-parameter adaptation mechanism, the complex multiple parameters uncertainty problem is simplified into online estimation of a single scalar parameter, which effectively reduces computational burden and implementation difficulty. Theoretical analysis shows that the proposed control strategy ensures boundedness of closed-loop signals while achieving high precision output tracking and strictly satisfying all state constraints. Finally, simulations and experiments verify the effectiveness and practicality of the method. Results demonstrate that the system output can track reference trajectories quickly and accurately under parametric uncertainties and external disturbances. The load position and air chamber pressure states strictly remain within preset constraints. The low-frequency vibration isolation performance is significantly improved. Note to Practitioners—This paper addresses a practical challenge in precision engineering: designing a control method for air-bearing vibration isolation systems while ensuring critical physical quantities never exceed safe constraints. Violating these constraints, such as load position and chamber pressure, can cause mechanical damage or system instability. The proposed method offers a practical solution by using a barrier function to transform constrained states into unconstrained variables. Keeping these new variables bounded automatically guarantees that original physical states remain within safe regions. To enable real-time implementation, two simplifications are introduced. First, DSC avoids complex backstepping derivations, making the control law easier to code. Second, a single-parameter adaptation mechanism aggregates multiple uncertainties into one scalar updated online, drastically reducing computational load and tuning effort. Validated on a physical three-degree-of-freedom platform, the method achieved accurate tracking, strict constraint satisfaction, and superior low-frequency vibration isolation compared to PID control. For practitioners, implementation requires only defining state bounds and tuning a small set of gains. A reliable and computationally efficient solution for high-precision systems operating under physical constraints is provided.