S. Di Cairano

MPC-Based Energy Management of a Power-Split Hybrid Electric Vehicle

A power-split hybrid electric vehicle (HEV) combines the advantages of both series and parallel hybrid vehicle architectures by utilizing a planetary gear set to split and combine the power produced by electric machines and a combustion engine. Because of the different modes of operation, devising a near optimal energy management strategy is quite challenging and essential for these vehicles. To improve the fuel economy of a power-split HEV, we first formulate the energy management problem as a nonlinear and constrained optimal control problem. Then two different cost functions are defined and model predictive control (MPC) strategies are utilized to obtain the power split between the combustion engine and electrical machines and the system operating points at each sample time. Simulation results on a closed-loop high-fidelity model of a power-split HEV over multiple standard drive cycles and with different controllers are presented. The results of a nonlinear MPC strategy show a noticeable improvement in fuel economy with respect to those of an available controller in the commercial Powertrain System Analysis Toolkit (PSAT) software and the other proposed methodology by the authors based on a linear time-varying MPC.

Vehicle Yaw Stability Control by Coordinated Active Front Steering and Differential Braking in the Tire Sideslip Angles Domain

Vehicle active safety receives ever increasing attention in the attempt to achieve zero accidents on the road. In this paper, we investigate a control architecture that has the potential of improving yaw stability control by achieving faster convergence and reduced impact on the longitudinal dynamics. We consider a system where active front steering and differential braking are available and propose a model predictive control (MPC) strategy to coordinate the actuators. We formulate the vehicle dynamics with respect to the tire slip angles and use a piecewise affine (PWA) approximation of the tire force characteristics. The resulting PWA system is used as prediction model in a hybrid MPC strategy. After assessing the benefits of the proposed approach, we synthesize the controller by using a switched MPC strategy, where the tire conditions (linear/saturated) are assumed not to change during the prediction horizon. The assessment of the controller computational load and memory requirements indicates that it is capable of real-time execution in automotive-grade electronic control units. Experimental tests in different maneuvers executed on low-friction surfaces demonstrate the high performance of the controller.

A stochastic model predictive control approach for series hybrid electric vehicle power management

This paper illustrates the use of stochastic model predictive control (SMPC) for power management in vehicles equipped with advanced hybrid powertrains. Hybrid vehicles use two or more distinct power sources for propulsion, and their complex powertrain architecture requires the coordination of all the subsystems to achieve target performances in terms of fuel consumption, driveability, component life-time, exhaust emissions. Many control strategies have been presented and successfully applied, mainly based on heuristics or rules and tuned on certain reference drive cycles. To take into account that cycles are not exactly known a priori in driving routine, this paper proposes a stochastic approach for the power management problem. We focus on a series hybrid electric vehicle (HEV), which combines an internal combustion engine and an electric motor. The power demand from the driver is modeled as a Markov chain estimated on several driving cycles and used to generate scenarios in the SMPC law. Simulation results over a standard driving cycle are presented to demonstrate the effectiveness of the proposed stochastic approach and compared with other deterministic approaches.

Model predictive control of magnetically actuated mass spring dampers for automotive applications

Mechatronic systems such as those arising in automotive applications are characterized by significant non-linearities, tight performance specifications as well as by state and input constraints which need to be enforced during system operation. This paper takes a view that model predictive control (MPC) and hybrid models can be an attractive and systematic methodology to handle these challenging control problems, even when the underlying process is not hybrid. In addition, the piecewise affine (PWA) explicit form of MPC solutions avoids on-line optimization and can make this approach computationally viable even in situations with rather constrained computational resources. To illustrate the MPC design procedure and the underlying issues, we focus on a specific non-linear process example of a mass spring damper system actuated by an electromagnet. Such a system is one of the most common elements of mechatronic systems in automotive systems, with fuel injectors representing a concrete example. We first consider a linear MPC design for the mechanical part of the system. The approach accounts for all the constraints in the system but one, which is subsequently enforced via a state-dependent saturation element. Second, a hybrid MPC approach for the mechanical subsystem is analysed that can handle all the constraints by design and achieves better performance, at the price of a higher complexity of the controller. Finally, a hybrid MPC design that also takes into account the electrical dynamics of the system is considered.

Model Predictive Control Tuning by Controller Matching

The effectiveness of model predictive control (MPC) in dealing with input and state constraints during transient operations is well known. However, in contrast with several linear control techniques, closed-loop frequency-domain properties such as sensitivities and robustness to small perturbations are usually not taken into account in the MPC design. This technical note considers the problem of tuning an MPC controller that behaves as a given linear controller when the constraints are not active (e.g., for perturbations around the equilibrium that remain within the given input and state bounds), therefore inheriting the small-signal properties of the linear control design, and that still optimally deals with constraints during transients. We provide two methods for selecting the MPC weight matrices so that the resulting MPC controller behaves as the given linear controller, therefore solving the posed inverse problem of controller matching, and is globally asymptotically stable.

Model Predictive Idle Speed Control: Design, Analysis, and Experimental Evaluation

Idle speed control is a landmark application of feedback control in automotive vehicles that continues to be of significant interest to automotive industry practitioners, since improved idle performance and robustness translate into better fuel economy, emissions and drivability. In this paper, we develop a model predictive control (MPC) strategy for regulating the engine speed to the idle speed set-point by actuating the electronic throttle and the spark timing. The MPC controller coordinates the two actuators according to a specified cost function, while explicitly taking into account constraints on the control and requirements on the acceptable engine speed range, e.g., to avoid engine stalls. Following a process proposed here for the implementation of MPC in automotive applications, an MPC controller is obtained with excellent performance and robustness as demonstrated in actual vehicle tests. In particular, the MPC controller performs better than an existing baseline controller in the vehicle, is robust to changes in operating conditions, and to different types of disturbances. It is also shown that the MPC computational complexity is well within the capability of production electronic control unit and that the improved performance achieved by the MPC controller can translate into fuel economy improvements.

The development of Model Predictive Control in automotive industry: A survey

Model Predictive Control (MPC) is an established control technique in chemical process control, due to its capability of optimally controlling multivariable systems with constraints on plant and actuators. In recent years, the advances in MPC algorithms and design processes, the increased computational power of electronic control units, and the need for improved performance, safety and reduced emissions, have drawn considerable interest in MPC from the automotive industry. In this paper we survey the investigations of MPC in the automotive industry with particular focus on the developments at Ford Motor Company. First, we describe the basic MPC techniques used in the automotive industry, and the early exploratory investigations. Then we present three applications that have been recently prototyped in fully functional production-like vehicles, highlighting the features that make MPC a good candidate strategy for each case. We finally present our perspectives on the next challenges and future applications of MPC in the automotive industry.

An MPC design flow for automotive control and applications to idle speed regulation

This paper describes the steps of a model predictive control (MPC) design procedure developed for a broad class of control problems in automotive engineering. The design flow starts by deriving a linearized discrete-time prediction model from an existing simulation model, augmenting it with integral action or output disturbance models to ensure offset-free steady-state properties, and tuning the resulting MPC controller in simulation. Explicit MPC tools are employed to synthesize the controller to quickly assess controller complexity, local stability of the closed-loop dynamics, and for rapid prototype testing. Then, the controller is fine-tuned by refining the linear prediction model through identification from experimental data, and by adjusting from observed experimental performance the values of weights and noise covariances for filter design. The idle speed control (ISC) problem is used in this paper to exemplify the design flow and our vehicle implementation results are reported.

Driver-assist steering by active front steering and differential braking: Design, implementation and experimental evaluation of a switched model predictive control approach

We investigate the coordination of active front steering and differential braking in a driver-assist steering system that aims at stabilizing the vehicle and achieving the desired yaw rate. Basing on a piecewise affine model of the vehicle steering dynamics formulated with respect to the tire slip angles and the steering angle we implement a switched model predictive controller to coordinate active front steering and differential braking. The switched controller is synthesized by multiparametric programming, resulting in a piecewise affine feedback law whose stability properties and computational effort can be analyzed with available tools. The controller response in different maneuvers is evaluated in simulations and experimentally on a low friction test track.

Nonlinear Model Predictive Control for power-split Hybrid Electric Vehicles

In this paper, a causal optimal controller based on Nonlinear Model Predictive Control (NMPC) is developed for a power-split Hybrid Electric Vehicle (HEV). The global fuel minimization problem is converted to a finite horizon optimal control problem with an approximated cost-to-go, using the relationship between the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagins minimum principle. A nonlinear MPC framework is employed to solve the problem online. Different methods for tuning the approximated minimum cost-to-go as a design parameter of the MPC are discussed. Simulation results on a validated high-fidelity closed-loop model of a power-split HEV over multiple driving cycles show that with the proposed strategy, the fuel economies are improved noticeably with respect to those of an available controller in the commercial Powertrain System Analysis Toolkit (PSAT) software and a linear time-varying MPC controller previously developed by the authors.