Model Prediction-Based Approach to Fault Tolerant Control with Applications

Abstract— Fault-tolerant control (FTC) is an integral component in industrial processes as it enables the system to continue robust operation under some conditions. In this paper, an FTC scheme is proposed for interconnected systems within an integrated design framework to yield a timely monitoring and detection of fault and reconfiguring the controller according to those faults. The unscented Kalman filter (UKF)-based fault detection and diagnosis system is initially run on the main plant and parameter estimation is being done for the local faults. This critical information\ud is shared through information fusion to the main system where the whole system is being decentralized using the overlapping decomposition technique. Using this parameter estimates of decentralized subsystems, a model predictive control (MPC) adjusts its parameters according to the\ud fault scenarios thereby striving to maintain the stability of the system. Experimental results on interconnected continuous time stirred tank reactors (CSTR) with recycle and quadruple tank system indicate that the proposed method is capable to correctly identify various faults, and then controlling the system under some conditions

Nonlinear estimation with sparse temporal measurements

Nonlinear estimators based on the Kalman filter, the extended Kalman filter (EKF) and unscented Kalman filter (UKF) are commonly used in practical application. The Kalman filter is an optimal estimator for linear systems; the EKF and UKF are sub-optimal approximations of the Kalman filter. The EKF uses a first-order Taylor series approximation to linearize nonlinear models; the UKF uses an approximation of the states' joint probability distribution. Long measurement intervals exacerbate approximation error in each approach, particularly in covariance estimation. EKF and UKF performance under varied measurement frequency is studied through two problems, a single dimension falling body and simple pendulum. The EKF is shown more sensitive to measurement frequency than the UKF in the falling body problem. However, both estimators display insensitivity to measurement frequency in the simple pendulum problem. The literature's lack of consensus as to whether the EKF or UKF is the superior nonlinear estimator may be explained through covariance approximation error. Tools are presented to analyze EKF and UKF measurement frequency sensitivity. Covariance is propagated forward using the approximations of the EKF and UKF. Each propagated covariance is compared for similarity with a Monte Carlo propagation. The similarity of the covariance matrices is shown to predict filter performance. Portions of the state trajectory susceptible to EKF divergence are found using the Frobenius norm of the Jacobian matrix, limiting the need to consider covariance propagation along the entire state trajectory. Long measurement intervals also reveal a commonly overlooked challenge in UKF application: sigma point selection methods may produce sigma point vec-tors that violate physical state constraints. Although the UKF can function under this condition over short measurement intervals, unexpected failure may occur without consideration of physical constraints. A novel constrained UKF, using the scaled unscented transform, is proposed to address this issue.http://archive.org/details/nonlinearestimat1094550547Commander, United States NavyApproved for public release; distribution is unlimited

Kalman Filtering With State Constraints: A Survey of Linear and Nonlinear Algorithms

The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results

Kalman Filtering With State Constraints: A Survey of Linear and Nonlinear Algorithms

The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results