Elsevier

Control Engineering Practice

Volume 21, Issue 12, December 2013, Pages 1884-1898
Control Engineering Practice

Lyapunov based predictive control of vehicle drivetrains over CAN

https://doi.org/10.1016/j.conengprac.2012.05.012Get rights and content

Abstract

Vehicle drivetrains are characterized by fast dynamics, subject to physical and control constraints, which make controller design for driveline oscillations damping a challenging problem. Furthermore, in current implementations, the connections between the controller and the physical plant are realized using a controller area network (CAN) as the communication medium, which introduces time-varying delays. As such, the goal of this paper is to provide a control design methodology that can cope with all these challenges and limitations and still yield an effective solution. To this end, firstly, a continuous-time model of a vehicle drivetrain is derived. Then, a method for determining a worst case upper bound on the delays that can be introduced by a CAN is presented, which enables the usage of a polytopic approximation technique to obtain a discrete-time model of the closed-loop CAN system. Thirdly, a non-conservative Lyapunov based predictive controller is designed for the resulting model with time-varying delays, polytopic uncertainty and hard constraints. Several tests performed using an industry validated drivetrain model and the Matlab toolbox TrueTime indicate that the proposed design methodology can handle both the performance/physical constraints and the strict limitations on the computational complexity, while effectively coping with time-varying delays. Preliminary real-time results further validate the proposed methodology.

Introduction

Recently, the greater demand for driveability and passenger comfort, which requires a reduction of the noise and vibration characteristics of vehicles, has led to the design of proper models for vehicle drivetrains and to the development of different control strategies to minimize the effects of drivetrain oscillations. When a vehicle is subjected to acceleration, the elasticity of the various components in the driveline may cause torsional vibrations or disturbances. The focus of this paper is on vibrational comfort, which is recognized as the most important factor for passenger comfort. The torsional vibrations can result in driveline or vehicle speed oscillations, also known as shuffle mode, which are low-frequency oscillations corresponding to the first resonance frequency of the driveline. These oscillations give rise, apart from material stress, to noticeable reduced driveability.

Various researches have been conducted on understanding and damping the driveline oscillations of conventional vehicles and numerous control strategies were reported in the literature, such as robust pole placement (Stewart, Zavala, & Flemming, 2005), H optimization (Lefebvre, Chevrel, & Richard, 2003), linear quadratic Gaussian control design with loop transfer recovery (LQG/LTR) (Berriri, Chevrel, & Lefebvre, 2008); (Fredriksson, Weiefors, & Egardt, 2002) and even model predictive control (MPC) (Lagerberg & Egardt, 2005); (Rostalski, Besselmann, Maric, Van Belsen, & Morari, 2007). Although the majority of the control strategies that are implemented on real vehicles are based on standard PID loops and look-up tables, it was shown that MPC has a large potential for control of automotive subsystems, e.g., semi-active suspensions (Canale, Fagiano, & Novara, 2006), brakes (ABS) (Anwar, 2007, Yoo and Wang, 2007), mechatronic actuators (Di Cairano et al., 2007, Hermans et al., 2009), driveline (Saerens, Diehl, Swevers, & Van den Bulck, 2008), rear active differential (Canale, Fagiano, & Razza, 2010), and engine (Di Cairano, Yanakiev, Bemporad, Kolmanovsky, & Hrovat, 2010). This is supported by the increased power of electronic control units that enable the implementation of more complex real-time control algorithms.

However, all of these control solutions assume that the sensors, controllers and actuators are directly connected, which are not realistic. Rather, in modern vehicles, the control signals from the controllers and the measurements from the sensors are exchanged using a communication network, i.e., controller area network (CAN), among control system components. This brings up an additional challenge, i.e., how to deal with the effects of the network-induced delays in the control loop. The delays may be unknown and time-varying and may degrade the performances of control systems designed without considering delays, up to the point where they can even destabilize the closed-loop system.

As such, the problem considered in this paper is to minimize the oscillations of a vehicle drivetrain while coping with the time-varying delays introduced by the communication network and the strict timing limitations. It is important to point out that suppressing drivetrain oscillations is equivalent with fast asymptotic stabilization of the torsion in the driveshaft. This explains the poor behavior, in this respect, obtained by standard output feedback controllers, such as PID, which only regulate the vehicle velocity. Therefore, it is important to design a controller with a stability guarantee. While MPC is increasingly seen as an attractive methodology for automotive applications, standard MPC strategies (Maciejowski, 2002), which typically require a sufficiently long prediction horizon to assure stability and performance, are likely to yield solutions that are too complex for driveline oscillations damping, even when delays are not present. Notice that the previously mentioned MPC solutions (Lagerberg and Egardt, 2005, Rostalski et al., 2007) do not offer an a priori closed-loop stability guarantee. For closed-loop MPC systems in an explicit piecewise affine form, stability can be checked a posteriori, but such an explicit form cannot be obtained for models with time-varying delays.

Motivated by the shortcomings of the existing controller design methods for drivetrain oscillation damping, the contribution of this paper is twofold. Firstly, a technique for estimating the maximum delay that can be introduced by a CAN is presented along with a standard continuous-time model of the vehicle drivetrain. This further enables the usage of the polytopic approximations modeling technique developed in Gielen et al. (2010) for general networked control systems (NCS). Secondly, a non-conservative stabilizing predictive control scheme is designed for the model of the closed-loop CAN system using the concept of a flexible control Lyapunov function (Lazar, 2009). The resulting control algorithm has the potential to satisfy the chronometric requirements, as it can be implemented as a low-complexity linear program (LP), while it offers a non-conservative solution to stabilization due to the flexibility of the Lyapunov function.

The TrueTime toolbox (for Matlab/Simulink) was used as the simulation environment, as it provides a realistic emulation of real-time networked control systems. Several benchmark scenarios for oscillation damping were implemented in TrueTime using a drivetrain model validated by Ford Research and Advanced Engineering, US. The results of the simulations, which include a comparison with standard PID control, indicate that the proposed predictive control approach has the potential to meet the required real-time control specifications. The proposed approach was also experimentally validated using an industrial HIL (Hardware-In-the-Loop) test-bench consisting of a Freescale based electronic control unit (which implements the controller) linked via a CAN bus with a dSPACE MicroAutoBox plant simulator.

The remainder of the paper is organized as follows. In Section 2 the control architecture of a network-controlled vehicle drivetrain is presented along with a state-space model of the drivetrain. A general method for establishing an upper bound on the time-varying delays induced by a CAN and a model for controller design that accounts for the CAN delays are also presented in Section 2. The Lyapunov based predictive control scheme is described in Section 3 along with stability results and implementation details. The TrueTime simulation results are presented in Section 4, some preliminary real-time results are illustrated in Section 5 and concluding remarks are summarized in Section 6.

Notation and basic definitions. R, R+, Z and Z+ are the real, non-negative real, integer and non-negative integer numbers. For every cR and ΠR, define Πc{kΠkc} and similarly Πc, RΠΠ and ZΠZΠ. For a vector xRn, let · denote an arbitrary p-norm and let [x]i,iZ[1,n] denote the ith component of x. Let xmaxiZ[1,n]|[x]i|, where |·| denotes the absolute value. For a matrix ZRm×n, let Z denote its transpose. Let z{zl}lZ+ with zlRn for all lZ+ denote an arbitrary sequence. Define zsup{zllZ+} and z[0,k]{zl}lZ[0,k]. A polyhedron, or a polyhedral set, in Rn is a set obtained at the intersection of a finite number of open and/or closed half-spaces. A polytope is a compact (closed and bounded) polyhedron. Let Co(·) denote the convex hull and let int(S) denote the interior of an arbitrary set S. A function φ:R+R+ belongs to class K if it is continuous, strictly increasing and φ(0)=0. A function φ:R+R+ is said to belong to class K if it is of class K and limsφ(s)=.

Section snippets

Drivetrain description

The automotive drivetrain is the mechanical system that transmits the engine power to the driving wheels. The aim is to increase the comfort by reducing the vibrational oscillations, which can be achieved by proper control of the power transmission. To this end, a suitable model of the drivetrain is required for controller design. Numerous models of conventional powertrains were proposed in the literature during the last years, such as: two inertias models, one inertia corresponding to the

Lyapunov based predictive control

The model developed in the previous section, which is defined by (19), (20) and the set of constraints (22), poses serious challenges to existing MPC design methodologies. For example, depending on the complexity of the polytopic approximation (Gielen & Lazar, 2009), long horizon MPC schemes typically lead to a computationally unfeasible solution due to the matrix uncertainty. State-of-the-art explicit MPC approaches, which may be able to cope with uncertain linear systems and can result in a

Simulation results

The continuous-time model (8) was implemented in Matlab/Simulink and two different control strategies were applied to damp driveline oscillations: a PID controller and the horizon-1 predictive controller proposed in this paper. The sampling period of the system was chosen as Ts=0.01s and the values of the parameters used in simulations were obtained with the help of Ford Research and Advanced Engineering, US, and are given in Table A1 in Appendix A.

In this section, three setups are considered:

Preliminary real-time results

The proposed approach was experimentally validated using an industrial HIL (Hardware-In-the-Loop) test-bench consisting of a Freescale based electronic control unit (which implements the controller) linked via a CAN bus with a dSPACE MicroAutoBox plant simulator.

MicroAutoBox represents a real-time system based on a DS1401 board, able to provide fast function prototyping—such as chassis control, power train and other rapid control applications. The plant model can be loaded from Matlab into

Conclusions

Different strategies for controlling the drivetrain oscillations and different methods to compensate the delays that appear in communication networks were reported in the literature, but none of them considers the drivetrain as a component of a networked control system. This paper proposed a novel method of modeling the delays induced by CAN for control purposes and a horizon-1 MPC strategy to minimize the drivetrain oscillations that can handle both the performance/physical constraints and the

References (37)

  • M. Canale et al.

    Semiactive suspension control using “fast” model predictive techniques

    IEEE Transactions on Control Systems Technology

    (2006)
  • S. Di Cairano et al.

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

    International Journal of Control

    (2007)
  • Di Cairano, S., & Kolmanovsky, I. (2010). Rate limited reference governor for network controlled systems. In 29th...
  • Di Cairano, S., Yanakiev, D., Bemporad, A., Kolmanovsky, I., & Hrovat, D. (2010). Model predictive powertrain control:...
  • J. Fredriksson et al.

    Powertrain control for active damping of driveline oscillations

    Vehicle System Dynamics

    (2002)
  • Gielen, R. H., & Lazar, M. (2009). Stabilization of networked control systems via non-monotone control Lyapunov...
  • Grotjahn, M., Quernheim, L., & Zemke, S. (2006). Modelling and identification of car driveline dynamics for anti-jerk...
  • Henriksson, D., Cervin, A., & Arzn Pierrot, K. E. (2003). True time: Real-time control system simulation with...
  • Cited by (92)

    • Real-Time nonlinear predictive controller design for drive-by-wire vehicle lateral stability with dynamic boundary conditions

      2022, Fundamental Research
      Citation Excerpt :

      In this way, the control signal is transmitted by a real-time communication system. Information exchange and data transmission are carried out between different subsystems through communication protocols such as a controller area network (CAN) and FlexRay [2,3]. Compared with a traditional point-to-point cable connection [4], this approach has the advantages of low cost, low weight and power requirements, simple installation and maintenance, and high reliability [5].

    • Stochastic stability of switching linear systems with application to an automotive powertrain model

      2022, Mathematics and Computers in Simulation
      Citation Excerpt :

      The most advanced model so far seems to be the one detailed in [7], since the authors of [7] have introduced a piecewise nonlinear model with three inertias. When compared with the models in [8,9,17,25], the model of [7] brings two important features: the clutch flexibility and the driveshaft flexibility—both features have improved the accuracy of the automotive powertrain model (see [7]). The model proposed in [7] will be useful to our approach, as described in the sequence.

    • An Active Front Steering System Design Considering the CAN Network Delay

      2023, IEEE Transactions on Transportation Electrification
    View all citing articles on Scopus
    View full text