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Title: Stabilizing Parameterization for Uncertain Delay Systems
Keywords: Delay processes, Stabilization, Stability robustness, Stabilizing parameter ranges, PID
Issue Date: 13-Dec-2013
Citation: LE BINH NGUYEN (2013-12-13). Stabilizing Parameterization for Uncertain Delay Systems. ScholarBank@NUS Repository.
Abstract: The focus of this thesis is on stabilizing parameterization for uncertain delay systems. Such a problem admits no analytical solutions in general. The first part of the thesis deals with the problem of determining the stabilizing controller gain and plant delay ranges for a strictly proper process with delay system in feedback configuration. The condition of the loop Nyquist plot?s intersection with the critical point is employed to graphically determine stability boundaries in the gain-delay space and stability of regions divided by these boundaries is decided with helps of a new perturbation analysis of delay on change of closed-loop unstable poles. As a result, all the stable regions are obtained and each stable region captures the full information on the stabilizing gain intervals versus any delay of the process. In the second part, the aforementioned problem for a bi-proper process is investigated. A bi-proper process is rare but causes great complications for the method, due to the new phenomena that do not exist for a strictly proper process, such as a non-zero gain at infinity frequency, which may cause infinite intersections of boundary functions within a finite delay range. A detail study into the properties of boundary functions from such processes shows that finite boundary functions are sufficient to determine all stable regions for finite parameter intervals. The formula is given for calculating this number. Moreover, the algorithms are established to find exact stabilizing gain and delay ranges, and they are illustrated by many kinds of processes including stable/unstable poles and minimum/non-minimum zeros. These new results, together with those in the first part, provide a complete solution for numerical parameterization of stabilizer for a general delay SISO process in terms of proportional control gain and delay. In the third part, the concept of stability boundaries is extend to the parameterized stability boundary, which transform boundary curves into boundary bands when one of the controller gains varies in a range. This eliminates the difficulty of using 3D graph to solve the problem with 3 parameter while maintaining the advantage of 2D method. The concept of boundary band is also useful for the robust problem, when the plant is not fixed but contains uncertainties. Finally, the graphical method is also extend to two-input two-output processes with time delay.
Appears in Collections:Ph.D Theses (Open)

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