Practical Solutions to the Non-minimum Phase and Vibration Problems under the Disturbance Rejection Paradigm

This dissertation tackles two kinds of control problems under the disturbance rejection paradigm (DRP): 1) the general problem of non-minimum phase (NMP) systems, such as systems with right half plane (RHP) zeros and those with time delay; 2) the specific problem of vibration, a prevailing problem facing practicing engineers in the real world of industrial control. It is shown that the DRP brings to the table a refreshingly novel way of thinking in tackling the persistently challenging problems in control. In particular, the problem of NMP has confounded researchers for decades in trying to find a satisfactory solution that is both rigorous and practical. The active disturbance rejection control (ADRC), originated from DRP, provides a potential solution. Even more intriguingly, the DRP provides a new framework to tackle the ubiquitous problem of vibration, whether it is found in the resonant modes in industrial motion control with compliant load, which is almost always the case, or in the microphonics of superconducting radio frequency (SRF) cavities in high energy particle accelerators. That is, whether the vibration is caused by the environment or by the characteristics of process dynamics, DRP provides a single framework under which the problem is better vii understood and resolved. New solutions are tested and validated in both simulations and experiments, demonstrating the superiority of the new design over the previous ones. For systems with time delay, the stability characteristic of the proposed solution is analyzed.