Robust Stability of Iterative Learning Control Schemes

A notion of robust stability is developed for iterative learning control in the context of disturbance attenuation. The size of the unmodelled dynamics is captured via a gap distance, which in turn is related to the standard H2 gap metric, and the resulting robustness certificate is qualitatively equivalent to that obtained in classical robust H∞ theory. A bound on the robust stability margin for a specific adaptive ILC design is established

Nu-gap Model Reduction in the Frequency Domain

In this paper a model reduction algorithm in the nu-gap metric is considered. The metric was originally developed to evaluate robustness of a controller for a given plant. In fact, the nu-gap metric induces the weakest topology in which stability is a robust property. All in all the nu-gap metric is perhaps the best metric to evaluate the distance between two systems in a closed loop setup. In the field of distributed control, if approximation of the subsystems is considered, such a metric can be vital for modeling purposes. The presented algorithm of model reduction in the nu-gap metric is based on semidefinite programming methods and exploits the frequency domain representation of the systems. Therefore it may be easily extended to incorporate into the optimization procedure constraints on a specific frequency region of a particular interest or the closed loop performance

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

Robust cross-country analysis of inequality of opportunity

International rankings of countries based on inequality of opportunity indices may not be robust vis-vis the specific metric adopted to measure opportunities. Indices often aggregate relevant information and neglect to control for normatively irrelevant distributional factors. This paper shows that gap curves can be estimated from cross-sectional data and adopted to test hypotheses about robust cross-country comparisons of (in)equality of opportunity. (C) 2019 The Authors. Published by Elsevier B.V

Behavioral uncertainty quantification for data-driven control

This paper explores the problem of uncertainty quantification in the behavioral setting for data-driven control. Building on classical ideas from robust control, the problem is regarded as that of selecting a metric which is best suited to a data-based description of uncertainties. Leveraging on Willems' fundamental lemma, restricted behaviors are viewed as subspaces of fixed dimension, which may be represented by data matrices. Consequently, metrics between restricted behaviors are defined as distances between points on the Grassmannian, i.e., the set of all subspaces of equal dimension in a given vector space. A new metric is defined on the set of restricted behaviors as a direct finite-time counterpart of the classical gap metric. The metric is shown to capture parametric uncertainty for the class of autoregressive (AR) models. Numerical simulations illustrate the value of the new metric with a data-driven mode recognition and control case study.Comment: Submitted to the 61st IEEE Conference on Decision and Contro

Robust Autopilot Design: H ∞ Loop shaping Control using Particle Swarm Optimization

International audienceIn this paper, a robust autopilot is designed such that the system stability is guaranteed in low altitude and short-range conditions. First, using the v-gap metric, the system is linearzed around the equilibrium point. Then, the robust H∞ loop shaping controller is built for the linear model. The proposed approach does not utilize the gain scheduling method, and guarantees the system stability throughout the flight envelope. Particle Swarm Optimization (PSO) algorithm is used along with the control approach to reduce the complicated tuning process of the weight functions. The weighting functions are optimized throughout the evolutionary algorithm to maximize the stability margin. From the simulations, it is proved that the stability margins achieved guarantees the stability of interceptor throughout the whole flight envelope

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.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Robust feedback linearization control of air-feed system in PEM fuel cell against practical uncertainty

In this paper robust feedback linearization control approach based on the gap metric analysis is proposed to control a Proton Exchange Membrane Fuel Cell (PEMFC). The oxygen excess ratio ( ) is regulated through adjustment of the air supply to avoid oxygen starvation. Furthermore regulation improves the efficiency whilst more net power will be delivered. In this paper a six order state variable PEM fuel cell is used as a plant whereas the system variations and disturbances are regarded as uncertainties to configure the perturbed plant. The gap metric analysis is gained in this paper to assess the difference between the perturbed plants and that of the nominal. Results of using the nonlinear control law reveal that the proposed feedback linearization control is robust against disturbances during the oxygen excess ratio regulation.Results verify that the measurement delays in super twisting algorithm excite un-modeled dynamics because of higher frequency in the oscillations. The proposed controller eliminates influence of un-modeled dynamic and delay of actuator and sensor. Furthermore the designed controller is found capable to attenuate the practical measurement noise effect (in terms of a stochastic uncertainty) in both of the frequency spectrum and also in the overall amplitude