Adaptive optimal control of active balancing systems for high-speed rotating machinery

Mass imbalance is a major source of harmful vibration of high-speed rotating machinery in a variety of industries. The precision and reliability of relatively fragile high-speed machine tools are limited by unbalance from various sources. Unbalance-induced vibration in high-speed turbomachinery contributes to significant production losses due to unscheduled shutdowns of petro-chemical manufacturing facilities and land, air and sea-based power generation plants. Off-line balancing techniques cannot address these problems due to changing process conditions. State-of-the-art active balancing systems typically require a priori modeling of plant dynamics and are not necessarily robust for processes with time-varying and nonlinear dynamics.; The research presented here consists of the development, analysis, and experimental validation of new adaptive optimal control approaches for achievin steady-state rejection of unbalance-induced vibration. Off-line balancing and active control methods are reviewed and modified as the basis for deriving adaptive control laws. A single-plane adaptive control law is derived that incorporates on-line system identification. This is accomplished by taking advantage of the active balancer's inherent capability to perturb the rotordynamic system. Experimental results illustrate the adaptive control performance for certain types of time-varying and nonlinear plant dynamics. An automatic tuning method is developed that adjusts adaptive and supervisory control parameters during control to enhance control performance. Experimental results confirm that this “auto-tuning” method eliminates trade-offs inherent in fixed-parameter adaptive control and simplifies end-user operation. A weighted least-squares optimal control strategy is derived for multiple-plane active balancing systems. Control effort and rate of change penalty terms are shown to enhance stability robustness of traditional non-adaptive control. The single-plane on-line system-identification method is extended for use with multiple-plane systems and a “dithering” method developed to ensure non-singular estimation during adaptive control. Tests on a flexible rotor test rig demonstrate the advantage of this adaptive optimal control over the traditional non-adaptive approach. Experimental results validate the effectiveness of the multiple-plane “influence coefficient” control approach for a turbomachine in actual operating conditions.