Multiple periodic disturbance rejection techniques for vibration isolation

Methods are developed to cancel the effects of time-invariant or slowly time-varying periodic disturbances, and experiments are performed on the Ultra Quiet Platform (UQP), a Steward Platform whose purpose is to isolating sensitive equipment on a spacecraft from vibrations due to slight imbalances in rotating equipment such as momentum wheels, reaction wheels, or control moment gyros. The time-domain Clear-Box disturbance rejection algorithm creates a disturbance-free difference equation model of the system from disturbance-corrupted data. Then it identifies the periodic disturbance in the time domain, and computes the steady-state periodic input that will cancel it. In the first part of this dissertation the frequency domain analog of this algorithm is generated and its advantages and disadvantages are assessed. In addition, an iteration loop is introduced that aims to eliminate any errors that remain due to errors in the identified model and identified disturbance. This method has the advantage over many repetitive control methods that it can handle multiple unrelated periodic disturbances. Furthermore, to handle situations where actuator saturation limits one's ability to cancel all disturbance components, an intelligent decision process based on quadratic programming is developed.; The Multiple Error LMS algorithm is a popular algorithm for eliminating error in control systems from periodic error sources. It has the disadvantage that one needs a disturbance correlated signal, which implies that one should install a sensor on each vibration source. The second part of this dissertation investigates the use of disturbance identification to supply the disturbance-correlated signal, without needing extra sensors. Experiments are performed on the UQP. It is shown that properly implemented the disturbance identification approach can give good results with Multiple Error LMS. The disturbance identification experiments use the Stewart platform geophone velocity sensors, which contain measurement noise, and these results are compared to results using a noisy disturbance source that is commanded to a shaker in the experiments. It appears that performance using the derived disturbance correlated signal can be roughly comparable to the use of a separate sensor for the purpose.; The third part of the dissertation considers repetitive control and develops methods of producing smooth updates and creating greater continuity in the control action. Repetitive control iteratively adjusts the command to a feedback controller in order to eliminate error caused by periodic disturbances. It is seen that repetitive control laws typically produced step or slope discontinuities in the command, and these can produce transient effects that slow the convergence processing, or influence the final error levels achieved. Here methods of eliminates step and slope discontinuities in the control action are developed, and simulation results show that there is significant improvement in performance. The methods include turning on the repetitive control at an appropriate time, waiting for transients to decay and for a zero error crossing before starting the next repetition updates, phasing in the learning, and phasing in each repetition.