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.

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

Active suspensions influencing the vertical dynamics of vehicles enable the improvement of ride comfort and handling characteristics compared to vehicles with passive suspensions. If the road height profile in front of the car is measured using vehicle sensors, more efficient control strategies can be applied. In this brief, two model predictive approaches for preview active suspension controllers are proposed and compared to the well-known optimal preview control approach. The considered active suspension consists of low bandwidth actuators in series with the spring and passive dampers. Equations of a linear full-car model are derived. The first model predictive controller optimizes the actuator displacements on a nonequidistant grid over the preview horizon. The second controller optimizes trajectories for heave, pitch, and roll of the vehicle body over the preview horizon using a quadratic program. Therefore, a model inversion is presented. The trajectories are formulated as a summation of nonequidistant B-spline basis functions and constraints on the input are incorporated in trajectory generation via the inverse vehicle model. Simulation results are presented and vehicle implementation using recorded road height data is conducted.

Design and Vehicle Implementation of Preview Active Suspension Controllers

Receding horizon control (RHC), also known as model predictive control (MPC), is a general purpose control scheme that involves repeatedly solving a constrained optimization problem, using predictions of future costs, disturbances, and constraints over a moving time horizon to choose the control action. RHC handles constraints, such as limits on control variables, in a direct and natural way, and generates sophisticated feed-forward actions. The main disadvantage of RHC is that an optimization problem has to be solved at each step, which leads many control engineers to think that it can only be used for systems with slow sampling (say, less than one Hz). Several techniques have recently been developed to get around this problem. In one approach, called explicit MPC, the optimization problem is solved analytically and explicitly, so evaluating the control policy requires only a lookup table search. Another approach, which is our focus here, is to exploit the structure in the optimization problem to solve it efficiently. This approach has previously been applied in several specific cases, using custom, hand written code. However, this requires significant development time, and specialist knowledge of optimization and numerical algorithms. Recent developments in convex optimization code generation have made the task much easier and quicker. With code generation, the RHC policy is specified in a high-level language, then automatically transformed into source code for a custom solver. The custom solver is typically orders of magnitude faster than a generic solver, solving in milliseconds or microseconds on standard processors, making it possible to use RHC policies at kilohertz rates. In this paper we demonstrate code generation with two simple control examples. They show a range of problems that may be handled by RHC. In every case, we show a speedup of several hundred times from generic parser-solvers.

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Code generation for receding horizon control

Improving the vehicle performance with active suspension using road-sensing algorithm

A new adaptive vehicle suspension control method is presented that adjusts the controller parametrization to the current driving state and thereby enables to significantly enhance ride comfort while the dynamic wheel load and the suspension deflection remain within safety critical bounds. To this end, the adaptive controller structure dynamically interpolates between differently tuned linear quadratic regulators governed by the dynamic wheel load and the suspension deflection. The stability of the adaptive controller structure is analyzed by means of a common Lyapunov function approach taking into account the nonlinear damper characteristic of the suspension system. In order to provide a realistic framework for the controller design and the performance analysis, a quarter-car test rig based on an all-terrain vehicle suspension that has been equipped with an electrical linear motor to realize an active suspension system, is employed as testbed for the study. On this test rig, the significant performance of the adaptive control concept is successfully validated in a comparison to benchmark suspension controllers.

Driving State Adaptive Control of an Active Vehicle Suspension System

The objective of a suspension system is to maximize the passenger ride comfort and vehicle road holding quality. Passive systems present a trade-off between these objectives and the required suspension travel. An appropriate active suspension control overcomes this tradeoff and provides maximum ride comfort and road holding quality within the available suspension travel. In this paper, we show model predictive control (MPC) to be a design of choice for control of active suspension systems utilizing previewed road information. MPC design explicitly incorporates all hard constraints on state, control and output variables. It generalizes the approaches based on feedback linearization and dynamic inversion from single step control to multiple step control over a receding prediction horizon. MPC is shown to provide excellent improvements in the ride and road handling qualities of the vehicle over realistic terrain profiles. MPC works well even in the presence of noise in the previewed information. Implementation of MPC on the UCB active suspension test rig also shows the feasibility of the MPC algorithm in real-time application.

K.J. Hedrick

Papers

Active suspension using preview information and model predictive control