Parameters for an electrochemistry-based Lithium-ion battery model are estimated using the homotopy optimization approach. A high-fidelity model of the battery is presented based on chemical and electrical phenomena. Equations expressing the conservation of species and charge for the solid and electrolyte phases are combined with the kinetics of the electrodes to obtain a system of differential-algebraic equations (DAEs) governing the dynamic behavior of the battery. The presence of algebraic constraints in the governing dynamic equations makes the optimization problem challenging: a simulation is performed in each iteration of the optimization procedure to evaluate the objective function, and the initial conditions must be updated to satisfy the constraints as the parameter values change. The ε-embedding method is employed to convert the original DAEs into a singularly perturbed system of ordinary differential equations, which are then used to simulate the system efficiently. The proposed numerical procedure demonstrates excellent perfor- * Corresponding author. The final publication is available at Elsevier via http://doi.org/10.1016/j.jpowsour.2015.04.154 © 2015 mance in the estimation of parameters for the Lithium-ion battery model, compared to direct methods that are either unstable or incapable of converging. The obtained results and estimated parameters demonstrate the efficacy of the proposed simulation approach and homotopy optimization procedure.

Plug-in hybrid electric vehicle (PHEV) development seems to be essential for a sustainable transportation system along with electric vehicles. An appropriate power management strategy for a PHEV determines how to blend the engine and the battery power in such a way that leads to significant fuel economy improvement and environmental footprint reduction. To evaluate and validate the controls design, software and hardware-in-the-loop (SIL/HIL) simulations are useful approaches, especially at the early stages of controls design. To conduct SIL/HIL tests, an accurate and relatively fast mathematical model of the real powertrain is required which solely contains the essential dynamics of the plant. In this paper, a physics-based model of a power-split plug-in powertrain is developed and implemented using MapleSim software. This model contains a chemistry-based lithium-ion battery pack, which can distinguish it from other models used in the literature, since the performance of a PHEV greatly depends on its battery. The symbolic computation power of MapleSim makes the model very suitable for real-time SIL/HIL tests.

A free-floating space robot with four linkages, two flexible arms and a rigid end-effector that are mounted on a rigid spacecraft; is studied in this paper. The governing equations are derived using Kane’s method. The powerful tools of Kane’s approach in incorporating motion constraints have been applied in the dynamic model. By including the motion constraints in the kinematic and dynamic equations, a two way coupling between the spacecraft motion and manipulator motion is achieved. The assumed mode method is employed to express elastic displacements, except that the associated admissible functions are supplanted by quasicomparison functions. By a perturbation approach, the resulting nonlinear problem is separated into two sets of equations: one for rigid-body maneuvering of the robot and the other for elastic vibrations suppression and rigid-body perturbation control. The kinematic redundancy of the manipulator system is removed by exploiting the conservation of angular momentum law that makes the rigid manipulator system nonholonimic. Nonholonomic constraints, resulted from the nonintegrability of angular momentum, in association with equations obtained from conservation of linear momentum and direct differential kinematics generate a set of ordinary differential equations that govern the motion tracking of the robot. The digitalized linear quadratic regulator (LQR) with prescribed degree of stability is used as the feedback control scheme to suppress vibrations. A numerical example is presented to show the numerical preferences of using Kane’s method in deriving the equations of motion and also the efficacy of the control scheme. Acquiring a zero magnitude for spacecraft attitude control moment approves the free-floating behavior of the space robot in which considerable amount of energy is saved.

The validity and accuracy of a high-fidelity mechanistic multibody model of a vertical piano action mechanism is examined experimentally and through simulation. An overview of the theoretical and computational framework of this previously presented model is given first. A dynamically realistic benchtop prototype mechanism was constructed and driven by a mechanical actuator pressing the key. For simulations, a parameterization based on geometric and dynamic component properties and configuration is used; initial conditions are established by a virtual regulation that mimics a piano technician's procedure. The motion of each component is obtained experimentally by high-speed imaging and automated tracking. Simulated response is shown to accurately represent that of the real action for two different (pressed) key inputs using a single fixed parameterization. Various specialized model features are separately evaluated. Proper simulated dynamic behavior supports the accuracy of the friction representation; this is especially so for softer key inputs which demand a more actively controlled playing technique. The accuracy of the contact model is confirmed by the proper timing and function of the mechanism, as the relationship between components is strongly dependent on the state of compression of the interface between them. The value of including three flexible components is weighed against their significant computational cost. Compared to a rigid fixed ground point target, hammer impact on a compliant string reduces impact force, contact duration, and postimpact hammer velocity to improve accuracy. Flexibility of the backcheck wire and hammer shank also strongly affects postimpact behavior of the mechanism. The sophisticated balance pivot model is seen to be valuable in creating a realistic key response, with compression of felt balance punching and lift-off of the key, very important for achieving the proper key–hammer relationship. Finally, two components unique to the vertical mechanism—the bridle strap and butt spring—are shown to be essential in controlling the hammer for detached key inputs, where the key is released before it has reached the front punching. Accurate postimpact response is important for proper simulation of repeated notes, as well as the “feel” of the action. In general, the results reported can be considered as a validation of the method for constructing and parameterizing a dynamically accurate multibody model of a specific prototype mechanism or system including compliant contacts and flexibility of some components, as well as ad hoc components to cover unusual dynamic behavior.

Summary Explicit model predictive control approach is a promising approach to fulfill automotive real‐time controls requirements. A key factor in the performance and real‐time capabilities of a predictive model‐based controller is the accuracy of the control‐oriented model. The control‐oriented model should capture the essential dynamics of the real plant and be adequately simple to make the controller implementable on a commercial hardware with limited memory and computational capabilities. In this study, control‐relevant parameter estimation is used to find a control‐oriented model for a real‐time predictive power management system for a plug‐in hybrid powertrain. Simulations, which are conducted using an equation‐based model of the powertrain, demonstrate a significant improvement of the power management system performance by improving the control‐oriented model with no effect on real‐time capabilities of the controller.

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The proper orthogonal decomposition (POD) is employed to reduce the order of small-scale automotive multibody systems. The reduction procedure is demonstrated using three models of increasing complexity: a simplified dynamic vehicle model with a fully independent suspension, a kinematic model of a single double-wishbone suspension, and a high-fidelity dynamic vehicle model with double-wishbone and trailing-arm suspensions. These three models were chosen to evaluate the effectiveness of the POD given systems of ordinary differential equations (ODEs), algebraic equations (AEs), and differential-algebraic equations (DAEs), respectively. These models are also components of more complicated full vehicle models used for design, control, and optimization purposes, which often involve real-time simulation. The governing kinematic and dynamic equations are generated symbolically and solved numerically. Snapshot data to construct the reduced subspace are obtained from simulations of the original nonlinear systems. The performance of the reduction scheme is evaluated based on both accuracy and computational efficiency. Good agreement is observed between the simulation results from the original models and reduced-order models, but the latter simulate substantially faster. Finally, a robustness study is conducted to explore the behavior of a reduced-order system as its input signal deviates from the reference input that was used to construct the reduced subspace.

The theoretical framework for constructing a fully mechanistic multibody dynamic model of a vertical piano action is described, and its general validity is established. Equations of motion are derived symbolically using a graph-theoretic formulation. Model fidelity is increased by introducing several novel features: (i) a new contact model for representing the compression of the felt-lined interfaces between interacting parts, capable of capturing the intermittent loading and unloading of these contacts occurring through the key stroke, as well as providing smooth transitions between these states; (ii) models for two important components that are unique to the vertical action, the bridle strap and the butt spring; (iii) a sophisticated key pivot model that captures both the rotational motion and the vertical translation of the key as it can lift off the balance rail under some conditions; (iv) flexible beam models for backcheck wire and hammer shank so as to predict observed vibrations in the response accurately; and (v) coupling of the mechanism model to a flexible stiff string model for realistic hammer impact. For simulation, parameters were obtained by experimental testing and measurement of a physical prototype vertical action. Techniques are described for the virtual regulation of the model to ensure that initial conditions and pseudostatic response accurately represent the precise configuration and desired relationships between the parts during the key stroke. Two input force profiles were used for simulations, a forte pressed (hard) and piano pressed touch (soft), typical of those measured at the key surface when activated by a pianist. Simulated response to these quite different inputs is described, and compared to experimental observations obtained from a physical prototype.