Nalin Chaturvedi

Rigid-Body Attitude Control

Rigid-body attitude control is motivated by aerospace applications that involve attitude maneuvers or attitude stabilization. The set of attitudes of a rigid body is the set of 3 X 3 orthogonal matrices whose determinant is one. This set is the configuration space of rigid-body attitude motion; however, this configuration space is not Euclidean. Since the set of attitudes is not a Euclidean space, attitude control is typically studied using various attitude parameterizations. Motivated by the desire to represent attitude both globally and uniquely in the analysis of rigid-body rotational motion, this article uses orthogonal matrices exclusively to represent attitude and to develop results on rigid-body attitude control. An advantage of using orthogonal matrices is that these control results, which include open-loop attitude control maneuvers and stabilization using continuous feedback control, do not require reinterpretation on the set of attitudes viewed as orthogonal matrices. The main objec tive of this article is to demonstrate how to characterize properties of attitude control systems for arbitrary attitude maneuvers without using attitude parameterizations.

Electrochemical Model Based Observer Design for a Lithium-Ion Battery

Batteries are the key technology for enabling further mobile electrification and energy storage. Accurate prediction of the state of the battery is needed not only for safety reasons, but also for better utilization of the battery. In this work we present a state estimation strategy for a detailed electrochemical model of a lithium-ion battery. The benefit of using a detailed model is the additional information obtained about the battery, such as accurate estimates of the internal temperature, the state of charge within the individual electrodes, overpotential, concentration and current distribution across the electrodes, which can be utilized for safety and optimal operation. Based on physical insight, we propose an output error injection observer based on a reduced set of partial differential-algebraic equations. This reduced model has a less complex structure, while it still captures the main dynamics. The observer is extensively studied in simulations and validated in experiments for actual electric-vehicle drive cycles. Experimental results show the observer to be robust with respect to unmodeled dynamics as well as to noisy and biased voltage and current measurements. The available state estimates can be used for monitoring purposes or incorporated into a model based controller to improve the performance of the battery while guaranteeing safe operation.

Inertia-Free Spacecraft Attitude Tracking with Disturbance Rejection and Almost Global Stabilization

We derive a continuous nonlinear control law for spacecraft attitude tracking of arbitrary continuously differentiable attitude trajectories based on rotation matrices. This formulation provides almost global stabilizability, that is, Lyapunov stability of the desired equilibrium of the error system as well as convergence from all initial states except for a subset for which the complement is open and dense. This controller thus overcomes the unwinding phenomenon associated with continuous controllers based on attitude representations, such as quaternions, that are not bijective and without resorting to discontinuous switching. The controller requires no inertiainformation,noinformation onconstant-disturbance torques,andonlyfrequencyinformation forsinusoidal disturbance torques. For slew maneuvers (that is, maneuvers with a setpoint command in the absence of disturbances), the controller specializes to a continuous, nonlinear, proportional–derivative-type, almost globally stabilizing controller, in which casethe torque inputs can be arbitrarily bounded a priori. For arbitrary maneuvers, we present an approximate saturation technique for bounding the control torques.

Adaptive Partial Differential Equation Observer for Battery State-of-Charge/State-of-Health Estimation Via an Electrochemical Model

This paper develops an adaptive partial differential equation (PDE) observer for battery state-of-charge (SOC) and state-of-health (SOH) estimation. Real-time state and parameter information enables operation near physical limits without compromising durability, thereby unlocking the full potential of battery energy storage. SOC/SOH estimation is technically challenging because battery dynamics are governed by electrochemical principles, mathematically modeled by PDEs. We cast this problem as a simultaneous state (SOC) and parameter (SOH) estimation design for a linear PDE with a nonlinear output mapping. Several new theoretical ideas are developed, integrated together, and tested. These include a backstepping PDE state estimator, a Pade-based parameter identifier, nonlinear parameter sensitivity analysis, and adaptive inversion of nonlinear output functions. The key novelty of this design is a combined SOC/SOH battery estimation algorithm that identifies physical system variables, from measurements of voltage and current only.

PDE estimation techniques for advanced battery management systems — Part II: SOH identification

A critical enabling technology for electrified vehicles and renewable energy resources is battery energy storage. Advanced battery systems represent a promising technology for these applications, however their dynamics are governed by relatively complex electrochemical phenomena whose parameters degrade over time and vary across material design. Moreover, limited sensing and actuation exists to monitor and control the internal state of these systems. As such, battery management systems require advanced identification, estimation, and control algorithms. In this paper we examine state-of-health (SOH) estimation, framed as a parameter identification problem for parabolic PDEs and nonlinearly parameterized output functions. Specifically, we utilize the swapping identification method for unknown parameters in the diffusion partial differential equation (PDE). A nonlinear least squares method is applied to the output function to identify its unknown parameters. These identification algorithms are synthesized from the single particle model (SPM). In a companion paper we examine a new battery state-of-charge (SOC) estimation algorithm based upon the backstepping method for PDEs.A critical enabling technology for electrified vehicles and renewable energy resources is battery energy storage. Advanced battery systems represent a promising technology for these applications, however their dynamics are governed by relatively complex electrochemical phenomena whose parameters degrade over time and vary across manufacturer. Moreover, limited sensing and actuation exists to monitor and control the internal state of these systems. As such, battery management systems require advanced identification, estimation, and control algorithms. In this paper we examine a new battery state-of-charge (SOC) estimation algorithm based upon the backstepping method for partial differential equations (PDEs). The estimator is synthesized from the so-called single particle model (SPM). Our development enables us to rigorously analyze observability and stability properties of the estimator design. In a companion paper we examine state-of-health (SOH) estimation, framed as a parameter identification problem for parabolic PDEs and nonlinearly parameterized output functions.

Optimal charging strategies in lithium-ion battery

There is a strong need for advanced control methods in battery management systems, especially in the plug-in hybrid and electric vehicles sector, due to cost and safety issues of new high-power battery packs and high-energy cell design. Limitations in computational speed and available memory require the use of very simple battery models and basic control algorithms, which in turn result in suboptimal utilization of the battery. This work investigates the possible use of optimal control strategies for charging. We focus on the minimum time charging problem, where different constraints on internal battery states are considered. Based on features of the open-loop optimal charging solution, we propose a simple one-step predictive controller, which is shown to recover the time-optimal solution, while being feasible for real-time computations. We present simulation results suggesting a decrease in charging time by 50% compared to the conventional constant-current / constant-voltage method for lithium-ion batteries.

Dynamics and control of a 3D pendulum

New pendulum models are introduced and studied. The pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force and control forces and moments. Several different pendulum models are developed to analyze properties of the uncontrolled pendulum. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to the 3D pendulum. Rigid pendulum and multi-body pendulum control problems are proposed. The 3D pendulum models provide a rich source of examples for nonlinear dynamics and control, some of which are similar to simpler pendulum models and some of which are completely new.

Asymptotic Smooth Stabilization of the Inverted 3-D Pendulum

The 3-D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom; it is acted on by gravity and it is fully actuated by control forces. The 3-D pendulum has two disjoint equilibrium manifolds, namely a hanging equilibrium manifold and an inverted equilibrium manifold. The contribution of this paper is that two fundamental stabilization problems for the inverted 3-D pendulum are posed and solved. The first problem, asymptotic stabilization of a specified equilibrium in the inverted equilibrium manifold, is solved using smooth and globally defined feedback of angular velocity and attitude of the 3-D pendulum. The second problem, asymptotic stabilization of the inverted equilibrium manifold, is solved using smooth and globally defined feedback of angular velocity and a reduced attitude vector of the 3-D pendulum. These control problems for the 3-D pendulum exemplify attitude stabilization problems on the configuration manifold SO(3) in the presence of potential forces. Lyapunov analysis and nonlinear geometric methods are used to assess global closed-loop properties, yielding a characterization of the almost global domain of attraction for each case.

Almost global attitude stabilization of an orbiting satellite including gravity gradient and control saturation effects

Control saturation effects new results are presented for the problem of attitude stabilization of a rigid satellite in a circular orbit. Most prior results on this problem have addressed use of linear controllers to achieve local asymptotic stability; this paper presents controllers that achieve near global asymptotic stability. This is accomplished by using globally defined models that incorporate gravity gradient effects and a definition of the attitude of the satellite with respect to the rotating local vertical local horizontal coordinate frame. Lyapunov methods are used to analyze the closed loop properties, but their application takes into account the geometry of the tangent bundle TSO(3) on which the global dynamics evolve. Furthermore, the designed control law accommodates control saturation effects

Modeling, estimation, and control challenges for lithium-ion batteries

Increasing demand for hybrid electric vehicles (HEV), plug-in hybrid electric vehicles (PHEV) and electric vehicles (EV) has forced battery manufacturers to consider energy storage systems that are better than contemporary lead-acid batteries. Currently, lithium-ion (Li-ion) batteries are believed to be the most promising battery system for HEV, PHEV and EV applications. However, designing a battery management system for Li-ion batteries that can guarantee safe and reliable operation is a challenge, since aging and other performance degrading mechanisms are not sufficiently well understood. As a first step to address these problems, we analyze an existing electrochemical model from the literature. Our aim is to present this model from a systems & controls perspective, and to bring forth the research challenges involved in modeling, estimation and control of Li-ion batteries. Additionally, we present a novel compact form of this model that can be used to study the Li-ion battery. We use this reformulated model to derive a simple approximated model, commonly known as the single particle model, and also identify the limitations of this approximation.