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 is a control strategy that has been successfully used over many years. Simplicity, robustness, a wide range of applicability and near-optimal performance are some of the reasons that have made PID control so popular in the academic and industry sectors. Recently, it has been noticed that PID controllers are often poorly tuned and some efforts have been made to systematically resolve this matter. In this paper, a brief summary of PID theory is given, then some of the most-used PID tuning methods are discussed and some of the more recent promising techniques are explored.

PID controllers: recent tuning methods and design to specification

Nested PID steering control for lane keeping in autonomous vehicles

http://www.ece.ualberta.ca/~marquez/journal_publications_files/papers/tan_cce_06.pdf

Comparison of some well-known PID tuning formulas

Brief paper: Fixed-order H∞ controller design for nonparametric models by convex optimization

A systematic design methodology for proportional-integral-derivative (PID) controllers is presented. Starting from data sets, a model of the system and its uncertainty bounds are obtained. The parameters of the controller are tuned by a convex optimization algorithm, minimizing a weighted difference between the actual loop transfer function and a target in an /spl Lscr//sub 2///spl Lscr//sub /spl infin// sense. The target selection is guided by the identified model and its uncertainty. The problem of disjoint data sets and/or different models for the same system is also addressed. The method has proved successful in numerous practical cases showing both expediency in controller design and implementation and improved performance over existing controllers.

Integrated system identification and PID controller tuning by frequency loop-shaping

A method includes obtaining at least one measurement of one or more controlled variables associated with an industrial process. The method also includes obtaining a linearized approximation of a process model representing the industrial process. The method further includes estimating a state of the industrial process using the at least one measurement, the linearized approximation, and a window-based state estimator. The method also includes generating at least one control signal for adjusting one or more manipulated variables associated with the industrial process. Generating the at least one control signal includes using the estimated state and model predictive control (MPC) logic. In addition, the method includes outputting the at least one control signal.

Apparatus and method for model predictive control (mpc) using approximate window-based estimators

One method includes obtaining a preliminary model associated with a system to be controlled and constructing a weighted model using one or more weighting factors. The method also includes identifying a final model of the system using the preliminary and weighted models, where the final model has a stability margin that is greater than an uncertainty associated with the final model. The method further includes controlling the system using a controller designed based on the final model. Another method includes identifying a first model associated with a system to be controlled, performing model order reduction to identify a second model, and controlling the system using a controller designed based on the second model. Performing the model order reduction includes reducing a weighted coprime factor model uncertainty between the first and second models.

Apparatus and method for system identification and loop-shaping controller design in a process control system

A model predictive controller (MPC) (100) for controlling physical processes includes a non-linear control section (110) that includes a memory (112) that stores a non-linear (NL) model that is coupled to a linearizer (114) that provides at least one linearized model, and a linear control section (118) that includes a memory (122) that stores a linear model. A controller engine (140) is coupled to receive both the linearized model and linear model. The MPC includes a switch (125) that in one position causes the controller engine to operate in a linear mode utilizing the linear model to implement linear process control and in another position causes the controller engine to operate in a NL mode utilizing the linearized model to implement NL process control. The switch can be an automatic switch configured for automatically switching between linear process control and NL process control.

Integrated linear/non-linear hybrid process controller

The main motivation for this work was the need for a systematic design of high-performance controllers for paper machines. An integrated identification and controller design approach, based on loop-shaping principles, is presented. Starting with time-domain input-output data, a coprime factorization of the plant is identified using linear least-squares techniques. The residual error from the identification is then used to obtain estimates of the coprime factor uncertainty that are translated to sensitivity and complementary sensitivity bounds for the closed-loop system. These bounds serve as a guide for the selection of a target loop and the controller is designed using H-infinity tools. The application of this approach is demonstrated on Honeywell's high-fidelity simulator. The simulations demonstrate the suitability of the approach and illustrate that the technique can be used to reliably provide high performance for both servo and regulatory control.

Sachindra K. Dash

Papers

Integrated system identification and PID controller tuning by frequency loop-shaping

Apparatus and method for model predictive control (mpc) using approximate window-based estimators

Apparatus and method for system identification and loop-shaping controller design in a process control system

Integrated linear/non-linear hybrid process controller

Loop-shaping controller design from input-output data: application to a paper machine simulator