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

System Identification I

This paper provides a survey of results in linear parameter-varying (LPV) control that have been validated by experiments and/or high-fidelity simulations. The LPV controller synthesis techniques employed in the references of this survey are briefly reviewed and compared. The methods are classified into polytopic, linear fractional transformation, and gridding-based techniques and it is reviewed how in each of these approaches, synthesis can be carried out as a convex optimization problem via a finite number of linear matrix inequalities (LMIs) for both parameter-independent and parameter-dependent Lyapunov functions. The literature is categorized with regard to the application, the complexity induced by the controlled system’s dynamic and scheduling orders, as well as the synthesis method. Exemplary cases dealing with specific control design problems are presented in more detail to point control engineers to possible approaches that have been successfully applied. Furthermore, key publications in LPV control are related to application achievements on a timeline.

A Survey of Linear Parameter-Varying Control Applications Validated by Experiments or High-Fidelity Simulations

Active flutter suppression, which is a part of the group of flight vehicle technologies known as active controls, is an important contributor to the effective solution of aeroelastic instability pr...

https://arc.aiaa.org/doi/pdf/10.2514/1.C034442

Aircraft Active Flutter Suppression: State of the Art and Technology Maturation Needs

/pdf/lpvtools-a-toolbox-for-modeling-analysis-and-synthesis-of-2jq30ngycw.pdf

LPVTools: A Toolbox for Modeling, Analysis, and Synthesis of Parameter Varying Control Systems ?

Flutter is an unstable oscillation caused by the interaction of aerodynamics and structural dynamics. It can lead to catastrophic failure and therefore must be strictly avoided. Weight reduction and aerodynamically efficient high aspect ratio wing design reduce structural stiffness and thus reduce flutter speed. Consequently, the use of active control systems to counter these adverse aeroservoelastic effects becomes an increasingly important aspect for future flight control systems. The paper describes the process of designing a controller for active flutter suppression on a small, flexible unmanned aircraft. It starts from a greybox model and highlights the importance of individual components such as actuators and computation devices. A systematic design procedure for an H∞-norm optimal controller that increases structural damping and suppresses flutter is then developed. A second key contribution is the development of thorough robustness tests for clearance in the absence of a high-fidelity nonlinear model.

/pdf/robust-control-design-for-active-flutter-suppression-3uymd2em1q.pdf

Robust control design for active flutter suppression

A model order reduction method is proposed for models of aeroservoelastic vehicles in the linear parameter-varying (LPV) systems framework, based on state space interpolation of modal forms. The dynamic order of such models is usually too large for control synthesis and implementation since they combine rigid body dynamics, structural dynamics and unsteady aerodynamics. Thus, model order reduction is necessary. For linear timeinvariant (LTI) models, order reduction is often based on balanced realizations. For LPV models, this requires the solution of a large set of linear matrix inequalities (LMIs), leading to numerical issues and high computational cost. The proposed approach is to use well developed and numerically stable LTI techniques for reducing the LPV model locally and then to transform the resulting collection of systems into a consistent modal representation suitable for interpolation. The method is demonstrated on an LPV model of the body freedom flutter vehicle, reducing the number of states from 148 to 15. The accuracy of the reduced order model (ROM) is confirmed by evaluating the ν-gap metric with respect to the full order model and by comparison to another ROM obtained by state-of-the-art LPV balanced truncation techniques.

/pdf/modal-matching-for-lpv-model-reduction-of-aeroservoelastic-2cqqpsywr7.pdf

Modal Matching for LPV Model Reduction of Aeroservoelastic Vehicles

Flutter is an unstable oscillation caused by the interaction of aerodynamics and structural dynamics. It is current practice to operate aircraft well below their open-loop flutter speed in a stable...

/pdf/robust-modal-damping-control-for-active-flutter-suppression-3tts2hsa7i.pdf

Robust Modal Damping Control for Active Flutter Suppression

The increasing size of modern wind turbines also increases the structural loads caused by effects such as turbulence or asymmetries in the inflowing wind field. Consequently, the use of advanced control algorithms for active load reduction has become a relevant part of current wind turbine control systems. In this paper, an individual blade pitch control law is designed using multivariable linear parameter-varying control techniques. It reduces the structural loads both on the rotating and non-rotating parts of the turbine. Classical individual blade pitch control strategies rely on single-control loops with low bandwidth. The proposed approach makes it possible to use a higher bandwidth since it accounts for coupling at higher frequencies. A controller is designed for the utility-scale 2.5 MW Liberty research turbine operated by the University of Minnesota. Stability and performance are verified using the high-fidelity nonlinear simulation and baseline controllers that were directly obtained from the manufacturer. Copyright © 2017 John Wiley & Sons, Ltd.

Load reduction on a clipper liberty wind turbine with linear parameter-varying individual blade pitch control

https://nottingham-repository.worktribe.com/preview/948554/TheisEtAl_18CEP_RobustControlDesignForLandingALargeCivilAircraftInCrosswind.pdf

Julian Theis

Papers

Robust control design for active flutter suppression

Modal Matching for LPV Model Reduction of Aeroservoelastic Vehicles

Robust Modal Damping Control for Active Flutter Suppression

Load reduction on a clipper liberty wind turbine with linear parameter-varying individual blade pitch control

Robust autopilot design for landing a large civil aircraft in crosswind