Fixed-Time Control of the Lifting Axis of a CNC Machine Using a Permanent Magnet Synchronous Motor and a Fixed-Time Nonlinear Observer

This paper introduces an adaptive fixed-time position controller (AFxTPC) designed for the lifting axis servo mechanism of a computer numerical control (CNC) plasma machine. It integrates a permanent magnet synchronous motor, gearbox, and ball screw into a unified electromechanical model. The proposed AFxTPC combines a fixed-time terminal sliding surface function with adaptive fixed-time sliding mode control to achieve fixed-time convergence, precise tracking, and robustness in the presence of parameter uncertainties. A specially designed reaching law guarantees accurate trajectory tracking, while the fixed-time terminal sliding surface function effectively minimizes chattering near the sliding manifold. Importantly, a novel fixed-time nonlinear disturbance observer is developed to simultaneously estimate the unmeasured system states and lumped disturbances in real time within a guaranteed initial-state-independent settling time. These estimated values are explicitly fed back into controller for active disturbance compensation. The stability of the overall closed-loop system is rigorously established using Lyapunov stability theory. Simulation results demonstrate that the proposed observer-based controller achieves superior performance compared with conventional proportional–integral–derivative (PID) and standard sliding mode controllers. It exhibits zero steady-state error, reduced overshoot, minimal chattering, and strong robustness over a wide range of operating conditions.