A Contraction Theory-Based Adaptive Robust Control for the Trajectory Tracking of a Pneumatic Cylinder

Adaptive robust control (ARC) has been applied to pneumatic systems successfully for its excellent performance and strong robustness. Although many researchers are already working on studying of the ARC, the stability analyses of these works are performed by the Lyapunov method. The contraction theory is a new proposed "differential" Lyapunov-like analytic tool for the nonautonomous nonlinear system. It can provide a more convenient analysis and richer design toolbox of the nonlinear system than Lyapunov method. This article intelligently brings the philosophy of contraction theory into the ARC design framework to form a contraction theory-based ARC (CT-ARC) for a pneumatic servo system. The proposed method offers more design choices than the traditional ARC. In addition, a command filter is employed to acquire the differential signal of the virtual control law. The stability analysis of the whole system is presented elegantly by the contraction theorem with consideration of the estimation error of the command filter. Furthermore, exponential convergence of the closed-loop system can be derived under specific conditions. Finally, various experiments for the trajectory tracking control of a pneumatic cylinder demonstrate the efficiency of CT-ARC.