Davorin David Hrovat

Hybrid model predictive control application towards optimal semi-active suspension

The optimal control problem of a quarter-car semi-active suspension has been studied in the past. Considering that a quarter-car semi-active suspension can either be modelled as a linear system with state dependent constraint on control (of actuator force) input, or a bi-linear system with a control (of variable damping coefficient) saturation, the seemingly simple problem poses several interesting questions and challenges. Does the saturated version of the optimal control law derived from the corresponding un-constrained system, i.e. “clipped-optimal”, remain optimal for the constrained case as suggested in some previous publications? Or should the optimal deviate from the “clipped-optimal” as suggested in other publications? If the optimal control law of the constrained system does deviate from its unconstrained counter-part, how different are they? What is the structure of the optimal control law? Does it retain the linear state feedback form (as the unconstrained case)? In this paper, we attempt to answer some of the above questions by utilizing the recent development in model predictive control (MPC) of hybrid dynamical systems. The constrained quarter-car semi-active suspension is modelled as a switching affine system, where the switching is determined by the activation of passivity constraints, force saturation, and maximum power dissipation limits. Theoretically, over an infinite prediction horizon the MPC controller corresponds to the exact optimal controller. The performance of different finite-horizon hybrid MPC controllers is tested in simulation using mixed-integer quadratic programming. Then, for short-horizon MPC controllers, we derive the explicit optimal control law and show that the optimal control is piecewise affine in state. In the process, we show that for horizon equal to one the explicit MPC control law corresponds to clipped LQR as expected. We also compare the derived optimal control law to various semi-active control laws in the literature including the well-known “clipped-optimal”. We evaluate their corresponding performances for both a deterministic shock input case and a stochastic random disturbances case through simulations.

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 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.

Hybrid Model Predictive Control of Direct Injection Stratified Charge Engines

This paper illustrates the application of hybrid modeling and model predictive control techniques to the management of air-to-fuel ratio and torque in advanced technology gasoline direct-injection stratified-charge (DISC) engines. A DISC engine is an example of a constrained hybrid dynamical system, because it can operate in two distinct modes (stratified and homogeneous) and because the mode-dependent constraints on the air-to-fuel ratio and on the spark timing need to be enforced during its operation to avoid misfire, knock, and high combustion variability. In this paper, we approximate the DISC engine dynamics as a two-mode discrete-time switched affine system. Using this approximation, we tune a hybrid model predictive controller with integral action based on online mixed-integer quadratic optimization, and show the effectiveness of the approach through simulations. Then, using an offline multiparametric optimization procedure, we convert the controller into an equivalent explicit piecewise affine form that is easily implementable in an automotive microcontroller through a lookup table of linear gains

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.

A model predictive control approach for combined braking and steering in autonomous vehicles

In this paper we present a Model Predictive Control (MPC) approach for combined braking and steering systems in autonomous vehicles. We start from the result presented in F. Borrelli et al. (2005) and P. Falcone et al. (2006), where a Model Predictive Controller (MPC) for autonomous steering systems has been presented. We formulate a predictive control problem in order to best follow a given path by controlling the front steering angle and the brakes at the four wheels independently, while fulfilling various physical and design constraints.

A hierarchical Model Predictive Control framework for autonomous ground vehicles

A hierarchical framework based on Model Predictive Control (MPC) for autonomous vehicles is presented. We formulate a predictive control problem in order to best follow a given path by controlling the front steering angle while fulfilling various physical and design constraints. We start from the low-level active steering-controller presented in [3], [9] and integrate it with a high level trajectory planner. At both levels MPC design is used. At the high-level, a trajectory is computed on-line, in a receding horizon fashion, based on a simplified point-mass vehicle model. At the low- level a MPC controller computes the vehicle inputs in order to best follow the desired trajectory based on detailed nonlinear vehicle model. This article presents the approach, the method for implementing it, and successful preliminary simulative results on slippery roads at high entry speed.

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.

Optimal active suspension control based on a half-car model

Simple yet, in practice, meaningful state-space formulations of the optimal suspension control problem for a half-car 2D vehicle model are considered. By using an efficient equivalent representation, a complete analytical solution of the related fourth-order linear quadratic problem is obtained. The problem structure and associated analytical results are used to deduce a number of important generic properties of the optimal solution, and these in turn form a basis for global, centralized, and decentralized optimal suspension performance studies.<<ETX>>

Application of gain scheduling to design of active suspensions

One of the main advantages of active vehicle suspensions (with respect to conventional passive) is that they can adapt to different road, speed and handling conditions. The present study proposes one approach towards a gain scheduling technique based on the estimated road profiles and optimal control laws developed previously. The effectiveness of the approach is illustrated through simulation results with the help of white noise and actual, measured road profiles.<<ETX>>