UCLA

This dissertation presents modeling, identification, fault detection, and control of an active magnetic bearing system, and the experimental results for applications in metal cutting and dynamic vibration suppression. A high order ARX identification method conducted within stabilized feedback loops followed by balanced truncation model reduction was efficient and effective in obtaining the open loop unstable multivariable AMBS dynamic model, which agrees well with the system's frequency response data. Also the severe flexible nature of the spindle is seen in the frequency response both while stationary and spinning, which facilitates the need for robust controller design. The experimentally obtained model is augmented to include the tip dynamics by impulse hammer testing that allows for the inclusion on cutting dynamics into the overall control system.

In cutting application there are two main concerns: the tip tracking a profile and avoidance of chatter instability. Therefore, based on the identified model, a two-step optimal repetitive controller was designed for minimal error tracking. The first controller consisted of a control input weighted linear quadratic control with integral action that ensured stability, broadband performance, and robustness. Then a plug-in multivariable repetitive controller with modifications for enhanced performance and non-harmonic compensation was designed by optimal model matching that highlights the classical trade-off between robustness and performance. A cutting force model was incorporated into the overall system, and stability lobes obtained for optimal cutting conditions.

Vibration reduction is crucial in applications of magnetic bearings such as energy storage. An adaptive feedforward control was seen to be effective in reducing housing vibrations even while the spin frequency is changing. The regressors were filtered through a multivariable filter obtained from gradient descent. The adaptive controller has a linear time invariant state space representation from which the deviations of the add-on adaptive from the nominal sensitivity and complementary sensitivity can be analyzed. Experimental results did indeed show that vibrations can be reduced even while the spindle speed is changing.

The single input single output adaptive inverse control was extended to the multivariable case and demonstrated to be effective in rejecting narrow and broadband disturbances. Two formulations that can accommodate multivariable plants were considered: the receding horizon adaptive control and the decoupling adaptive control. Both methods need a multivariable adaptive filter such as RLS or LMS; in this thesis a multivariable lattice RLS filter was chosen for its numerical stability and $O(N)$ complexity. Experimental results on the magnetic bearing system show the effectiveness of both control schemes.

Lastly, there were two main results for the standard single phase boost rectifier: 1) The formulation of a linear model in the DQ domain suitable for controller design 2) A MIMO repetitive add-on controller with peak filter modification was designed using the linear model to reduce harmonics not compensated for by a nominal controller. In the process of deriving the linear model, analysis of the equilibrium points gave the boost condition for the rectifier. Experimental results proved the effectiveness of using the linear model for controller design and the repetitive controller for reducing harmonics. The methodology can be used for designing controllers that operate at near unity power factor.