Singularity-Free Nonlinear Position Control Using Time-Varying Barrier Lyapunov Function for Permanent Magnet Synchronous Motors

Recently, controllers using the barrier Lyapunov function (BLF) are widely used to guarantee the tracking error (or state) constraint. A BLF can be defined only when the error is within a predefined boundary. Thus, overall stability cannot be guaranteed when the error exceeds the predefined boundary owing to unavoidable reasons such as external disturbance. In addition, near the boundary, the singularity problem causes the peaking phenomenon in the control input. To overcome this problem, BLF-based singularity-free nonlinear position control is designed for permanent magnet synchronous motors (PMSMs). A state-dependent boundary as a smooth function of the error is proposed to suppress the error when it exceeds the predefined boundary. When the error exceeds the predefined boundary, the proposed boundary increases according to the error. A nonlinear position controller is designed using the BLF and state-dependent boundary. The tracking error can always be controlled to be kept within the boundary by the position controller. When the tracking error exceeds the predefined boundary, the tracking error can return to the predefined boundary with the finite control input. The singularity problem can be solved using the proposed boundary which is the smooth function. A disturbance observer (DOB) is designed to estimate the disturbance. The performance of the proposed method is verified by simulations and experiments.