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Title: | Design and implementation of state-space controllers for nonlinear and unstable processes | Authors: | Ha Thuy Tu | Keywords: | State-space controller;Identity luenberger observer;Kalman-Bucy filter;Algorithms;PID controller;Nonlinear control algorithms | Issue Date: | 2015 | Publisher: | Vietnamese-German University | Abstract: | Almost all phenomena and systems in reality are nonlinear, e.g. weather events, animal birth or motor rotation, and many of them are unstable. How to control an unstable nonlinear process, therefore, becomes a vital research requirement. Studying how to control a process involves studying how to model dynamics of the process and studying algorithms to operate that model as desired. Both mathematical modeling task and algorithm finding task cannot be separated in control theory. Dynamics of a system are usually modeled by differential equations, and the higher the order of differential equations, the more dynamic the system is. In this thesis, we study how to control a strongly nonlinear and highly unstable system whose dynamics is equivalent to a fourth order differential equation. In other words, an algorithm is designed to keep the process output to follow the reference input signal. The system is represented by a process of four integrators connected in series, and a mathematical model for the process is constructed. Both conventional and modern control theories are employed, but the only later one is able to stabilize this high dynamic process. We prove mathematically that the conventional PID-based controllers cannot stabilize this strongly nonlinear process. The advance of state-space control theory is to take into account internal states of the system. Nonetheless, values of the states of the process are not available. Two well-known methods are applied to estimate the values of states from the input and output of the process. We also prove that the methods Identity Luenberger observer and Kalman-Bucy filtering have the same final structure in application even though each method is developed from different philosophy. The Kalman-Bucy filter is derived from the discrete-time Kalman filter which is a practicing of the well-known least-squares estimation technique in a recursive way. The art of using the estimator is discussed in the thesis as well. Beside applying state-space control theory to solve the stabilizing problem, we study several ways to tackle the tracking problem. The combined solution provides the final algorithm to control the highly unstable nonlinear four-integrator process. |
URI(1): | http://epub.vgu.edu.vn/handle/dlibvgu/898 |
Appears in Collections: | Mechatronics & Sensor Systems Technology (MSST) |
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