| Non-contact, actively controlled magnetic bearings for machine-tool spindles have the potential to satisfy the machine-tool industry's demand for high-speed, high-precision machining. However, these systems, based on electromagnetic attraction, are challenging to control because they contain inherently nonlinear dynamics that are open loop unstable. Additionally, the machine-tool operating environment contains several disturbances that excite the inherent nonlinearity of these active-magnetic bearings and, thus, limit the performance and stability of the industry standard, linear-control techniques. Typical disturbances include machining forces, rotor unbalance, eddy current forces, flexible rotor dynamics, gyroscopic loads, dynamic model parameter variations, flux leakage from electromagnet, and cross-coupling terms of the rotor dynamics. For this research, these typical disturbances are lumped into two categories: those represented by force disturbances on the levitated object: and those represented by parameter variations on the parametric system model.; To accommodate these disturbances and compensate for the nonlinear dynamics, three new control laws based on the backstepping design approach have been developed, simulated, evaluated, and implemented. These controllers are derived using a simple dynamic model of the magnetic-levitation system. formulated in the output-feedback form, which is shown to encompass not only active-magnetic bearings, but all forms of uncoupled, multiple degree-of-freedom magnetic levitation and suspension systems. The three new nonlinear controllers are compared with a benchmark, linear compensator and a standard feedback-linearization compensator using the metrics of Lyapunov stability, step-response performance, control effort, force disturbance-rejection performance, robustness to parameter variations, and cost and complexity of implementation. Experimental implementation and evaluation of performance, stability, robustness and force disturbance rejection is performed on a 1-DOF magnetic-levitation system.; The new, robust, adaptive, nonlinear control system presented in this research is shown to be both analytically and experimentally superior to the benchmark linear compensator and the standard feedback-linearization controller in stability, step-response performance, disturbance rejection performance, and robustness to mass variations. This control system is proven globally asymptotically stable within the saturation limits of the sensor and actuator. All control systems developed in this research are applicable not only to active-magnetic bearings on machine-tool spindles, but to any magnetic-levitation system including vibration-isolation systems, wind-tunnel suspension devices, precision-positioning systems, etc. |
