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Title: Stabilization and control of unstable time delay systems
Keywords: unstable processes, time delay, stabilization, control performance, PID controller
Issue Date: 16-May-2012
Source: LEE SEE CHEK (2012-05-16). Stabilization and control of unstable time delay systems. ScholarBank@NUS Repository.
Abstract: Control theories and designs for stable delay-free systems have been well developed in research society and widely adopted in industry. Study of time delay systems remains as a hot research topic while the unstable systems are gaining great attention from researchers recently. Control of unstable delay systems is the most challenging and difficult case and becomes a research frontier in the process control, and its progress is yet at a preliminary stage. Unlike stable system, simply detuning the controller is not a trivial solution to achieve stability of the closed loop. PID and lead-lag controller are the two most popular type of the controllers used in industrial control (often in single loop configuration). In this thesis, Nyquist stability criterion combined with some algebraic analysis are used to perform frequency domain analysis which then leads to establishment of stabilizabilty conditions and controller design parameterization. Particularly, for all-pole process, and first order processes with zero dynamics, both necessary and sufficient stabilizability conditions are derived and presented. Stabilizability conditions (necessary and/or sufficient) for more complex processes with zero dynamics are also derived. As seen from the PID stabilizability results in literature, whether a first-order unstable time delay process can be stabilized or not depends on the time delay magnitude. When the normalized time delay exceeds 2, PID controller has no stabilization solution. In this thesis, a controller of higher order form is developed and stabilization is achieved for the time delay beyond such bound. The method used to tune such a stabilizer is either internal model control (IMC) principle or genetic algorithm. Performance of a control system is also equally important as stabilization. A stabilized unstable process may exhibit large overshoot, prolonged settling time, poor disturbance response, etc. In this thesis, an IMC-like scheme is proposed for better performance and stabilization. The scheme can suit a wide range of processes with an arbitrary high order of stable lags and permits a larger time delay bound. Simulations results show a better performance than other comparable schemes from literature. Unstable multivariable (MIMO) systems exists and pose a more difficult control problem than that of a single variable (SISO) case due the interaction concern from other loops. In this thesis, a design scheme for multiloop P/PI/PD/PID control has been developed for a MIMO system that can contain a combination of stable and unstable loop. The stabilizability and controller design for SISO case developed earlier part of the thesis is used in MIMO multiloop controller design. Gershgorin band principle is used to ensure the interactions of other loops are within the range such that the stability achieved for each individual closed loop is still maintained. The schemes and results presented in this thesis have both practical values and theoretical contributions to the newly emerged research interest in control research of unstable system and dynamics.
Appears in Collections:Ph.D Theses (Open)

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