Observer-based Fault Detection in Nonlinear Systems

Interests in fault detection and isolation for nonlinear systems have grown significantly in recent years due to the fact that most of the systems, we face in practice, are nonlinear in nature. There exist a number of techniques for fault detection, among them; the so-called observer-based fault detection is widely studied. In addition, this technique has been proven efficient in detecting faults. In a typical observer-based scheme, the process of fault detection is carried out in two steps: residual generation and residual evaluation. The purpose of residual generation is to produce the so-called residual signal by comparing the process outputs with their estimates generated by the observer. Roughly speaking, the residual signal, thus generated, carries the information of faults only. It means that under fault-free operation, the residual should go to zero and deviates only in the presence of fault. However, due to model uncertainties and unknown inputs (process disturbances, measurement noises, and faults of no interest), the residual signal is non-zero even in the fault-free operation of the process. In order to extract the information of faults in the presence of model uncertainties and unknown inputs, additional efforts need to be done. The process of residual evaluation serves this purpose. In this step, some function of the residual signal (evaluation function) is compared with a bound, the so-called threshold, regarding all possible unknown inputs and model uncertainties. An alarm is generated if the former exceeds the later which shows the presence of fault. Selection of a suitable threshold is very critical task in fault detection. The performance of a typical fault detection system can be evolved by a threshold. If it is selected too low, some unknown inputs may cause the evaluated residual to cross it which results into a false alarm. Conversely, selecting it too high may result into a missed detection, which means some set of faults may remain undetected. This thesis presents novel methods for designing observer-based residual generator (fault detection filters) and threshold computation scheme for nonlinear uncertain systems subject to unknown inputs. The objective of designing fault detection filter is to generate a residual signal which is robust against unknown inputs and sensitive to faults. Exploiting the tools of game theory and dissipation inequality, three kinds of fault detection filters are proposed. These filters are designed with the objectives: to enhance sensitivity of the residual signal to faults, to improve robustness of the residual signal against unknown inputs, and to simultaneously provide sensitivity to faults and robustness against the unknown inputs. Similarly, the objective of designing a threshold computation scheme is to eliminate the possibility of false alarms and ensures the detectability of small faults so that the performance of fault detection system can be improved. For this purpose, various kinds of thresholds for nonlinear systems are proposed. These thresholds include constant thresholds, adaptive thresholds, and dynamic threshold. For designing constant thresholds, a framework based on signal norms is proposed. Utilizing the tools from robust control theory and linear matrix inequality, algorithms are derived for different kinds of thresholds. The framework for adaptive threshold is also proposed using signal norms. In this scheme, the resultant threshold is a function of the instantaneous energies of the control inputs and as a result less conservative as compared to the constant threshold. For designing dynamic threshold, a dynamic system is proposed based on deriving an inequality on the modulus of the residual signals. This dynamic system takes the information of the instantaneous values of the control input, a bound on model uncertainties and unknown inputs and generates a variable threshold accordingly. The threshold, thus generated, fits as close to the residual signal as possible under faultfree operation. The fault detection methodologies proposed in this thesis are expressed in the form of algorithms that can be directly implemented. This shows that the proposed schemes are computationally tractable and user oriented. These algorithms are tested with the numerical examples in the respective chapters and with the benchmark problems; that is, three-tank system (DTS200) and the inverted pendulum control system (LIP100) to demonstrate their applicability and use.