Alf J. Isaksson

Identification of ARX-models subject to missing data

Parameter estimation when the measurement information may be incomplete is discussed. An ARX model is used as a basic system representation. The presentation covers both missing output and missing input. First reconstruction of the missing values is discussed. The reconstruction is based on a state-space formulation of the system, and is performed using Kalman filtering or fixed-interval smoothing formulas. Several approaches to the identification problem are presented, including a new method based on the EM (expectation maximization) algorithm. The different approaches are tested and compared using Monte Carlo simulations. The choice of method is always a tradeoff between estimation accuracy and computational complexity. According to the simulations the gain in accuracy using the EM method can be considerable if many data are missing. >

Brief Analytical PID parameter expressions for higher order systems

Most approaches to feedback synthesis are numerical design techniques that produce their results in form of numerical values for the controller parameters. In contrast, analytical design techniques produce the controller parameters as explicit expressions that are a function of open-loop system parameters and the desired closed loop. Advantages include fast commissioning in terms of physical system parameters, gain scheduling without extra design effort and analytical sensitivity insights. So far, it has not been known how to derive analytical PID expressions for higher than second-order systems. The paper proposes a technique to address this problem, analyses its properties, demonstrates computational simplicity and shows that its performance is comparable to known numerical techniques.

Design and performance of mid-ranging controllers

Abstract Mid-ranging control applications are multivariate and often involve input constraints. Although some strategies have been reported to work well in industry, no systematic comparison has ever been made. The purpose of this report is to compare these schemes to a model-based predictive control (MPC) approach designed specifically for constrained multivariable control problems. The results indicate that although there are special cases where the existing schemes work reasonably well, MPC is best able to solve the problem in the general case.

On sensor scheduling via information theoretic criteria

We prove the optimality of open-loop control for the sensor scheduling problem of linear Gauss Markov systems using information theoretic criteria. We use dynamic programming arguments to show the data independence on the design of the controller when the objective is to maximize the information about the underlying hidden state. The aim is to compute the sequence of active sensors, using information theoretic criteria, such that the information on the state of the underlying system is maximized. In the second part of the paper, we propose a scheme that considerably reduces the computational burden in computing optimal open-loop sensor schedules. Our scheme is basically an enumeration scheme with optimal pruning. Exploiting a special property of the Riccati equation, we can ignore sensor schedules without the possibility of deleting the optimal sensor sequence.

Best choice of coordinate system for tracking coordinated turns

A standard approach to tracking is to use the extended Kalman filter (EKF) applied to a nonlinear state-space model. We compare two conceivable choices of state variables for modeling civil aircrafts. One where Cartesian velocities are used and one where absolute velocity and heading angle are used. In both choices, Cartesian coordinates are used for position and angular velocity for turning. It is shown that the latter state vector always performs better. This is proven by considering the linearization error made in the extended Kalman filter applied either to a time-continuous model or a discretized model. The result is supported by a Monte Carlo simulation study.

A Method for Detection of Stiction in Control Valves

Abstract There has been an increasing interest in automatic control performance monitoring in recent years. The aim of such monitoring tools is to detect deterioration such as increased variability, oscillating behaviour, saturation or off-sets. Easy and efficient methods have been presented in the literature. After having detected a deteriorated control performance, one would like a monitoring tool to give hints of the possible cause of the deterioration. We will in this contribution suggest a method which allows automatic classification of one important reason for a detected control performance deterioration, namely static friction (stiction) in control valves. The suggested approach uses methodology from the fault-detection field and involves a model-based nonlinear observer and statistical hypothesis testing using a likelihood ratio test. Only little process knowledge, as time-delay, measurements of control signal and process output and some usually known valve parameters are needed. The method is evaluated on industrial data.

Identification of Time Varying Systems Through Adaptive Kalman Filtering

Abstract An approach to identification of time varying systems is presented and evaluated using computer simulations. The approach is built upon the similarities between recursive least squares identification and Kalman filtering. The parameter variations are modelled as process noise in a state space model, and then identified using adaptive Kalman filtering. A method for adaptive Kalman filtering is described. The simulations indicate that this approach is superior to previous methods based on adjusting the forgetting factor. This improvement is however gained at the price of a significant increase in computational complexity.

Neural trees-using neural nets in a tree classifier structure

The concept of tree classifiers is combined with the popular neural net structure. Instead of having one large neural net to capture all the regions in the feature space, the authors suggest the compromise of using small single-output nets at each tree node. This hybrid classifier is referred to as a neural tree. The performance of this classifier is evaluated on real data from a problem in speech recognition. When verified on this particular problem, it turns out that the classifier concept drastically reduces the computational complexity compared with conventional multilevel neural nets. It is also noted that these data make it possible to grow trees online from a continuous data stream.<<ETX>>

A parametric statistical approach to FDI for the industrial actuator benchmark

Abstract A parametric statistical approach to the industrial actuator fault-detection and isolation benchmark is presented. An algorithm for detecting a change in the dynamics of a linear system is formulated as a set of sequential probability ratio tests of the innovations from a bank of Kalman filters. The algorithm is extended to allow estimation of a disturbance using a generalised likelihood ratio test. Modifications are proposed for when the model is nonlinear and the modeling error is significant. The algorithm is evaluated using the benchmark test data and is shown to provide low detection delays while being robust to noise, disturbances and model error.

An iterative method for identification of ARX models from incomplete data

Describes a very simple and intuitive algorithm to estimate parameters of ARX models from incomplete data sets. An iterative scheme involving two least squares steps and a bias correction is all that is needed.