Adaptive Robust Control for Nonlinear Mechanical Systems With Inequality Constraints and Uncertainties

The inequality constraints, system nonlinearities, parameter uncertainties, and external disturbances are always unavoidable in practical mechanical systems. This article proposes an adaptive robust control (ARC) algorithm from the view of servo constraint following to tackle the control problem of mechanical systems subject to the above factors. For the inequality constraints, a creative diffeomorphism which could convert the two-sided bounded state variables to the unbounded ones is explored, which could render the transformed nonlinear system free from inequality constraints. For the system uncertainties, a leakage-type ARC algorithm is developed, which could render the system the practical stability. The permanent magnet linear motor (PMLM) system is utilized as a typical application to verify the proposed state transformation and ARC approach. Numerical simulations show that the displacement of the PMLM system could well track the desired trajectory without violating the given bound line.