Kartik B. Ariyur

Extremum seeking control for discrete-time systems

We present an extremum seeking control algorithm for discrete-time systems applied to a class of plants that are represented as a series combination of a linear input dynamics, a static nonlinearity with an extremum, and a linear output dynamics. By using the two-time scale averaging theory, we derive a mild sufficient condition under which the plant output exponentially converges to an O(/spl alpha//sup 2/) neighborhood of the extremum value, where /spl alpha/ is the magnitude of modulation signal. The sufficient condition is related to positive realness of linear parts of the plant but only at the modulation frequency. The algorithm is illustrated with a brief simulation study.

An adaptive algorithm for control of combustion instability

We propose an adaptive algorithm for control of combustion instability suitable for reduction of acoustic pressure oscillations in gas turbine engines, and main burners and augmentors of jet engines over a large range of operating conditions, and supply an experimental demonstration of oscillation attenuation, the first for a large industrial-scale gas turbine combustor. The algorithm consists of an Extended Kalman Filter based frequency tracking observer to determine the in-phase component, the quadrature component, and the magnitude of the acoustic mode of interest, and a phase shifting controller actuating fuel-flow, with the controller phase tuned using extremum-seeking. The paper also identifies a closed-loop model with phase-shifting control of combustion instability from experimental data; supplies stability analysis of the adaptive scheme based upon the identified model, and stable extremum-seeking designs used in experiments.

Formation Flight Optimization Using Extremum Seeking Feedback

A comprehensive design procedure based on extremum seeking for minimum power demand formation e ight is presented, the e rst with performance guarantees. The procedure involves the design of a new wake robust formation hold autopilot and transformation of the closed-loop aircraft dynamics to a form in which a newly available rigorous design procedure for extremum seeking is applicable. The design procedure is applied to a formation of Lockheed C-5s, extending the use of maximum performance formation e ight to large transports. By the use of availableexperimental wake data of the C-5, a model of the aircraft in the wakeis developed that models aerodynamic interference as feedback nonlinearities. Thus, this work is also the e rst to attain stable extremum seeking for a plant with nonlinear feedback. Optimal formation e ight is attained by online minimization of an easily measurable objective, the pitch angle of the wingman.

Analysis and design of multivariable extremum seeking

The paper provides a multivariable extremum seeking scheme, the first for systems with general time-varying parameters. We derive a stability test in a simple SISO format and develop a systematic design algorithm based on standard LTI control techniques to satisfy the stability test. We also supply an analytical quantification of the level of design difficulty in terms of the number of parameters and in terms of the shape of the unknown equilibrium map. Moreover, we remove the requirement of slow forcing for plants with strictly proper output dynamics (and consequent slow convergence) present in earlier works.

Control of formation flight via extremum seeking

We present a comprehensive design procedure based on extremum seeking for minimum power demand formation flight, the first with performance guarantees. The procedure involves the design of a new wake robust formation hold autopilot, and transformation of the closed loop aircraft dynamics to a form in which a newly available rigorous design procedure for extremum seeking is applicable. We apply the design procedure on a formation of Lockheed C-5s, extending the use of maximum performance formation flight to large transports. Using available experimental wake data of the C-5, we develop a model of the aircraft in the wake that models aerodynamic interference as feedback nonlinearities. Thus, our work is also the first to attain stable extremum seeking for a plant with nonlinear feedback. Optimal formation flight is attained by online minimization of an easily measurable objective, the pitch angle of the wingman.

Feedback attenuation and adaptive cancellation of blade vortex interaction on a helicopter blade element

Blade vortex interaction (BVI) noise has been recognized as the primary determinant of the helicopters far field acoustic signature. Given the limitations of design in eliminating this dynamic phenomenon, there exists a need for control. We believe that this paper is the first model-based effort to attempt the same. We present the application, first of feedback control strategies, and then of adaptive cancellation on Hariharan and Leishmans linear aerodynamic model of a trailing edge flap. Lift fluctuations caused by vortices are taken as output disturbance. The contribution of the vortices to lift is obtained from Leishmans (1996) indicial model for gusts. The use of an active structure for actuation is assumed, and the actuator is approximated as a lag element. To design an adaptive cancellation scheme that is applicable not only to BVI but also to general problems with periodic disturbances, we start with the classical sensitivity method, and arrive at an adaptive scheme whose stability we discuss via averaging. Sacks et al. (1996) arrived at the same result by introducing a phase advance into a pseudogradient scheme.

Slope seeking and application to compressor instability control

This work introduces slope seeking, a new idea for non-model based adaptive control. It involves driving the output of a plant to a value corresponding to a commanded slope of its reference-to-output map. To achieve this objective, we introduce a slope reference input into a sinusoidal perturbation-based extremum seeking scheme; derive a stability test for single parameter slope seeking, and then develop a systematic design algorithm based on standard linear SISO control methods to satisfy the stability test. We then extend the results to the multi variable case of gradient seeking. Finally, we illustrate near-optimal compressor operation under slope seeking feedback through a simulation study upon the well-known Moore-Greitzer model of compressor instability.

On the extremum seeking of model reference adaptive control in higher-dimensional systems

We develop a method for the model reference adaptive control (MRAC) of first order systems via extremum seeking. We show, in special cases in which there exists a partial knowledge of parameter values, proofs of global and exponential convergence of both the tracking and parameter tracking errors. We then extend the proposed method from first order systems to linear systems of any higher dimensions. We prove that our method has similar properties as MRAC. Results are partially illustrated through simulations of a simplified roll rate model of a fixed wing aircraft.

Autonomous tracking of a ground vehicle by a UAV

We propose a generally applicable method for the tracking of ground vehicles by aerial vehicles. The method does not require any modifications to the guidance and control of the UAV. It only requires the capability to follow waypoint commands. Sensing of ground vehicle position with significant time delays is assumed. The delays model the time of image processing, and the communication delays involved in sending data to a ground station, performing the computations and receiving the results on the UAV. Variants of the method have been tested successfully on the field and may see widespread deployment.

Reactive inflight obstacle avoidance via radar feedback

Avoidance of unmapped obstacles is critical to autonomous flight in forested areas and urban canyons. The small vehicles capable of navigating in these spaces necessarily cannot carry the heavy and sophisticated sensor packages carried on large aircraft. We propose simple reactive feedback laws that enable obstacle avoidance for a hover-capable unmanned aerial vehicle (UAV) using a crude low resolution, small field of view radar sensor. The basic component in these laws is the reduction in the velocity component in the direction of the obstacle. We illustrate the performance of these feedback laws on a point mass double integrator model with velocity and acceleration limits. Simulation results in both 2-D and 3-D settings are presented.