Optimal State Estimation

Model-based predictive control (MPC) describes a set of advanced control methods, which make use of a process model to predict the future behavior of the controlled system. By solving a—potentially constrained—optimization problem, MPC determines the control law implicitly. This shifts the effort for the design of a controller towards modeling of the to-be-controlled process. Since such models are available in many fields of engineering, the initial hurdle for applying control is deceased with MPC. Its implicit formulation maintains the physical understanding of the system parameters facilitating the tuning of the controller. Model-based predictive control (MPC) can even control systems, which cannot be controlled by conventional feedback controllers. With most of the theory laid out, it is time for a concise summary of it and an application-driven survey. This review article should serve as such. While in the beginnings of MPC, several widely noticed review paper have been published, a comprehensive overview on the latest developments, and on applications, is missing today. This article reviews the current state of the art including theory, historic evolution, and practical considerations to create intuitive understanding. We lay special attention on applications in order to demonstrate what is already possible today. Furthermore, we provide detailed discussion on implantation details in general and strategies to cope with the computational burden—still a major factor in the design of MPC. Besides key methods in the development of MPC, this review points to the future trends emphasizing why they are the next logical steps in MPC.

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Review on model predictive control: an engineering perspective

Optimisation of operating parameters on the performance characteristics of a free piston engine linear generator fuelled by CNG–H2 blends using the response surface methodology (RSM)

In this paper a real-time capable hierarchical nonlinear model predictive control framework for the energy management of a hybrid electric vehicle is presented. As high-level energy management, nonlinear model predictive control is employed. Therefore, a nonlinear optimal control problem is formulated using a control-oriented internal model derived from high-fidelity models and experimental data. The multiple shooting algorithm and an Euler backward scheme are used to discretize the optimal control problem. The resulting nonlinear problem is solved in real-time using Sequential Quadratic Programming. A rule-based gear choice and engine on / off strategy is added. Actuator dynamics and drivability are addressed in a fast low-level linear time-variant model predictive controller. The result is analyzed and compared to the optimal solution obtained by dynamic programming using a simplified model of the vehicle.

Real-Time Nonlinear Model Predictive Control for the Energy Management of Hybrid Electric Vehicles in a Hierarchical Framework*

Innovative air path concepts for turbocharged spark-ignition engines with exhaust gas recirculation impose high demands on the control due to nonlinearities and cross-couplings. This contribution i...

Model predictive air path control for a two-stage turbocharged spark-ignition engine with low pressure exhaust gas recirculation:

Nonlinear Model Predictive Control for the Starting Process of a Free-Piston Linear Generator

In this paper a hierarchical model predictive control framework for the energy management of a hybrid electric vehicle is extended by replacing the supervisory linear model predictive controller with a nonlinear model predictive controller. The nonlinear system dynamics of a parallel hybrid electric vehicle are incorporated into a nonlinear optimal control problem which is solved at each time instance. The discretization of the continuous time system dynamics is realized via direct multiple shooting. The low-level linear model predictive controller considers the actuator dynamics for optimal tracking of the driver's torque demand while the high-level controller considers the slow dynamics of the vehicle and the battery. The proposed strategy is validated in simulation with the worldwide harmonized light vehicles test cycle and compared to a hierarchical model predictive control framework with linearized system dynamics.

Nonlinear Hierarchical Model Predictive Control for the Energy Management of a Hybrid Electric Vehicle

For increasing the efficiency and simultaneously decreasing pollutant emissions of internal combustion engines, innovative air path concepts such as turbocharged gasoline engines with exhaust gas recirculation (EGR) are in the focus of current research. These air and EGR path concepts impose high demands on the process control due to the nonlinearities and cross-couplings. This contribution presents a physics-based modeling approach and a nonlinear model predictive controller (NMPC) for the air path control of a sequentially two-stage turbocharged gasoline engine with low pressure EGR. By using EGR at high loads, the in-cylinder temperature can be lowered, reducing the knock probability, while at the same time preventing the need for enrichment of the air/fuel ratio. As air and EGR path are cross-coupled and show different delay times, a model predictive control (MPC) concept is proposed. Therefore, the air and EGR path are modeled in a physical manner, where possible.The model set up is based on a small amount of dyno-run measurement data acquired with a test vehicle. The model is built up such that it can be used within a MPC algorithm.The proposed control concept consists of an extended Kalman Filter for state and disturbance estimation and a NMPC controller considering the dynamic behavior of the air and EGR path. Subsequently, the nonlinear control concept for the two-stage turbocharged spark-ignited (SI) engine with Low Pressure EGR is implemented on a rapid control prototyping hardware, validated via simulative tests and compared to a linear MPC.

Martin Keller

Papers

Model predictive air path control for a two-stage turbocharged spark-ignition engine with low pressure exhaust gas recirculation:

Nonlinear Model Predictive Control for the Starting Process of a Free-Piston Linear Generator

Real-Time Nonlinear Model Predictive Control for the Energy Management of Hybrid Electric Vehicles in a Hierarchical Framework*

Nonlinear Hierarchical Model Predictive Control for the Energy Management of a Hybrid Electric Vehicle

Physics-Based Modeling and MPC for the Air Path of a Two-Stage Turbocharged SI Engine with Low Pressure EGR