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

http://eprints.gla.ac.uk/312/1/Optimal_Contr_Nonlinear_Syst_(_ePrint_312).pdf

Brief Optimal control of nonlinear systems: a predictive control approach

This paper addresses the prediction accuracy enhancement problem in the context of continuous-time model predictive control (MPC) by using a disturbance observer. The disturbance estimation is introduced in the output prediction to correct the errors caused by disturbances and uncertainties, which eventually leads to the desired offset-free tracking performance. Due to such a different design philosophy, the computational burden of the proposed method will be significantly reduced as compared with the existing offset-free MPCs for disturbed systems. Another promising feature of the proposed method lies in its nominal performance recovery property. The workability of the proposed method is validated by its application to a dc–dc buck converter system.

Design of a Prediction-Accuracy-Enhanced Continuous-Time MPC for Disturbed Systems via a Disturbance Observer

A class of nonlinear PID controllers is derived for nonlinear systems using a nonlinear generalised predictive control (NGPC) approach. First, the disturbance decoupling ability of the NGPC is discussed. For a nonlinear system where the disturbance cannot be decoupled, a nonlinear observer is designed to estimate the offset. By selecting the nonlinear gain function in the observer, it is shown that the closed-loop system under optimal generalised predictive control with the nonlinear observer is asymptotically stable. It is pointed out that this composite controller is equivalent to a nonlinear controller with integral action. As a special case, for a nonlinear system with a low relative degree, the proposed nonlinear controller reduces to a nonlinear PI or PID predictive controller, which consists of a nonlinear PI or PID controller and a prediction controller. The design method is illustrated by an example nonlinear mechanical system.

/pdf/nonlinear-pid-predictive-controller-1dms7sh5qd.pdf

Nonlinear PID predictive controller

Finite Dill'erenzlOsung von elektrodynamiscben Problemen Die Einfiihrung der finiten Differenzmethode in Studentenkursen war bisher auf einfache ProbIerne beschriinkt, die so gut wie nichts mit der Welt, in der Studenten leben, zu tun hatten. In diesem Artikel stellen wir in einfacher Form einige nichttriviale Probleme aus dem Alltag vor, wie sie im Unterricht an der Temple University behandelt wurden.

Book Review: Adaptive Optimal Control: the thinking man's GPCAdaptive Optimal Control: the thinking man's GPC:BITMEADR. R., GEVERSM. and WERTZV. (Prentice-Hall, 1990, 244 pp., £32.95)

The multivariable continuous-time generalised predictive controller (CGPC) is recast in a state-space form and shown to include generalised minimum variance (GMV) and a new algorithm, predictive GMV (PGMV) as special cases. Comparisons are drawn with the exact linearisation methods of nonlinear control, and it is noted that, unlike the transfer function approach, the state-space approach extends readily to the nonlinear case. The resulting state space design algorithms are conceptually and algorithmically simpler than the corresponding transfer function based versions and have been realised as a freely available Matlab tool-box.

H. Demircioglu

Papers

Multivariable continuous-time generalised predictive control: a state-space approach to linear and nonlinear systems