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Power-split hybrid electric vehicles (HEV) employ a speed reduction gear (SRG) mainly to enhance acceleration performance. However, the full potentials of an additional gear on fuel economy and acceleration performance have not yet been thoroughly investigated due to a vast design space: 432 configurations with three design variables (i.e. two planetary gear ratios and a final drive gear ratio). In this paper, a systematic speed reduction gear design methodology is proposed to analyze the impact of a speed reduction (multiplication) gear on the performance of input- and output-split HEVs and select an optimal configuration. First, the physical and virtual design spaces of SRG (SMG) are defined and the relationship between two design spaces are identified. Second, performance metrics are evaluated within the virtual design space using the proposed simplified lever. The proposed approach completely eliminates the redundancy present in the physical design spaces, and thus, the impact of SRG (SMG) on the performance of input- and output-split configurations can be analyzed with the minimum computational burden. Lastly, the selected gear ratio is converted back to the physical planetary gear connections. The results confirm that SRG (SMG) can potentially either improve or deteriorate the acceleration performance and the fuel economy of split HEVs. Therefore, the full potential of speed reduction or multiplication gear should be thoroughly analyzed when designing split hybrid electric vehicles.

Predicting future motions of surrounding vehicles and driver’s intentions are essential to avoid future potential risks. The predicting future motions, however, is very challenging because the future cannot be deterministically known a priori and there are infinitely many possible future trajectories. Prediction becomes far more challenging when trying to foresee distant future. This paper proposes a probabilistic motion prediction algorithm that can accurately compute the likelihood of multiple target lanes and trajectories of surrounding vehicles by using the artificial neural network; more specifically radial base function network (RBFN). The RBFN prediction algorithm estimates the likelihood of each lane being the driver’s target lane in categorical distributions and the corresponding future trajectories in parallel. In order to demonstrate the effectiveness of the proposed prediction algorithm, it is applied for the predictive cruise control problem. Chance-constrained model predictive control (CCMPC) is utilized because the chance constraints in CCMPC can handle collision uncertainties associated with future uncertainties from the proposed prediction algorithm. The RBFN-based CCMPC simulation is conducted for several risky cut-in scenarios and compared with the state-of-the-art Interactive Multiple Model (IMM)-based prediction algorithm. The simulation results show that the RBFN-based CCMPC achieves higher collision avoidance success rate than that of the IMM-based CCMPC while using smaller actuator inputs and providing higher passenger comforts. Furthermore, the RBFN-based CCMPC showed high robustness to false braking during near lane-change (lane-keeping) scenarios.

The lane keeping system (LKS), a promising driver assistance system, is essential for autonomous vehicles. In real-world road conditions, it can be quite challenging because LKS must stay within the lane without causing passenger discomfort while both disturbances (e.g., road curvature, wind gusts, and hydroplaning) and model uncertainties in parameters [e.g., vehicle mass, center of gravity (CG), and tire cornering stiffness] are present. In this paper, the performance limits and tradeoffs between three performance criteria (lane tracking, stability robustness, and passenger comfort) are first investigated by exploring the entire design space of three prominent controllers, i.e., proportional–integral–derivative, linear–quadratic–Gaussian, and H-infinity ( $\text{H}_{\infty }$ ). Then, a sensitivity study on the vehicle parameters is conducted in order to investigate the impact of the parameters on the three performance metrics. Based on the aforementioned studies, this paper concludes that a robust controller can provide the maximum performance limit with respect to the lane tracking and stability robustness, when properly designed. However, it is observed that the robust controller is still sensitive to a few design and model parameters, such as look-ahead distance and CG. Therefore, the sensitivity study suggests that for vehicles with excessive mass and CG changes, such as SUVs and trucks, the adaptation of controller and look-ahead distance may be necessary to maximize both tracking performance and passenger comfort over a wide range of vehicle speeds.

The used battery packs with inhomogeneous cells suffer from energy loss and poor state of charge (SOC) estimation accuracy. In order to reduce the cell-to-cell variations by minimizing the energy loss and SOC estimation error, they need to be reconfigured. In this paper, a framework for cell selection method is developed. To describe the cell characteristics, the first-order RC model is selected. Then, the cell testing profile with static capacity and dynamic parameter test is proposed. By means of the linear squares estimation, the cell parameters such as nominal capacity and dynamic parameters are obtained. Lastly, a screening algorithm minimizes the cell-to-cell variations with respect to both nominal capacity and dynamic parameters. Thereby, the optimal combination of selection parameters (σ-range for nominal capacity and weighting factors for dynamic parameters) is studied customized to the design requirements (number of packs and number of cells within pack). The results of case study imply that the developed framework reduces the maximum cell-to-cell variation by 60–70%. The reconfigured second-life packs can be offered with lower price compared to new battery packs by guaranteeing reliable energy supply. Therefore, they are the cost-effective and reliable energy storage solution for stationary power applications.

In practice, many autonomous vehicle developers put a tremendous amount of time and efforts in tuning and calibrating the path tracking controllers in order to achieve robust tracking performance and smooth steering actions over a wide range of vehicle speed and road curvature changes. This design process becomes tiresome when the target vehicle changes frequently. In this study, a model-based Linear Quadratic Gaussian (LQG) Control with adaptive Q-matrix is proposed to efficiently and systematically design the path tracking controller for any given target vehicle while effectively handling the noise and error problems arise from the localization and path planning algorithms. The regulator, in turn, is automatically designed, without additional efforts for tuning at various speeds. The performance of the proposed algorithm is validated based on KAIST autonomous vehicle. The experimental results show that the proposed LQG with adaptive Q-matrix has tracking performance in both low (15kph) and high (45kph) speed driving conditions better than those of other conventional tracking methods like the Stanley and Pure-pursuit methods.

Previously, an equivalent consumption minimization strategy (ECMS) was developed that provides near-optimal performance of hybrid vehicles based on an adaptation of equivalence factor from state of charge feedback. However, under real-world driving conditions with uncertainties, such as hilly roads, ECMS requires a predictive scheme utilizing future driving information in order to prevent a loss of optimality. In this paper, we synthesize predictive ECMS in a feedforward way to adjust the equivalence factor based on its theoretical connection with future driving statistics, in a systematic manner. First, a useful noncausal adaptation strategy is extracted from dynamic programming results. Then, the inverse problem is formulated and solved to derive an explicit representation of the constant optimal equivalence factor with justified assumptions. Finally, a causal, predictive adaptation strategy using this closed-form solution is synthesized to mimic the noncausal one, and its effectiveness is evaluated for fuel cell hybrid electric vehicles. Results show that if the predicted statistical information reflects well the future driving conditions, the proposed strategy accurately estimates the constant optimal equivalence factor, including the jump behavior, thereby yielding less than 1.5% loss of fuel optimality. Moreover, this approach is extendible to other configurations.

Path tracking control is an important technology for the safety and comfort of autonomous vehicles. In tracking problems, vehicle lateral motion is highly affected by the desired path curvature, which is known as disturbance, and thus the controller performance can be additionally improved by using it in an optimal control method. This paper presents an augmented linear quadratic Gaussian (LQG) controller for reducing tracking errors and estimating accurate states. The proposed LQG is designed based on the augmented state space model, which contains lateral error dynamic model and curvature disturbance model induced from path mathematical properties. With optimal gain achieved through augmentation, the proposed method calculates the front steering wheel control input in the controller and performs state estimation in the observer by considering the tracking error and curvature simultaneously. The controller is implemented in real-time on an autonomous vehicle for driving experiments. The results show improved performance in comparison with conventional LQG without augmentation.

Platoon formation of highway vehicles has the potential to significantly enhance road safety, improve highway utility, and increase traffic efficiency. However, various uncertainties and disturbances that are present in real-world driving conditions make the implementation of vehicular platoon a challenging problem. This study presents an H-infinity control method for a platoon of heterogeneous vehicles with uncertain vehicle dynamics and uniform communication delay. The requirements of string stability, robustness and tracking performance are systematically measured by the H-infinity norm, and explicitly satisfied by casting into the linear fractional transformation format. A delay-dependent linear matrix inequality is derived to numerically solve the distributed controllers for each vehicle. The performances of the controlled platoon are theoretically analysed by using a delay-dependent Lyapunov function which includes a linear quadratic function of states during the delay period. Simulations with a platoon of heterogeneous vehicles are conducted to demonstrate the effectiveness of the proposed method under random parameters and external disturbances.

The model predictive control (MPC) is implemented by repeatedly solving an open loop optimal control problem (OCP). For the real-time implementation, the OCP is often discretized with evenly spaced time grids. This evenly spaced discretization, however, is accurate only if sufficiently small sampling time is used, which leads to heavy computational load. This paper presents a method to efficiently and accurately compute the continuous-time MPC problem based on the pseudospectral discretization, which utilizes unevenly spaced collocation points. The predictive horizon is virtually doubled by augmenting a mirrored horizon such that denser collocation points can be used towards the current time step, and sparser points can be used towards the end time of predictive horizon. Then, both state and control variables are approximated by Lagrange polynomials at only a half of LGL (Legendre-Gauss-Lobatto) collocation points. This implies that high accuracy can be achieved with a much less number of collocation points, which results in much reduced computational load. Examples are used to demonstrate its advantages over the evenly spaced discretization.

The switching based control is an effective way to handle systems with large and fast varying uncertainties. Many conventional methods, however, do not use robust controllers to stabilize each model, and thus need a large number of controllers to ensure the stability of systems with large uncertainties. Under the structure of supervisory control, this paper presents a robust multiple model switching control (RMMSC) method using H ∞ control for MIMO linear systems with large parametric uncertainty. The proposed method uses H ∞ controller to maximize the stability region of each model with uncertainties, and thus to significantly reduce the number of candidate controllers. The candidate controllers are designed by using linear matrix inequality (LMI), and an exponentially decaying switch index is proposed to select the proper controller by estimating the system norm of each model uncertainty. Using such switch index, the closed-loop control system is then equivalent to a switching system with smaller uncertainty whose system norm can be predefined by designers. The robust stability under arbitrary switching conditions is proven by the small gain theorem; and for slow switching conditions, the acceptable dwell time for stability is analyzed and presented. The effectiveness of this method is demonstrated with the second order inertial system with large model uncertainties.

Control of plug-in hybrid electric vehicles (PHEVs) poses a different challenge from that of the conventional hybrid electric vehicle (HEV) because the battery energy is designed to deplete throughout the drive cycle. In particular, when the travel distance exceeds the all-electric range (AER) of a PHEV and when tailpipe emissions are considered, optimal operation of the PHEV must consider optimization of the performance over a time horizon. In this paper, we develop a method to synthesize a supervisory powertrain controller (SPC) that achieves near-optimal fuel economy and tailpipe emissions under known travel distances. We first find the globally optimal solution using the dynamic programming (DP) technique, which provides an optimal control policy and state trajectories. Based on the analysis of the optimal state trajectories, a new variable energy-to-distance ratio (EDR), θ, is introduced to quantify the level of battery state-of-charge (SOC) relative to the remaining distance. This variable plays an important role in adjusting both energy and catalyst thermal management strategies for PHEVs. A novel extraction method is developed to extract adjustable engine on/off, gear-shift, and power-split strategies from the DP control policy over the entire state space. Based on the extracted results, an adaptive SPC that optimally adjusts the engine on/off, gear-shift, and power-split strategies under various EDR and catalyst temperature conditions was developed to achieve near-optimal fuel economy and emission performance.

Control of Plug-in Hybrid Electric Vehicles (PHEVs) poses a different challenge from that of the conventional Hybrid Electric Vehicle (HEV) due to the fact that the battery energy is depleted throughout the drive cycle. In particular, when the travel distance exceeds the All Electric Range (AER) of a PHEV, control of the PHEV is no longer trivial. In this paper, we develop a method for the synthesis of the supervisory powertrain controller (SPC) that achieves near-optimal performance under known travel distances. We first find the globally optimal solution using the dynamic programming (DP) technique, which serves as a benchmark of achievable performance. By analyzing the DP results, a variable Energy-to-Distance Ratio (EDR), θ, is introduced to quantify the level of battery state-of-charge (SOC) with respect to the remaining distance. This variable was found to play an important role in the energy management of PHEVs, and an adaptive SPC that adjusts engine on/off and gear-shift strategies under a wide range of θ conditions was proposed using a comprehensive extraction method. Simulation results confirm that the proposed adaptive SPC achieves near-optimal (

Among others, a reliable threat prediction algorithm is one of the key enabling technologies for the commercialization of the automated driving systems and other driver assistance systems. Previous algorithms that use Time-to-Collision (TTC) as a measure of threat tend to assume constant state and constant input; e.g. constant yaw rate and constant acceleration. Although the predictability of these algorithms is acceptable within a one second time horizon, it becomes invalid for predictions over one second because yaw rate and acceleration are highly unlikely to be constant. Therefore, in this paper, we propose a threat prediction algorithm that can accurately predict TTC over a longer time horizon based on future trajectory predictions of a surrounding vehicle. First, a comprehensive set of local path candidates is generated along the curvilinear coordinates using a quintic (5th order) polynomial with respect to the arc-length corresponding to the different lateral offsets. Trajectory prediction of a surrounding vehicle is accomplished by introducing target lane detection, which is estimated according to the amount of difference between the current motion and the centerline of the driving lane. Based on these future vehicle trajectories, TTC is computed by comparing the entrance and exit time of two vehicles into and out of the conflict area where the occupied spaces of two vehicles overlap. Finally, in order to provide threat assessment results, the inverse TTC values obtained above are plotted on a 2-dimensional trajectory plane where each set of the tangential acceleration and the initial yaw acceleration values represents each local path candidate. Thus, these threat assessment results can be directly utilized to determine a driving strategy of autonomous vehicles.

Nowadays, power-split hybrid electric vehicles (PS-HEV) are very popular mainly thanks to the success of Toyota Prius. Despite their superior performance, the design and control of PS-HEVs are non-trivial due to the large number of design candidates and the complex control problems. For instance, there exist twelve ways to connect the four components (two motor/generators, an engine, and a driving wheel) with a single planetary gear-set (PG), and the number increases to 1152 possible configurations when using two PGs. Moreover, if we consider the final drive (FD) and PG ratios as design variables, finding the best design becomes intractable. In this study, we introduce a simple yet powerful way to find the optimal designs of single PG PS-HEVs. The suggested method consists of two parts — full-load analysis and light-load analysis. The full-load analysis computes 0–100kph times to evaluate acceleration performance of all designs using instantaneous optimization approach. The light-load analysis evaluates the fuel economy of selected designs (designs with acceptable acceleration performance) using equivalent consumption minimization strategy (ECMS). Note that the sun-to-ring (SR) gear ratio and the FD ratio are considered design variables, and thus one can see how fuel economy and acceleration performance of each configuration vary with SR and FD ratios. Based on these analyses, the optimal design that balances full-load and light-load performances can be selected.Copyright © 2014 by ASME

Single particle models (SPM) are usually limited to low currents, which is a serious constrain for the usage of such models into vehicular battery management systems. The present study develops a physics-based ordinary differential equation (ODE) model, which is called extended single particle model (ESPM). In order to maintain the physical significance of the ODE model, a first-principle electrochemical partial differential equations (PDE) model is directly converted into an ODE model using volume-average method. The simulation results show that the ESPM model achieves an accuracy improvement of at least 14% when compared to the standard SPM for various levels of current inputs with only slight increase in computation time. The developed model paves the way for further improvements towards high-current, electrochemical ODE models with high physical significance and low computation burden.

Past research on hybrid electric vehicles (HEVs) focused primarily on improving their fuel economy. Emission reduction is another important performance attribute that needs to be addressed. When emissions are considered for hybrid vehicles with a gasoline engine, horizon-based optimization methodologies should be used because the light-off of the three-way catalytic converter heavily depends on the warming-up of catalyst temperature. In this paper, we propose a systematic design method for a cold-start supervisory control algorithm based on the dynamic programming (DP) methodology. First, a system-level parallel HEV model is developed to efficiently predict tailpipe emissions as well as fuel economy. The optimal control problem for minimization of cold-start emissions and fuel consumption is then solved via DP. Since DP solution cannot be directly implemented as a real-time controller, more useful control strategies are extracted from DP solutions over the entire state space via the comprehensive extraction method. The extracted DP results indicate that the engine on/off, gear-shift, and power-split strategies must be properly adjusted to achieve fast catalyst warm-up and low cold-start tailpipe emissions. Based on DP results, we proposed a rule-based control algorithm that is easy to implement and adjust while achieving near-optimal fuel economy and emission performance.

For driving cycles that require use of the engine (i.e. the trip distance exceeds the All Electric Range (AER) of a Plug-in Hybrid Electric Vehicle (PHEV) or a driving cycle demands power exceeding the battery peak power), the catalyst temperature management for reduced tailpipe emissions is a challenging control problem due to the frequent and extended engine shut-down and catalyst cool-down. In this paper, we develop a method to synthesize a supervisory powertrain controller (SPC) that achieves near-optimal fuel economy and tailpipe emissions under known travel distances. We first find the globally optimal solution using dynamic programming (DP), which provides an optimal control policy and state trajectories. Based on the analysis of the optimal state trajectories, a variable Energy-to-Distance Ratio (EDR) is introduced to quantify the level of battery state-of-charge (SOC) relative to the remaining distance. A novel two-dimensional extraction method is developed to extract engine on/off, gear-shift, and power-split control strategies as functions of both EDR and the catalyst temperature from the DP control policy. Based on the extracted results, an adaptive SPC that optimally adjusts the engine on/off, gear-shift, and power-split strategies under various EDR and catalyst temperature conditions was developed to achieve near-optimal fuel economy and emission performance.

The parallel hybrid electric vehicle (HEV) with a single pre-transmission electric motor (the P2 configuration) has a challenging drivability issue during engine-starts because the motor must simultaneously provide the propulsion torque demand and start the engine. The goal of this study is to present a design process to achieve optimal balance between these two conflicting goals. We first develop a control-oriented HEV powertrain model to accurately predict the engine, clutch, and vehicle dynamics. Assuming that the clutch torque can be accurately estimated and perfectly cancelled, an optimal engine-start control problem is formulated to minimize engine-start time while accurately supplying the driver torque demand simultaneously. This nonlinear constrained optimal control problem is solved numerically using Dynamic Programming (DP). DP results show that a proper constant clutch pressure level, which leads to constant torque disturbance that is easy to cancel out using the motor, can achieve near-optimal performance. Furthermore, the DP control policy is found to be time-invariant, and thus can be directly implemented in the form of a full state feedback controller.Copyright © 2011 by General Motors

Active suspension has been widely studied in recent decades but the implementation of the single-input, single-output (SISO) force-control architecture that many of the prior studies use has had limited success due to the lightly damped zeros. The inherent trade-off between robust stability and road disturbance attenuation for SISO control architecture is the main culprit. In this paper, we study whether the single-input, two-output (SITO) control architecture provides sufficient degrees of freedom in the control synthesis. First, a quarter car model with an electromagnetic motor is derived and the improved LQG/LTR design technique is employed to simultaneously recover both stability robustness and disturbance attenuation properties at the expense of measurement noise sensitivity. It was found that if the control system is restricted to SISO architecture, sprung mass acceleration is the most promising choice among practical measurements. Both classical and modern control approaches are used to analyze the effectiveness of the proposed method and its closed-loop performance. Simulation results show that stability robustness and disturbance attenuation can be dramatically improved by the SITO architecture over its SISO counterpart.

Under hilly road conditions, it is difficult to achieve near-optimal performance of energy management strategy (EMS) of fuel cell hybrid electric vehicle (FCHEV). In order to achieve near-optimality, optimal state reference trajectory is predicted based on future information, and thus reference tracking controller is often considered as real-time predictive EMS. There are two approaches depending on in what way the predicted reference will be used as follows: 1) position-based predictive EMS for tracking position- dependent reference, 2) time-based predictive EMS for tracking time-dependent reference. In this paper, analytical sensitivity analysis based on Pontryagin’s minimum principle (PMP) is performed to prove robustness of position-based predictive EMS with respect to velocity uncertainty. First, optimal control problem is formulated in time and position domain, and PMP approach is used to derive boundary value problem (BVP) that achieves global optimality. Then, sensitivity differential equations are developed which describe sensitivity of original BVP with respect to velocity uncertainty. Finally, these equations will be solved simultaneously with the original BVP to compute first-order sensitivity of time- and position- dependent optimal state. Results show that sensitivity of time-dependent optimal state is much bigger than that of position-dependent optimal state because velocity uncertainty can change predicted travel time, and this effect on sensitivity is significant. Therefore, predictive EMS should use current position to track position-dependent optimal state reference in terms of the robustness with respect to velocity uncertainty.