Minimization of power losses in active magnetic bearing control

A solution to the problem of AMB control with reduced electrical power losses will be presented in this thesis. The proposed control solution will be founded on the integrator backstepping technique, which decouples the rotor stabilization problem from the bias flux design problem. It further allows for the easy redesign of the control law to compensate for uncertainties in the AMB system. A class of nonlinear controllers will be developed that reduces the AMB power losses in comparison to standard fixed-bias controllers, while containing no control singularity. Control laws will be presented for the standard AMB operating mode where both electromagnets are active at all times, as well as for the “energy-saving” operating mode where only a single electromagnet is active at any given time. The main contribution of this work is the development of a smart bias flux, and function of the rotor position and velocity. General conditions motivated by physical and mathematical properties are developed for the functional form of the bias, ensuring the reduction of power losses and the avoidance control singularities without affecting the closed-loop system stability. Simulation results also illustrate the interesting role the smart bias plays in stabilizing the rotor. Note that while the power loss discussion in this thesis is focused on ohmic losses, the proposed control strategies also help reduce eddy current- and hysteresis-induced losses due to their proportionality to the magnetic flux

On the stability of the Kuramoto model of coupled nonlinear oscillators

We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value, the synchronized state is locally asymptotically stable, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.Comment: 8 Pages. An earlier version appeared in the proceedings of the American Control Conference, Boston, MA, June 200

Space-Time Sampling for Network Observability

Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and less fragile to where and when samples are collected. It is shown that under what conditions taking coarse samples from a network will contain the same amount of information as a more finer set of samples. Our goal is to estimate initial condition of linear time-invariant networks using a set of noisy measurements. The observability condition is reformulated as the frame condition, where one can easily trace location and time stamps of each sample. We compare estimation quality of various sampling strategies using estimation measures, which depend on spectrum of the corresponding frame operators. Using properties of the minimal polynomial of the state matrix, deterministic and randomized methods are suggested to construct observability frames. Intrinsic tradeoffs assert that collecting samples from fewer subsystems dictates taking more samples (in average) per subsystem. Three scalable algorithms are developed to generate sparse space-time sampling strategies with explicit error bounds.Comment: Submitted to IEEE TAC (Revised Version