Optimal Dynamic Inversion: Towards Safety, Reliability and Performance with Application to the Active Magnetic Bearing System
- Author(s): rouhani, shahin
- Advisor(s): Tsao, Tsu-Chin
- et al.
Rotating machinery is commonly used in mechanical systems, including machining tools, aircraft gas turbine engines, and other industrial applications. However, the synchronous vibration due to the rotor mass unbalance is the common disturbance source encountered in rotor operations. Unbalance occurs when the rotor's inertia axis does not match its axis of geometry. Given the cost and difficulty of the perfect balancing and the current trend for high-speed operations, which is directly correlated with the greater centrifugal unbalance forces, vibration control is essential in improving achieving longer bearing, spindle, and tool life in high-speed machining. As opposed to conventional ball bearings, Active Magnetic Bearings (AMBs) provide both the contact-less support and the possibility for applying real-time force to regulate the rotor-dynamic behaviors. This additional control facility allows the rotor to spin around its principal axis of inertia if a sufficient air gap exists between the rotor and housing. Consequently, by annihilating the rotor's centrifugal force, the rotor vibration dramatically decreases and no reaction forces are transmitted to the housing. Beyond the functionality of AMB in reducing the rotor vibration, the aspects of safety and reliability have become important in all rotor operations. The AMB is a highly nonlinear and open-loop unstable system, and therefore it is common that the control system includes different controllers, tailored for different regimes of the operating conditions. However, the stability of the entire control system depends on the flawless operation of its sensors and actuators. Otherwise, the malfunctioning of any system components may disturb the stability of the supported rotor resulting in damage to the whole system. Hence, to ensure the safe operation and reliable performance of AMB, an online Fault Detection and Isolation (FDI) scheme is necessary to identify the faulty components and safeguard the system to remain in a safe region when faults are detected.
Given the inherited cost and complexity of adding redundant physical components, this dissertation presents a novel model-based FDI scheme for the AMB based on analytical redundancy by integrating two linear estimators called the Game-Theoretic Detection Filter (GTDF) and the Unknown Input Observer (UIO). Optimal inversion filters for both estimation and compensation are also introduced for the unified framework of the integrated fault detection, estimation, and Disturbance Observer-Based Control (DOBC) that safely switches between controllers when faults are detected. By extending and exploiting the Youla parameterization of stabilizing controllers, where the robust feedback control, the fault detection, and DOBC are realized by a bank of full-order state observers running in parallel, the controller in each regime always stabilizes the AMB. Lastly, a novel multi-variable Adaptive Feedforward Control (AFC) scheme featured by optimal delay-inversion-based compensation is proposed and implemented for its premium on stability and its simplicity in selecting the delay length as the single design parameter for the multi-variable controller to suppress the synchronous vibrations during varying and constant speed operations.