Generalized LFT-Based Representation of Parametric Uncertain Models

In this paper, we introduce a general descriptor-type linear fractional transformation (LFT) representation of rational parametric matrices. This is a generalized representation of arbitrary rationally dependent multivariate functions in LFT-form. As applications, we develop explicit LFT-realizations of the transfer-function matrix of a linear descriptor system whose state-space matrices depend rationally on a set of uncertain parameters. The resulting descriptor LFT-based uncertainty models generally have smaller orders than those obtained by using the standard LFT-based modelling approach. An example of an uncertain vehicle model illustrates the capability of the method

Robust Quasi-LPV Controller Design via Integral Quadratic Constraint Analysis

Reduced cost of sensors and increased computing power is enabling the development and implementation of control systems that can simultaneously regulate multiple variables and handle conflicting objectives while maintaining stringent performance objectives. To make this a reality, practical analysis and design tools must be developed that allow the designer to trade-off conflicting objectives and guarantee performance in the presence of uncertain system dynamics, an uncertain environment, and over a wide range of operating conditions. As a first step towards this goal, we organize and streamline a promising robust control approach, Robust Linear Parameter Varying control, which integrates three fields of control theory: Integral Quadratic Constraints (IQC) to characterize uncertainty and nonlinearities, Linear Parameter Varying systems (LPV) that formalizes gain-scheduling, and convex optimization to solve the resulting robust control Linear Matrix Inequalities (LMI). To demonstrate the potential of this approach, it was applied to the design of a robust linear parametrically varying controller for an ecosystem with nonlinear predator-prey-hunter dynamics

Model based fault detection for two-dimensional systems

Fault detection and isolation (FDI) are essential in ensuring safe and reliable operations in industrial systems. Extensive research has been carried out on FDI for one dimensional (1-D) systems, where variables vary only with time. The existing FDI strategies are mainly focussed on 1-D systems and can generally be classified as model based and process history data based methods. In many industrial systems, the state variables change with space and time (e.g., sheet forming, fixed bed reactors, and furnaces). These systems are termed as distributed parameter systems (DPS) or two dimensional (2-D) systems. 2-D systems have been commonly represented by the Roesser Model and the F-M model. Fault detection and isolation for 2-D systems represent a great challenge in both theoretical development and applications and only limited research results are available. In this thesis, model based fault detection strategies for 2-D systems have been investigated based on the F-M and the Roesser models. A dead-beat observer based fault detection has been available for the F-M model. In this work, an observer based fault detection strategy is investigated for systems modelled by the Roesser model. Using the 2-D polynomial matrix technique, a dead-beat observer is developed and the state estimate from the observer is then input to a residual generator to monitor occurrence of faults. An enhanced realization technique is combined to achieve efficient fault detection with reduced computations. Simulation results indicate that the proposed method is effective in detecting faults for systems without disturbances as well as those affected by unknown disturbances.The dead-beat observer based fault detection has been shown to be effective for 2-D systems but strict conditions are required in order for an observer and a residual generator to exist. These strict conditions may not be satisfied for some systems. The effect of process noises are also not considered in the observer based fault detection approaches for 2-D systems. To overcome the disadvantages, 2-D Kalman filter based fault detection algorithms are proposed in the thesis. A recursive 2-D Kalman filter is applied to obtain state estimate minimizing the estimation error variances. Based on the state estimate from the Kalman filter, a residual is generated reflecting fault information. A model is formulated for the relation of the residual with faults over a moving evaluation window. Simulations are performed on two F-M models and results indicate that faults can be detected effectively and efficiently using the Kalman filter based fault detection. In the observer based and Kalman filter based fault detection approaches, the residual signals are used to determine whether a fault occurs. For systems with complicated fault information and/or noises, it is necessary to evaluate the residual signals using statistical techniques. Fault detection of 2-D systems is proposed with the residuals evaluated using dynamic principal component analysis (DPCA). Based on historical data, the reference residuals are first generated using either the observer or the Kalman filter based approach. Based on the residual time-lagged data matrices for the reference data, the principal components are calculated and the threshold value obtained. In online applications, the T2 value of the residual signals are compared with the threshold value to determine fault occurrence. Simulation results show that applying DPCA to evaluation of 2-D residuals is effective.Doctoral These