Balancing three matrices in control theory

Several problems from control theory are presented which are sensitive to badly scaled matrices. We were specially concerned with the algorithms involving three matrices, thus we extended the Ward\u27s balancing algorithm for two matrices. Numerical experiments confirmed that balancing three matrices can produce an accurate frequency response matrix for descriptor linear systems, it can also improve the solution of the pole assignment problem via state feedback and the determination of the controllable part of the system

Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system

Balancing three matrices in control theory

Several problems from control theory are presented which are sensitive to badly scaled matrices. We were specially concerned with the algorithms involving three matrices, thus we extended the Ward\u27s balancing algorithm for two matrices. Numerical experiments confirmed that balancing three matrices can produce an accurate frequency response matrix for descriptor linear systems, it can also improve the solution of the pole assignment problem via state feedback and the determination of the controllable part of the system

On the computation of the fundamental subspaces for descriptor systems

In this paper, we investigate several theoretical and computational aspects of fundamental subspaces for linear time-invariant descriptor systems, which appear in the solution of many control and estimation problems. Different types of reachability and controllability for descriptor systems are described and discussed. The Rosenbrock system matrix pencil is employed for the computation of supremal output-nulling subspaces and supremal output-nulling reachability subspaces for descriptor systems

Predictive control approaches to fault tolerant control of wind turbines

This thesis focuses on active fault tolerant control (AFTC) of wind turbine systems. Faults in wind turbine systems can be in the form of sensor faults, actuator faults, or component faults. These faults can occur in different locations, such as the wind speed sensor, the generator system, drive train system or pitch system. In this thesis, some AFTC schemes are proposed for wind turbine faults in the above locations. Model predictive control (MPC) is used in these schemes to design the wind turbine controller such that system constraints and dual control goals of the wind turbine are considered. In order to deal with the nonlinearity in the turbine model, MPC is combined with Takagi-Sugeno (T-S) fuzzy modelling. Different fault diagnosis methods are also proposed in different AFTC schemes to isolate or estimate wind turbine faults.The main contributions of the thesis are summarized as follows:A new effective wind speed (EWS) estimation method via least-squares support vector machines (LSSVM) is proposed. Measurements from the wind turbine rotor speed sensor and the generator speed sensor are utilized by LSSVM to estimate the EWS. Following the EWS estimation, a wind speed sensor fault isolation scheme via LSSVM is proposed.A robust predictive controller is designed to consider the EWS estimation error. This predictive controller serves as the baseline controller for the wind turbine system operating in the region below rated wind speed.T-S fuzzy MPC combining MPC and T-S fuzzy modelling is proposed to design the wind turbine controller. MPC can deal with wind turbine system constraints externally. On the other hand, T-S fuzzy modelling can approximate the nonlinear wind turbine system with a linear time varying (LTV) model such that controller design can be based on this LTV model. Therefore, the advantages of MPC and T-S fuzzy modelling are both preserved in the proposed T-S fuzzy MPC.A T-S fuzzy observer, based on online eigenvalue assignment, is proposed as the sensor fault isolation scheme for the wind turbine system. In this approach, the fuzzy observer is proposed to deal with the nonlinearity in the wind turbine system and estimate system states. Furthermore, the residual signal generated from this fuzzy observer is used to isolate the faulty sensor.A sensor fault diagnosis strategy utilizing both analytical and hardware redundancies is proposed for wind turbine systems. This approach is proposed due to the fact that in the real application scenario, both analytical and hardware redundancies of wind turbines are available for designing AFTC systems.An actuator fault estimation method based on moving horizon estimation (MHE) is proposed for wind turbine systems. The estimated fault by MHE is then compensated by a T-S fuzzy predictive controller. The fault estimation unit and the T-S fuzzy predictive controller are combined to form an AFTC scheme for wind turbine actuator faults