Ashish Krupadanam

Self-tuning control of a nonlinear model of combustion instabilities

We present a self-tuning scheme for adapting the parameters of a PI controller proposed by Fung and Yang (1992) for stabilization of a Culick-type model of nonlinear acoustic oscillations in combustion chambers. Our adaptation criterion is Lyapunov-based and its objective is the regulation of nonlinear pressure oscillations to zero. We focus on a two-mode model and first develop a design based on an assumption that the amplitudes of the two modes are available for measurement. Instead of estimating the damping coefficients of each mode (which are dependent on the unknown air/fuel ratio), the Lyapunov approach allows us to adapt the parameters of the controller directly. The adaptation mechanism is designed to stabilize both modes and prevent the phenomenon observed by Billoud, Galland, Huu, and Candel (1992), whose adaptive controller stabilizes the first but (under some conditions) apparently destabilizes the second mode. We also prove that the adaptation mechanism is robust to a time delay inherent to the actuation approach via heat release. In order to avoid requirements for sophisticated sensing of the mode amplitudes needed for feedback, we also develop an adaptation scheme which employs only one pressure sensor. Our approach is based on the idea to use the squares of the pressure and its derivative instead of the squares of the amplitudes of the modes to drive the adaptation. In order for the adaptation scheme to be implementable, it is also necessary to know the control input matrix of the system. Rather than performing a complicated linear ID procedure, we propose a simple nonlinear ID approach that exploits the quadratic character of the nonlinearities and identifies the input matrix from steady-state limit cycle data. Simulations illustrate the capability of the scheme to attenuate limit cycles without the knowledge of the growth coefficients.

Adaptive stabilization of nonlinear acoustic oscillations in combustion chambers

We present a self-tuning scheme for adapting the parameters of a PI controller proposed by Fung-Yang (1992) for stabilization of a Culick-type model of nonlinear acoustic oscillations in combustion chambers. Our adaptation criterion is Lyapunov-based. We focus on a two-mode model and develop a design based on an assumption that the amplitudes of the two modes are available for measurement. The adaptation mechanism is designed to stabilize both modes and prevent the phenomenon observed by Billoud et al. (1992) whose adaptive controller stabilizes the first but destabilizes the second mode. We also prove that the adaptation mechanism is robust to a time delay inherent to the actuation approach via heat release. We also develop an adaptation scheme which employs only one pressure sensor. Our approach is based on the idea to use the squares of the pressure and its derivative. Simulations illustrate the capability of the scheme to attenuate limit cycles without the knowledge of the growth coefficients.

A Reduced-Order Model of a Lithium-Ion Cell Using the Absolute Nodal Coordinate Formulation Approach

The widespread use of lithium-ion batteries motivates the need for robust battery management systems (BMSs) that can both observe the internal states of a cell and update degraded physical parameters over time. Many models that are capable of accurately replicating the internal dynamics of cells during high discharge and charging cycles contain too many states to perform real-time estimation, and many models that contain a reasonable number of states for estimation do not adequately replicate the performance of cells at higher rates. In this paper, a model is proposed based on the absolute nodal coordinate formulation approach, which includes as its states concentration levels at different spatial locations within the solid electrode and electrolyte. Its behavior is demonstrated through simulation results reproducing high performance solutions and tractable state representation for use with advanced BMSs.