Robust Observers for Nonlinear Large Scale Interconnected Systems

Some control design schemes need system states to develop controllers. In real applications, it might not be possible to measure all system states due to the cost of sensors or any technical issues. Therefore, Observers are needed to estimate unavailable states and then use the estimated states in control design schemes.

This thesis focuses on the development of robust observers for nonlinear large-scale interconnected systems. System structures of nonlinear interconnected systems have been considered in the design to reduce conservatism and different techniques have been utilised in observer design to enhance the robustness. The main developments in this thesis include:

A robust observer is designed for nonlinear interconnected systems with uncertainties where both the nominal isolated subsystems and interconnections are nonlinear. A novel variable structure dynamic system is designed to estimate the state variables of the interconnected systems asymptotically.

Sliding mode techniques have been utilised to design observers for a class of interconnected systems with both structured and unstructured uncertainties. For structured uncertainties, a robust sliding mode observer is designed using the distribution matrix of the uncertainties to guarantee that the error dynamics are asymptotically stable. For unstructured uncertainties, an ultimately bounded approximate observer is proposed to estimate the system states.

In the case that the interconnected systems have unknown time varying parameters, adaptive observers are developed to estimate both the system states and the unknown time varying parameters simultaneously. A variable structure control technique is utilized to guarantee that the corresponding error dynamical system is convergent asymptotically while the parameter estimation error is uniformly ultimately bounded. Moreover, adaptive sliding mode observer is proposed to estimate the inaccessible states in presence of unknown time-varying parameters.

This thesis also provides case studies on applications of the proposed methods. A case study of a coupled inverted pendulum system shows the practicality of the variable structure observer. The designed sliding mode observer is applied to a multi-machine power system, and the simulation is provided to demonstrate the validity and effectiveness of the designed observer. A coupled inverted pendulum system and a quarter-car suspension system are employed to explain the designed observation scheme and to demonstrate that the designed adaptive observers can be applied to practical systems effectively.