The Study On The Nonlinear Control Of Unstable Systems

The nonlinear control of unstable systems is an active field of research because many mechanical control systems with fewer controls than the number of configuration variables are very popular. Typically, the Magnetic Suspension Steel Ball System (MSSBS) and the Arm Driven Inverted Pendulum System (ADIPS) are typical second-order and high order unstable systems, respectively, which are very suitable to be used as the test beds for nonlinear control techniques aimed at unstable systems. The main contribution of this dissertation is as follows:For the linearization the mathematical model of a nonlinear system, the Taylor series and Lagrange's equation were adopted. These mathematical tools which are good enough to describe the response of the real system as closely as possible were proposed to linearize the mathematical model of unstable nonlinear systems.For nonlinear control second-order unstable systems, with the MSSBS is a represent, control method based on Fuzzy Lead Phase Compensate Control (FLPCC) method was adopted. Fuzzy logic combined with lead phase compensate control help control problem in second-order changing parameters unstable systems easily. Via simulation and experiment on real test bed, this control method shows successful, flexible and the good performance of controller.For nonlinear control high-order unstable systems, with the ADIPS is a represent, control method based on Adaptive Gain Scheduling Linear Quadratic Regulate Control (AGSLQRC) was adopted. Adaptive gain scheduling control combined with LQR control can solve control problem in high-order changing set point unstable systems successfully. Via simulation and experiment on real system, this method shows stable, smooth, robust and the high performance of controller.With the study of nonlinear control of unstable systems the main theme, this dissertation performed a detailed survey of relevant research reports. The mathematical tools were combined with the suitable control method in providing an entire set of solutions for nonlinear control of unstable systems. Experiment results proved that the proposed set of solutions is capable of controlling two typical unstable systems within robust, smooth, stable and high performance.