Jorge Sofrony

Anti-windup synthesis using Riccati equations

The aim of this paper is to give a novel solution to the full order anti-windup (AW) compensation problem for stable systems with input saturation. The solution is obtained by “completing the square” in three steps and requires the solution to a single bounded-real Riccati equation, characterized by the open-loop plants norm. The Riccati equation plays the role of the LMIs usually found in anti-windup synthesis, but, in addition to its numerical advantages, it yields a family of anti-windup compensators with the same performance. This family of compensators is parameterized by a matrix which is intimately linked with both the poles of the anti-windup compensator and the robustness properties of the closed-loop saturated system. Thus, this matrix allows a robust anti-windup problem to be solved in a straightforward and intuitive manner. The effectiveness of the proposed technique is demonstrated on a simple example.

Anti-windup compensation of rate saturation in an experimental aircraft

This paper describes the design, flight testing and accompanying analysis of two anti-windup (AW) compensators for an experimental aircraft - the German Aerospace Centers (DLR) advanced technologies testing aircraft (ATTAS). The AW compensators were designed to reduce the deleterious effects of rate-saturation of the aircrafts actuators on handling qualities. The AW compensators were flight-tested and assessed using the resulting pilot comments, in the form of handling qualities ratings (HQRs) and pilot-involved-oscillation ratings (PIORs), and flight test data. These media demonstrate that the AW compensators improved the predictability and handling of the aircraft. The results also provide an initial understanding of the relationship between the theory and design choices for AW controllers and the response of the piloted aircraft during periods of rate saturation.

Anti-windup synthesis for systems with rate-limits using Riccati equations

This article develops an anti-windup (AW) scheme for systems with rate-limited actuators. The main results show how a full-order AW compensator can be synthesised using an algebraic Riccati equation and several free parameters. A further result then shows how the free parameters may be chosen to influence, in an intuitive way, the local gain of the system and the size of the region of attraction. The results are of interest due to their low computational burden and hence their applicability to the systems of large state dimension.

Path planning of mobile robots using potential fields and swarms of Brownian particles

This paper proposes an algorithm for trajectory planning based on the motion of Brownian particles. One of the most popular approaches in path planning is to use the artificial potential fields method which, due to its easiness in implementation, might attract the robot towards a local minimum configuration, thus preventing it from reaching the desired final destination. Although there are different approaches to deal with this drawback, their modeling lacks the simplicity of the potential fields, adding thus an extra complexity to the problem. The solution proposed here combines the strengths of both approaches: it is easy to analyze and to implement, just like in the potentials method, while it preserves the robustness against local minima of more complex particle swarm models. An approximate analysis for the deterministic version of the selected model was performed and it was observed, via simulations, that the results obtained after this simplification were consistent with the behavior of the stochastic system.

Anti-windup synthesis for PIO avoidance in an experimental aircraft

This paper demonstrates the application of a recently developed anti-windup technique for systems with rate-saturated actuators, to a realistic flight control example. The paper makes two contributions: firstly a new approach to tuning the anti-windup compensator is devised, allowing a transparent trade-off between performance and the size of an estimate of the region of attraction. Secondly, the anti-windup algorithm is applied to a nonlinear simulation model of the longitudinal and lateral dynamics of an experimental aircraft. The results show the potential of anti-windup to lessen an aircrafts susceptibility to pilot-induced-oscillations. This promise has since been confirmed in flight tests

Flight testing of low-order anti-windup compensators for improved handling and PIO suppression

This paper presents the results of recent flight tests of several anti-windup (AW) compensators on the German Aerospace Centres (DLR) Advanced Technologies Testing Aircraft (ATTAS). The objectives of the tests were twofold: to demonstrate the potential for rigorously designed low order AW compensators to reduce the pilot-involved-oscillation (PIO) proneness of the aircraft and improve the handling qualities; and to compare a variety of low-order AW compensators to determine the importance of different design parameters. The AW compensators were assessed based on pilot handling qualities ratings (HQRs) and PIO ratings (PIORs). These ratings, and supporting pilot comments and flight data, demonstrate that the AW compensators improved the handling qualities and reduced the PIO proneness of the aircraft, albeit to different degrees. The results also provide a basic understanding of the relationship between design parameters and the response of the piloted aircraft during periods of rate saturation.

Vortex Particle Swarm Optimization

This paper presents an optimization algorithm based on self-propelled particle swarms which exploit vorticity features in order to avoid local minima; the proposed algorithm is termed Vortex Particle Swarm Optimization (VPSO). The optimization algorithm switches between translational and dispersion behavior of the swarm to enhance the exploration of the search space and to avoid getting trapped in local minima. These two types of behavior are induced by choosing the swarm as a collection of coupled, second-order oscillators where it is possible, via suitable parameter selection to switch between translational (convergence) and vortex-like movements (dispersion). This idea mimics living organism strategies such as foraging and predator avoidance. Performance of the algorithm is studied via simulation results of well-known 2D test functions.

ℒ 2 gain bounds for systems with slope-restricted nonlinearities

This paper proposes a new method for calculating a bound on the ℒ 2 gain of a system consisting of a linear time invariant (LTI) part and a static nonlinear part, which is odd, bounded, zero at the origin and has a restriction on its slope. The problem is posed in the IQC framework and the ℒ 2 gain bound is found by solving a set of linear matrix inequalities (LMIs). The novelty of the paper lies in the use of a recent characterisation of the multiplier for systems with slope-restricted nonlinearities. Examples illustrate the effectiveness of the results against the state-of-the-art.

Haptic simulator for training of Total Knee Replacement

This paper presents a novel orthopaedic surgery simulator, capable of analyzing, processing and displaying medical images. These newly added capabilities allows the reconstruction of multiple three-dimensional models, and their integration into a virtual environment. The main contribution of this work is the developement of a new mixed graphical model (surface and volumetric) that allows simulation of bone machining in real time.

Deciding on optimal assistance policies in haptic shared control tasks

This paper presents a haptic assistant that enhances task performance and human-machine interaction via a gain-scheduled impedance controller. The assistance strategy proposed builds on decision-making studies and models first proposed in the field of cognitive science and combines these models with a gain-scheduled impedance control technique in order to enhance human machine interaction in a tracking task with environmental uncertainties. This paper explores the Drift-Diffusion Model as decision making model and proposes an adaptive impedance control strategy that enhances both, task performance and human-machine interaction.