Constrained real-time control of hydromechanical powertrains – methodology and practical application☆
Introduction
This paper addresses the control of the hydromechanical powertrain of mobile working machines such as diggers or wheel loader vehicles. The structure of the considered powertrain is sketched in Fig. 1. The prime mover is an internal diesel combustion engine which provides a mechanical power, i.e. a torque MICE at a respective rotational speed ωICE. The diesel combustion engine is decoupled from the drive side and the wheels by means of a hydraulic transmission. The hydraulic transmission essentially consists of two components, i.e. an axial piston pump (APP) as well as an axial piston motor (APM) [8], [9], [10], [16], which are coupled on a high and a low pressure level, pHi and pLo, respectively, see Fig. 1. The APP transforms the mechanical power of the combustion engine to a hydraulic power, i.e. a pressure difference at a respective volume flow QP, which is again transformed back to mechanical power by the APM.
The above described decoupling by the hydraulic transmission brings several advantages. For instance, it is possible to operate the combustion engine in an emission- or efficiency-optimal set-point. Moreover, the wheel’s rotational speed can be continuously adjusted, such that the hydraulic transmission serves as a continuous variable hydrostatic transmission. The usage of hydraulic components, i.e. APMs and APPs, allows the cost-efficient handling of high powers on a comparatively small space. Additionally, it enables the robust realization of common driving manoeuvres which would be a strain on a mechanical gear such as e.g. reverse manoeuvres, i.e. the deceleration from full speed to standstill and the acceleration in the opposite driving direction.
The principal construction and the function of the APM is similar to the one of the APP. Both are composed of a cylinder barrel which contains the pistons. The axis of the drive shaft draws an adjustable angle with the axis of the pistons or the swash plate, respectively, which is called ’swivel angle’ α. Hence, a translational piston stroke causes a rotation of the drive shaft, just as a rotating drive shaft causes a translational piston stroke, which then results in a compression of the fluid [9], [15].
The main task of the control of the hybrid powertrain concerns the precise realization of the (a-priori unknown) movement command given by the driver through a gas pedal operation or by the driving strategy algorithm [11]. For this purpose, it is necessary to design an electronic controller for the respective nonlinear swivel angle displacement systems of the APM and the APP, since the swivel angle α regulates both the motor torque MM and the pump pressure difference Δp.
The swivel angle displacement systems of the APM and the APP are schematically shown in Figs. 2 and 3. Both displacement systems share some common properties but are different in detail. They both consist of a hydraulic control cylinder with a spring-centered piston which is mechanically coupled to the swivel cradle. The position of the piston can be adjusted by the resulting volume flow on the piston, which is regulated via the single electro-proportional (EP) valve in the case of the APM or the two pressure control valves in the case of the APP. The valve tappets are reset with restoring springs and in the case of the APM they are further connected to the piston with coupling springs. Note that the mentioned coupling springs represent a stabilizing mechanical controller for the swivel angle.
The swivel angle displacement of the APM operates in an electro-proportional way, i.e., a given stationary input current in the solenoid of the EP valve results in a proportional stationary swivel angle. Consequently, this EP property can be utilized in order to control the swivel angle in a trivial manner. In the case of the APP, the swivel angle displacement depends on the restoring forces and thus behaves very nonlinearly. Concerning the design of an electronic control strategy for the above described swivel angle displacements, it is worth mentioning that both the APM and the APP lack a swivel angle sensor in series production such that only feedforward control approaches come into consideration. However for the case of the APP, a pressure sensor is available which can be utilized in order to realize an additional feedback controller.
Furthermore, it is of importance to account for state and input constraints. Constraints are for example the mechanical stops in the control cylinder and the valve(s), the safety limited pump pressure, as well as the limits of the available electrical input current.
The aim of this contribution is to derive and demonstrate an electronic control strategy for the swivel angle of the APM as well as for the pressure difference over the APP, which satisfies the above mentioned properties and which has a low complexity regarding implementation and application on a standard vehicle ECU. Usually, the APP and APM are controlled in sequence in dependence on the actual velocity and the gas pedal position for the desired velocity, see e.g. [9], [10]. However by controlling the pressure difference, the driver can directly control the wheel torque leading to a more sensitive control of the vehicle. The consideration of constraints in addition to the a-priori unknown reference signals leads to a challenging control problem. Nowadays, the most common control technique associated with the considered constrained control task is model predictive control (MPC) [12], [17], [18]. However, a prediction is only possible to some extent due to the a-priori unknown shape of the reference signal. In addition, MPC relies on the numerical online solution of an optimization problem, which typically leads to a high computational burden and which requires a more expensive hardware as well as more complex control algorithms compared to standard ones.
With respect to an electronic control concept for the swivel angle and the pump pressure, respectively, the goal is to combine the simplicity of flatness-based approaches [8], [13], [14], [18] in terms of design and computational performance with the optimality and constraint satisfaction of MPC [12]. This means that the control concept should exploit structural model properties such as differential flatness [1] on the one hand side as well as instantaneously available information at its best on the other. A suitable concept in this regard is the methodology presented in [2], [3], [5] for feedforward controlled nonlinear SISO systems as well as in [2], [4] for feedback controlled linear (and linearised) SISO systems. Hence, the respective ideas are transferred and tailored in this work to the nonlinear swivel angle displacement systems from Figs. 2 and 3.
The paper is structured as follows: In Section 2, a nonlinear flat SISO system model of second order is derived for each of the considered components, i.e. the APM’s swivel angle displacement and the APP’s pressure adjustment. Furthermore, the control problem is briefly stated together with a compact system-theoretic description and the definition of the considered constraints. The constrained flatness-based swivel angle feedforward control strategy for the APM and the constrained flatness-based tracking controller for the pump pressure of the APP is synthesized in course of Section 3. Subsequently, Section 4 demonstrates the proposed control algorithms by means of simulation studies as well as vehicle measurements on the test track. Section 5 concludes the paper and points out further interesting aspects for future work.
Section snippets
Modelling of the adjustment systems of the hydromechanical components
This section considers the adjustment systems of the two main components of the hydraulic transmission individually and describes for each the derivation of a flat nonlinear reduced order model for the subsequent control design discussed in Section 3. In particular, Section 2.1 considers an APM in bent-axis construction and the respective dynamics of the swivel angle displacement, whereas in Section 2.2, the focus lies on the APP in swash plate design and the relevant dynamics of the pump
Synthesis of constrained control strategies
The synthesis of the real-time control strategy for the hybrid powertrain depicted in Fig. 1 is described in the following. First, a constrained flatness-based feedforward controller for the APM’s swivel angle is derived in Section 3.1. Then, Section 3.2 proposes a constrained flatness-based tracking controller for the pressure difference over the APP.
Practical demonstration of the derived control strategies
The control algorithms developed in the previous section are implemented for their respective components and demonstrated in the wheel loader vehicle environment. The current section presents and discusses the achieved measurement results. First, the constrained feedforward controller for the APM is considered and tested by means of a simulated and measured swivel angle step response13 in Section 4.1. In Section 4.2, the constrained
Conclusion
In this contribution, a constrained real-time control concept for hybrid powertrains consisting of an axial piston motor and pump is presented. The control approach exploits the property of differential flatness of the nonlinear swivel angle and pressure adjustment systems in order to derive the constrained control approaches for the APM and the APP. Both control algorithms consist of a flatness-based feedforward controller as well as a constrained trajectory planner by means of a switched
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Steffen Joos studied Electrical Engineering and Information Technology at the Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany, where he received his Bachelor and Master degree in 2013 and 2015, respectively. From 2015 until 2018, he worked at the Corporate Sector Research and Advance Engineering of the Robert Bosch GmbH in Renningen, Germany, as a participant of the doctoral program. He received his Ph.D. (Dr.-Ing.) degree from the Ulm University, Ulm, Germany, in 2019. Since 2019,
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2021, MechatronicsCitation Excerpt :However, it increases the complexity of the system. Zips et al. [10] and Joos et al. [11] have proposed advanced control strategies that were implemented in the hydraulic drive of a wheel loader. The said control strategies are based on the feed-forward and feed-back control with a non-linear compensation.
Steffen Joos studied Electrical Engineering and Information Technology at the Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany, where he received his Bachelor and Master degree in 2013 and 2015, respectively. From 2015 until 2018, he worked at the Corporate Sector Research and Advance Engineering of the Robert Bosch GmbH in Renningen, Germany, as a participant of the doctoral program. He received his Ph.D. (Dr.-Ing.) degree from the Ulm University, Ulm, Germany, in 2019. Since 2019, he is employed as development engineer in the field of vehicle motion control for automated driving at the Robert Bosch GmbH in Abstatt, Germany. His current research interests include trajectory planning and control algorithms for constrained nonlinear systems as well as their application to real-time systems.
Adrian Trachte studied Engineering Cybernetics at the University Stuttgart, Stuttgart, Germany, and received his Dipl.-Ing. degree in 2008. He received his Ph.D. (Dr.-Ing.) from the TU Dresden, Dresden, Germany, in 2015 participating in the doctoral program at Bosch Rexroth in the group for advanced development for mobile controls and functions. Since 2012, he is project manager at the Corporate Sector Research and Advance Engineering of the Robert Bosch GmbH in Renningen, Germany, in the group for Control Engineering.
Matthias Bitzer is Senior Expert for Control Engineering at the Corporate Sector Research and Advance Engineering of the Robert Bosch GmbH in Renningen, Germany. He studied Engineering Cybernetics at the University of Stuttgart, Stuttgart, Germany, and the University of Wisconsin-Madison, Madison, USA. He received his Dipl.-Ing. degree in 1998 and his Ph.D. (Dr.-Ing.) degree in 2004, both from the University of Stuttgart. Before joining Bosch in 2004, he has been working as a research associate at the Institute for System Dynamics and Control of the University of Stuttgart.
Knut Graichen received the Dipl.-Ing. degree in Engineering Cybernetics and the Ph.D. (Dr.-Ing.) degree from the University of Stuttgart, Stuttgart, Germany, in 2002 and 2006, respectively. In 2007, he was a Post-Doctoral Researcher with the Centre Automatique et Systèmes, MINES ParisTech, France. In 2008, he joined the Automation and Control Institute, Vienna University of Technology, Vienna, Austria, as a Senior Researcher. From 2010 until 2019, he has been a Professor with the Institute of Measurement, Control and Microtechnology, Ulm University, Ulm, Germany. Since 2019, he is full professor and head of the Chair of Automatic Control at the Friedrich Alexander University Erlangen-Nürnberg, Germany. His current research interests include distributed, nonlinear, and model predictive control of dynamical systems with applications to mechatronic, robotic, and networked systems. He is Deputy Editor-in-Chief of Control Engineering Practice.