Limits on achievable robustness against coprime factor uncertainty

We consider the problem of robustness optimization against normalized coprime factor uncertainty in single-input, single-output systems. We show that loop shapes known from classical analysis to be inconsistent with closed-loop robust stability will tend to have poor optimal robustness. Such loop shapes include those with a high crossover frequency relative to a nonminimum phase zero, a low crossover frequency relative to an unstable pole, or a rapid rolloff rate near gain crossover. Our results consist of a set of lower bounds on the optimal cost of the robustness optimization problem, each lower bound being appropriate to one of these three problematic loop shapes. The lower bounds are derived using the Poisson integral, and display the qualitative relationship between the loop shape and the level of optimal robustness.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31238/1/0000144.pd

Secure Degrees of Freedom for Gaussian Channels with Interference: Structured Codes Outperform Gaussian Signaling

In this work, we prove that a positive secure degree of freedom is achievable for a large class of Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wire-tap channel, the 2-user interference channel with confidential messages, the 2-user interference channel with an external eavesdropper. Best known achievable schemes to date for these channels use Gaussian signaling. In this work, we show that structured codes outperform Gaussian random codes at high SNR when channel gains are real numbers.Comment: 6 pages, Submitted to IEEE Globecom, March 200

Dynamic operability assessment : a mathematical programming approach based on Q-parametrization

Bibliography: pages 197-208.The ability of a process plant to guarantee high product quality, in terms of low variability, is emerging as a defining feature when distinguishing between alternative suppliers. The extent to which this can be achieved is termed a plant's dynamic operability and is a function of both the plant design and the control system design. In the limit, however, the closedloop performance is determined by the properties inherent in the plant. This realization of the interrelationship between a plant design and its achievable closed-loop performance has motivated research toward systematic techniques for screening inherently inferior designs. Pioneering research in the early 1980's identified right-half-plane transmission zeros, time delays, input constraints and model uncertainty as factors that limit the achievable closedloop performance of a process. Quantifying the performance-limiting effect of combinations of these factors has proven to be a challenging problem, as reflected in the literature. It is the aim of this thesis to develop a systematic procedure for dynamic operability assessment in the presence of combinations of performance-limiting factors. The approach adopted in this thesis is based on the Q-parametrization of stabilizing linear feedback controllers and involves posing dynamic operability assessment as a mathematical programming problet? In the proposed formulation, a convex objective function, reflecting a measure of closed-loop performance, is optimized over all stable Q, subject. to a set of constraints on the closed-loop behavior, which for many specifications of interest is convex. A discrete-time formulation is chosen so as to allow for the convenient hand.ling of time delays and time-domain constraints. An important feature of the approach is that, due to the convexity, global optimality is guaranteed. Furthermore, the fact that Q parametrizes all stabilizing linear feedback controllers implies that the performance at the optimum represents the best possible performance for any such controller. The results are thus not biased by controller type or tuning, apart from the requirement that the controller be linear

Modelling for Robust Feedback Control of Fluid Flows

This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial differential-algebraic equations (the Navier-Stokes equations), the majority of established control theory assumes models of much greater simplicity, in that they are firstly: linear, secondly: described by ordinary differential equations, and thirdly: finite-dimensional. Linearisation, where appropriate, overcomes the first disparity, but attempts to reconcile the remaining two have proved difficult. This paper addresses these two problems as follows. Firstly, a numerical approach is used to project the governing equations onto a divergence-free basis, thus converting a system of differential-algebraic equations into one of ordinary differential equations. This dispenses with the need for analytical velocity-vorticity transformations, and thus simplifies the modelling of boundary sensing and actuation. Secondly, this paper presents a novel and straightforward approach for obtaining suitable low-order models of fluid flows, from which robust feedback controllers can be synthesised that provide~\emph{a~priori} guarantees of robust performance when connected to the (infinite-dimensional) linearised flow system. This approach overcomes many of the problems inherent in approaches that rely upon model-reduction. To illustrate these methods, a perturbation shear stress controller is designed and applied to plane channel flow, assuming arrays of wall mounted shear-stress sensors and transpiration actuators. DNS results demonstrate robust attenuation of the perturbation shear-stresses across a wide range of Reynolds numbers with a single, linear controller

Controller Design with Real Parametric Uncertainty

A number of techniques have been developed in recent years for the analysis and design of controllers which are robust with respect to structured complex uncertainty. In particular the complex μ synthesis procedure has been successfully applied to a number of engineering problems. However the presence of real parametric uncertainty in the problem description substantially complicates matters, so that standard complex μ synthesis techniques are no longer adequate. In this paper we develop a procedure to tackle the mixed (real and complex) μ synthesis problem. This procedure involves a "D,G-K iteration" between computing the mixed μ upper bound and solving an H∞ optimal control problem, and has guaranteed convergence to a local minimum of the (nonconvex) problem. The procedure has been implemented in software, and several controller designs are compared with the corresponding complex μ synthesis designs

Application of robust control in unmanned vehicle flight control system design

The robust loop-shaping control methodology is applied in the flight control system design of the Cranfield A3 Observer unmanned, unstable, catapult launched air vehicle. Detailed linear models for the full operational flight envelope of the air vehicle are developed. The nominal and worst-case models are determined using the v-gap metric. The effect of neglecting subsystems such as actuators and/or computation delays on modelling uncertainty is determined using the v-gap metric and shown to be significant. Detailed designs for the longitudinal, lateral, and the combined full dynamics TDF controllers were carried out. The Hanus command signal conditioning technique is also implemented to overcome actuator saturation and windup. The robust control system is then successfully evaluated in the high fidelity 6DOF non-linear simulation to assess its capability of launch stabilization in extreme cross-wind conditions, control effectiveness in climb, and navigation precision through the prescribed 3D flight path in level cruise. Robust performance and stability of the single-point non-scheduled control law is also demonstrated throughout the full operational flight envelope the air vehicle is capable of and for all flight phases and beyond, to severe launch conditions, such as 33knots crosswind and exaggerated CG shifts. The robust TDF control law is finally compared with the classical PMC law where the actual number of variables to be manipulated manually in the design process are shown to be much less, due to the scheduling process elimination, although the size of the final controller was much higher. The robust control law performance superiority is demonstrated in the non-linear simulation for the full flight envelope and in extreme flight conditions