There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Fractional Differential Equations

A most critical and important issue surrounding the design of automatic control systems with the successively increasing complexity is guaranteeing a high system performance over a wide operating range and meeting the requirements on system reliability and dependability. As one of the key technologies for the problem solutions, advanced fault detection and identification (FDI) technology is receiving considerable attention. The objective of this book is to introduce basic model-based FDI schemes, advanced analysis and design algorithms and the needed mathematical and control theory tools at a level for graduate students and researchers as well as for engineers.

Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools

Artificial neural networks (ANNs) constitute a class of flexible nonlinear models designed to mimic biological neural systems. In this entry, we introduce ANN using familiar econometric terminology and provide an overview of ANN modeling approach and its implementation methods. † Correspondence: Chung-Ming Kuan, Institute of Economics, Academia Sinica, 128 Academia Road, Sec. 2, Taipei 115, Taiwan; ckuan@econ.sinica.edu.tw. †† I would like to express my sincere gratitude to the editor, Professor Steven Durlauf, for his patience and constructive comments on early drafts of this entry. I also thank Shih-Hsun Hsu and Yu-Lieh Huang for very helpful suggestions. The remaining errors are all mine.

Artificial neural networks

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

PID Control in the Third Millennium

IMC based Robust PID design: Tuning guidelines and automatic tuning

PID Tuning.- Model-based PID Tuning.- Tuning Rules for Integral and Unstable Systems.- Robust Tuning of PID Controllers.- PID Tuning for Smooth Control.- PID Control of MIMO Processes.- Feedforward plus PID Control.- PID-based Control Structures.- Robust Multivariable PID Controller Design.- Identification for PID Control.- Design based on the Characterization of all Stabilizing PID Controllers.- Fragility Evaluation of PID Controller Tuning Rules.- Performance Assessment for PID Control.- Industrial Applications of PID Control.- Fractional-order PID Control.- Nonlinearisation of PID Control.- Data-driven PID Control.- Predictive Control Approach for PID Controller Design.

Ramon Vilanova

Papers

PID Control in the Third Millennium

IMC based Robust PID design: Tuning guidelines and automatic tuning

PID control in the Third Millennium : lessons learned and new approaches

Applying variable dissolved oxygen set point in a two level hierarchical control structure to a wastewater treatment process

PID control in terms of robustness/performance and servo/regulator trade-offs: A unifying approach to balanced autotuning