Stability Analysis and Controller Design of Complex Dynamic Systems with Unknown Structures and Measurements

In control theory and control engineering, it is well known that the accurate model of a control plant is hard or even impossible to get. The uncertain system structures make it hard to design controllers with required control performances, and sometimes may even affect the observability, controllability and stability. In addition, the sensor measurements play a critical role in feedback controller design process. However, in real-world applications where sensors are operated in complicated industrial environments, it is common that the value measured by a sensor has variations from the real system state. The output from a practical sensor consists not only of true signals but also of disturbances. Thus, the uncertain measurement is another issue that affects both the performances and the stability of a control system. The aim of this dissertation is to develop new control approaches and to provide rigorous stability analysis for some complex planar systems with unknown structures and measurements. Motivated by some new ideas from homogeneous system theory and some classic ideas from linear system theory such as lead compensator and integral controller, this dissertation develops novel control approaches for some complex planar systems with unknown structures and measurements. Firstly we design a feedback controller for a class of nonlinear planar systems with unknown coefficients in system structures and measurements, and then extend the result to a more generalized system by providing necessary and sufficient conditions of stability. Then by taking advantage of the stability-increasing capability of a lead compensator, we propose a dynamic output feedback controller for a class of nonlinear systems with unknown structures and measurements. Next, we employ the idea of the integral controller to design controllers and then extend the result to the case of actuator saturation for a class of planar systems with unknown measurements. Finally we propose an output feedback integral controller for a class of planar systems with unknown measurements by constructing a novel observer.

Some examples and the related simulation studies verify the effectiveness of the proposed methods. The simple form controllers of the proposed approaches make them easy to be realized and applied in practical applications. The stability conditions and the Lyapunov functions proposed in this dissertation can provide a novel way to design controllers and analysis stability for some nonlinear planar systems.