Cluster solutions in networks of weakly coupled oscillators on a 2D square torus

We consider a model for an N × N lattice network of weakly coupled neural oscilla- tors with periodic boundary conditions (2D square torus), where the coupling between neurons is assumed to be within a von Neumann neighborhood of size r, denoted as von Neumann r-neighborhood. Using the phase model reduction technique, we study the existence of cluster solutions with constant phase differences (Ψh, Ψv) between adjacent oscillators along the horizontal and vertical directions in our network, where Ψh and Ψv are not necessarily to be identical. Applying the Kronecker production representation and the circulant matrix theory, we develop a novel approach to analyze the stability of cluster solutions with constant phase difference (i.e., Ψh,Ψv are equal). We begin our analysis by deriving the precise conditions for stability of such cluster solutions with von Neumann 1-neighborhood and 2 neighborhood couplings, and then we generalize our result to von Neumann r-neighborhood coupling for arbitrary neighborhood size r ≥ 1. This developed approach for the stability analysis indeed can be extended to an arbitrary coupling in our network. Finally, numerical simulations are used to validate the above analytical results for various values of N and r by considering an inhibitory network of Morris-Lecar neurons.

The Delay-Dependent DOFC for Damping Inter-Area Low-Frequency Oscillations in an Interconnected Power System Considering Packet Loss of Wide-Area Signals

In this paper, the inter-area low-frequency oscillations are restrained in the interconnected power system by making use of the delay-dependent wide-area dynamic output feedback controller (DOFC). Modal analysis is adopted to obtain the modes of inter-area oscillation to be controlled and the Schur truncation model reduction technique is represented to reduce the order of the power system. The augmented closed-loop system model, where the transmission delay and packet loss of wide-area signals are considered, is established. The sufficient conditions of exponentially mean-square stable are obtained according to Lyapunov’s stability theory. Finally, case studies are carried out on a two-area four-machine power system, where our proposed controller, a conventional controller, and the wide-area damping controller in the existing references are installed, respectively. The simulation results under different external disturbances, packet loss rates, and delays are presented to show the effectiveness and advantages of our proposed controller.

Development and validation of nonlinear dynamic engine airpath models for real-time advanced control application

This paper proposes model reduction techniques for reducing engine airpath models in real-time (RT), for a control oriented application in an engine equipped with high pressure exhaust gas recirculation (EGR-HP) and single stage turbocharger. There are two major challenges addressed by authors: First, reducing the order without compromising the performance in terms of accuracy by decoupling the nonlinear coupled differential equations of airpath system in-order to use them in real-time processor-in-loop control application. A model reduction technique based on different dynamic characteristics between thermodynamic states followed by semi-implicit Euler (SIE) numerical method to solve coupled dynamic multi-input multi-output (MIMO) differential equation models is demonstrated. Second, the authors have proposed a novel method to calculate gas mass flow via compressor, coupled with engine airpath model in real-time. The proposed models of airpath system coupled with turbocharger models for a diesel engine is validated with experimental data to evaluate performance of pressures, temperatures, mass flows at relevant components. The developed airpath model is used for calculating thermodynamic properties in real-time for state of art engine control unit (ECU) in production engine and become basis for feedforward as well as closed loop control of airpath variables for real-time system. Authors further propose to use this modeling approach for calculating airpath system variables for exhaust aftertreatment system, injection system, and for virtualization of sensor values in airpath systems.

Development of a Harmonic Balance Method-Based Numerical Strategy for Blade-Tip/Casing Interactions: Application to NASA Rotor 37

In this study, a frequency-domain approach based on the harmonic balance method coupled to a predictor-corrector continuation algorithm is implemented for the qualitative analysis of blade-tip/casing contacts in aircraft engines. Unilateral contact and dry friction are taken into account through a regularized penalty law. To enhance the robustness of the methodology, particular attention is paid to the mitigation of the Gibbs phenomenon. To this end, the employed Alternating Frequency/Time scheme features a Lanczos σ-approximation so that spurious oscillations of the computed nonlinear contact forces become negligible. This approach is applied in combination with a model reduction technique on an industrial compressor blade: NASA rotor 37. In order to assess the influence of both the contact law regularization and the Lanczos σ-approximation, obtained results are thoroughly compared to an existing time integration-based numerical strategy relying on a Lagrange multiplier-based approach for contact treatment and that was previously confronted to experimental results. Presented results underline the very good agreement between the proposed methodology and the reference time integration numerical strategy. The proposed developments thus complement existing results on blade-tip/casing contact adding a much needed qualitative understanding of the interaction and an accurate assessment of the contact stiffening phenomenon.