Anuradha M. Annaswamy

Response of a laminar premixed flame to flow oscillations: A kinematic model and thermoacoustic instability results

Combustion instability is a resonance phenomenon that arises due to the coupling between the system acoustics and the unsteady heat release. The constructive feedback between the two processes, which is known to occur as a certain phase relationship between the pressure and the unsteady heat release rate is satisfied, depends on many parameters among which is the acoustic mode, the flame holder characteristics, and the dominant burning pattern. In this paper, we construct an analytical model to describe the dynamic response of a laminar premixed flame stabilized on the rim of a tube to velocity oscillation. We consider uniform and nonuniform velocity perturbations superimposed on a pipe flow velocity profile. The model results show that the magnitude of heat release perturbation and its phase with respect to the dynamic perturbation depend primarily on the flame Strouhal number, representing the ratio of the dominant frequency times the tube radius to the laminar burning velocity. In terms of this number, high-frequency perturbations pass through the flame while low frequencies lead to a strong response. The phase with respect to the velocity perturbation behaves in the opposite way. Results of this model are shown to agree with experimental observations and to be useful in determining how the combustion excited mode is selected among all the acoustic unstable modes. The model is then used to obtain a time-domain differential equation describing the relationship between the velocity perturbation and the heat release response over the entire frequency range.

Adaptive control of nonlinear systems with a triangular structure

In this paper, we introduce two distinct types of nonlinear dynamical systems, /spl Tscr//sub 1/ and /spl Tscr//sub 2/, both of which possess a triangular structure. It is shown that all systems belonging to /spl Tscr//sub 1/ can be made stable and that if they belong to a subclass /spl Tscr//sub 1s/, the stability holds globally. A precise characterization of the general class of nonlinear systems transformable to /spl Tscr//sub 1/ is carried out. The second class, /spl Tscr//sub 2/, corresponds to a set of second-order nonlinear differential equations and is motivated by problems that occur in mechanical systems. It is shown that global tracking can be achieved for all systems in /spl Tscr//sub 2/. A constructive approach is used in all cases to develop the adaptive controller, and both stabilization and tracking are shown to be realizable. Simple examples are given to illustrate the different classes of nonlinear systems as well as the idea behind the approach used to stabilize them. >

Adaptive control in the presence of input constraints

This paper deals with the problem of adaptively controlling a linear time-invariant plant in the presence of constraints on the input amplitude. We introduce a new adaptive algorithm which ensures that the plant can be locally stabilized. In addition to the standard assumptions which are required for adaptive control in the ideal case, an upper bound on the plant control parameter is required to be known. The results are evaluated by simulation studies. >

Adaptive control of continuous time systems with convex/concave parametrization

This paper deals with adaptive control of a class of nonlinear dynamic systems with nonlinear parametrization. In this class, the state variables are assumed to be accessible and the nonlinearity in the parameters is assumed to be either convex or concave. By introducing a tuning function and an adaptive law based on a min-max strategy, it is shown that such a class of dynamic systems can be adaptively controlled in a stable manner. Global boundedness of the overall adaptive system and tracking to within a desired precision are established with the new adaptive controller. The proposed controller is applied to a precise-positioning problem in the presence of nonlinearly parametrized friction dynamics. It is shown that the controller leads to position errors and friction compensation that are orders of magnitude better than those based on estimation of linear parametrizations. The fact that the new parameter estimation strategy used is distinct from the traditionally used gradient schemes, permits the expansion of the scope of adaptive control, which has been restricted hitherto, in most cases, to systems with linear parametrization.

Adaptive Control of Quadrotor UAVs: A Design Trade Study With Flight Evaluations

This brief describes the application of direct and indirect model reference adaptive control to a lightweight low-cost quadrotor unmanned aerial vehicle platform. A baseline trajectory tracking controller is augmented by an adaptive controller. The approach is validated using simulations and flight tested in an indoor test facility. The adaptive controller is found to offer increased robustness to parametric uncertainties. In particular, it is found to be effective in mitigating the effects of a loss-of-thrust anomaly, which may occur due to component failure or physical damage. The design of the adaptive controller is presented, followed by a comparison of flight test results using the existing linear and augmented adaptive controllers.

Robust adaptive control in the presence of bounded disturbances

The model reference adaptive control of a linear plant subjected to bounded disturbances is considered. By analyzing a set of nonlinear differential equations, it is shown that the global behavior of the adaptive system depends upon the persistent excitation of the reference input as well as the amplitude of the external disturbances. The principal contribution of the paper is the derivation of sufficient conditions on the persistent excitation of the reference input, given the maximum amplitude of disturbance, for the signals in the adaptive system to be globally bounded.

An adaptive Smith-controller for time-delay systems with relative degree n* ≤ 2

Abstract This paper addresses the control of time-delay systems whose relative degree does not exceed two. An adaptive Smith controller together with an adaptive law similar to the delay-free case is proposed. By using Lyapunov–Krasovskii functionals for an appropriate model transformation of the original system, semiglobal stability of the closed-loop system and asymptotic convergence of the output error is established. Strict positive realness together with the low relative degree of the plant is exploited to establish the stability properties. Robustness properties of the adaptive controller are briefly discussed.

Persistent excitation in adaptive systems

The importance of the concept of persistent excitation (PE) in adaptive identification and control has been recognized for some time. Recently it has become evident that it also plays a central role in many questions related to the robustness of adaptive systems. There is every reason to believe that arguments involving this concept will continue to feature prominently in the analysis of most of the important problems of adaptive control. Hence there is a real need for a deeper understanding of the concept. The paper is written with three objectives. The first, which is tutorial in nature, is to provide a general framework for the discussion of persistent excitation and to collect results in the area, which are scattered throughout the adaptive literature. The second objective is to present some new results related to the uniform asymptotic stability (u.a.s.) and robustness of adaptive systems and the relation of PE to the stability properties of a class of non-linear systems. The final objective is to di...

Adaptive air fuel ratio control for internal combustion engines

This paper treats the control of engine air-to-fuel ratio from the perspective of adaptive control of time-delay systems. High accuracy of engine air-to-fuel ratio control is required to meet stringent emissions regulations. Two adaptive controller designs are considered. The first design is based on feed-forward adaptation while the second design is based on both feedback and feedforward adaptation incorporating the developed adaptive posicast controller. The two adaptive designs are compared with the baseline controller using simulations and vehicle experiments.

Active control in combustion systems

Over the past decade, active control has been investigated in combustion systems as a means of preventing thermoacoustic instabilities from degrading the system performance. More recently, attempts to control instability and emissions as well as to satisfy other performance criteria have also been pursued. In this article, the authors review control problems in continuous combustion processes, the need for active control, and current status of the field. Despite the success reported in experimental investigations, a systematic procedure by which active control can be designed and implemented is currently not available. In particular, a theoretical framework which includes an investigation of the resonant nature of the thermoacoustic instability, an understanding of the significance of the mixing of modes and the dynamic impact of acoustic drivers, and the incorporation of the subtle coupling among the different physical processes of heat, mass, and momentum addition, as well as acoustics, turbulence, and chemistry, has not been developed. As an example of what can be accomplished using such a theoretically based approach, in this article the authors also review the results of their efforts expended thus far in the area of active control of a premixed combustor. The authors discuss the highlights of a feedback model proposed in Annaswamy et al. (1995) which captures the dominant dynamic features of the combustor. The authors demonstrate that their model captures the effects of several interacting modes, the mean-flow and mean-heat release in the combustor, and the locations of the actuator-sensor pair, and provides guidelines for an active control design. The authors suggest a systematic procedure for designing an active controller that provides an appropriate compensating action and results in improved performance.