Geometric-control formulation and averaging analysis of the unsteady aerodynamics of a wing with oscillatory controls

Differential-geometric-control theory represents a mathematically elegant combination of differential geometry and control theory. Practically, it allows exploitation of nonlinear interactions between various inputs for the generation of forces in non-intuitive directions. Since its early developments in the 1970s, the geometric-control theory has not been duly exploited in the area of fluid mechanics. In this paper, we show the potential of geometric-control theory in the analysis of fluid flows, exemplifying it as a heuristic analysis tool for discovery of symmetry-breaking and unconventional force-generation mechanisms. In particular, we formulate the wing unsteady aerodynamics problem in a geometric-control framework. To achieve this goal, we develop a reduced-order model for the unsteady flow over a pitching–plunging wing that is (i) rich enough to capture the main physical aspects (e.g. nonlinearity of the flow dynamics at large angles of attack and high frequencies) and (ii) efficient and compact enough to be amenable to the analytic tools of geometric nonlinear control theory. We then combine tools from geometric-control theory and averaging to analyse the developed reduced-order dynamical model, which reveals regimes for lift and thrust enhancement mechanisms. The unsteady Reynolds-averaged Navier–Stokes equations are simulated to validate the theoretical findings and scrutinize the underlying physics behind these enhancement mechanisms.

Estimation of exogenous drivers to predict COVID-19 pandemic using a method from nonlinear control theory

The currently ongoing COVID-19 pandemic confronts governments and their health systems with great challenges for disease management. Epidemiological models play a crucial role, thereby assisting policymakers to predict the future course of infections and hospitalizations. One difficulty with current models is the existence of exogenous and unmeasurable variables and their significant effect on the infection dynamics. In this paper, we show how a method from nonlinear control theory can complement common compartmental epidemiological models. As a result, one can estimate and predict these exogenous variables requiring the reported infection cases as the only data source. The method allows to investigate how the estimates of exogenous variables are influenced by non-pharmaceutical interventions and how imminent epidemic waves could already be predicted at an early stage. In this way, the concept can serve as an “epidemometer” and guide the optimal timing of interventions. Analyses of the COVID-19 epidemic in various countries demonstrate the feasibility and potential of the proposed approach. The generic character of the method allows for straightforward extension to different epidemiological models.

Design, Modeling, and Differential Flatness Based Control of Permanent Magnet-Assisted Synchronous Reluctance Motor for e-Vehicle Applications

This paper presents the utilization of differential flatness techniques from nonlinear control theory to permanent magnet assisted (PMa) synchronous reluctance motor (SynRM). The significant advantage of the proposed control approach is the potentiality to establish the behavior of the state variable system during the steady-state and transients operations as well. The mathematical models of PMa-SynRM are initially proved by the nonlinear case to show the flatness property. Then, the intelligent proportional-integral (iPI) is utilized as a control law to deal with some inevitable modeling errors and uncertainties for the torque and speed of the motor. Finally, a MicroLab Box dSPACE has been employed to implement the proposed control scheme. A small-scale test bench 1-KW relying on the PMa-SynRM has been designed and developed in the laboratory to approve the proposed control algorithm. The experimental results reflect that the proposed control effectively performs high performance during dynamic operating conditions for the inner torque loop control and outer speed loop control of the motor drive compared to the traditional PI control.

Operator-Based Nonlinear Control of Calorimetric System Actuated by Peltier Device

Recently, the development of SiC and GaN high-performance semiconductor devices has led to higher efficiency in power conversion equipment. In order to perform thermal design of power conversion equipment and evaluation of the equipment, it is necessary to measure the power loss of the equipment with high accuracy. In a previous study, a system to measure the power loss from the amount of heat emitted from power conversion devices using a Peltier device was proposed. In this study, aiming to improve the measurement accuracy, the temperature dependence of the thermal conductivity of a Peltier device, which was treated as a constant value in the previous study, was considered. The control system considering the temperature dependence of the thermal conductivity was designed based on operator theory, which is a nonlinear control theory. The simulation and experimental results show that the measurement accuracy was improved when the power loss was 10 W and 15 W compared to the case without considering the temperature dependence. In addition, the measurement time was reduced by about 100 s by considering the temperature dependence. The effectiveness of the proposed system was shown when the power loss was 10 W and 15 W.

Leader-Following Regional Multiple-Bipartite Consensus for Networked Lagrangian Systems with Coopetition Interactions

This paper investigates the leader-following regional multiple-bipartite consensus problems of networked Lagrangian systems (NLSs) in coopetition networks. Our framework expands the application scopes of traditional regional consensus in cooperative networks. With the aid of a novel auxiliary variable embedded in the control protocols, the final states of NLSs are guaranteed to realise multi-regional symmetry in the constructed multiple symmetric regions. By utilising the characteristic of acyclic topology in the structurally balanced graph, the stability of the closed system is performed by perturbation analysis theory, nonlinear control theory, functional analysis theory, and so on. Finally, the effectiveness of our approach is verified by numerical simulations.

Assessment of the Impact of Electric Vehicle Batteries in the Non-Linear Control of DC Microgrids

Several efforts need to be performed in transportation and energy production to mitigate the current environmental issues that are related to fossil fuel use. The implementation of DC microgrids and the use of electric vehicles seem to be an adequate solution. However, various technical challenges have to be addressed, like grid stability issues. Thus, this case report assesses the impact of an electric vehicle load in a DC microgrid, subject to nonlinear control theory. The EV battery pack is modeled and simulated. Subsequently, it is included as a load in an available model of nonlinear control of DC microgrids. The results demonstrate high stability with this new load and the feasibility of its implementation.

Performance Limitations in Sensorimotor Control: Trade-Offs Between Neural Computation and Accuracy in Tracking Fast Movements

The ability to move fast and accurately track moving objects is fundamentally constrained by the biophysics of neurons and dynamics of the muscles involved. Yet the corresponding trade-offs between these factors and tracking motor commands have not been rigorously quantified. We use feedback control principles to quantify performance limitations of the sensorimotor control system (SCS) to track fast periodic movements. We show that (1) linear models of the SCS fail to predict known undesirable phenomena, including skipped cycles, overshoot and undershoot, produced when tracking signals in the “fast regime,” while nonlinear pulsatile control models can predict such undesirable phenomena, and (2) tools from nonlinear control theory allow us to characterize fundamental limitations in this fast regime. Using a validated and tractable nonlinear model of the SCS, we derive an analytical upper bound on frequencies that the SCS model can reliably track before producing such undesirable phenomena as a function of the neurons' biophysical constraints and muscle dynamics. The performance limitations derived here have important implications in sensorimotor control. For example, if the primary motor cortex is compromised due to disease or damage, the theory suggests ways to manipulate muscle dynamics by adding the necessary compensatory forces using an assistive neuroprosthetic device to restore motor performance and, more important, fast and agile movements. Just how one should compensate can be informed by our SCS model and the theory developed here.

On Problem of Partial Detectability for Nonlinear Discrete-Time Systems

Discrete (finite-difference) systems are widely used in modern nonlinear control theory. One of the main problems of a qualitative study of such systems is the problem of stability of the zero equilibrium position, which has great generality. In most works, such a stability problem is analyzed with respect to all variables that determine the state of the system. However, for many cases important in applications, it becomes necessary to analyze a more general problem of partial stability: the stability of the zero equilibrium position not for all, but only with respect to some given part of the variables. Such a problem is often also considered as auxiliary problem in the study of stability with respect to all variables. In this way, the corresponding concepts and problems of detectability of the studied system arise, which play an important role in the process of analysis of nonlinear controlled systems. Then, more general problems of partial detectability were posed, within the framework of which the situation was studied when stability from a part of variables implies stability not with respect to all, but with respect to more part of the variables. This article studies a nonlinear discrete (finite-difference) system of a general form that admits a zero equilibrium position. Easily interpreted conditions are found on the structural form of the system under consideration that determine its partial detectability, for which stability over a given part of the variables of the zero equilibrium position means its stability with respect to the other, more part of the variables. In this case, the stability with respect to the remaining part of the variables is uncertain and can be investigated additionally. In the process of analyzing this problem of partial detectability, the concept of partial null-dynamics of the system under study is introduced. An application of the obtained results to the stabilization problem with respect to part of the variables of nonlinear discrete controlled systems is given.