# Advanced Controller Development Based on eFMI with Applications to Automotive Vertical Dynamics Control

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Vertical Dynamics Control Problem

## 3. The eFMI Workflow

## 4. The Controller Design Process Using the eFMI Workflow

#### 4.1. Assembling the High-Fidelity Model

#### 4.2. Design and Parametrization of the Controller

- Vertical dynamics module: This module is designed to account for road-induced disturbances. A skyhook controller addresses the comfort requirement by controlling the dampers in such a way that the chassis vertical acceleration is minimized. In addition, this module also includes a groundhook controller which minimizes the dynamic wheel load to comply with the road holding requirement.
- Motion module: This module predicts the vehicle motion resulting from the driver inputs. For example, the vehicle stationary lateral acceleration is calculated from the steering wheel angle by means of a steady-state single-track model. The vehicle longitudinal acceleration is determined from the accelerator or brake pedal inputs and additional signals (e.g., gear or vehicle velocity).
- Feed-forward module: The aim of the feed-forward module is to compensate the driver-induced disturbances based on the predicted vehicle motion. Based on the predicted longitudinal and lateral acceleration at the vehicle’s center of gravity, geometric relationships are used to calculate the damper forces required to compensate for the resulting chassis pitch and roll motion. By means of an inverse damper model, the required force is mapped to a damper current. However, only dissipative forces within a fixed operating range can be applied, since semi-active dampers are used.
- Minimal damping module: This module additionally ensures driving safety and overall vehicle stability by limiting the minimum damper force. For this purpose, a characteristic curve is used that depends on the vehicle velocity and increases the damping with rising vehicle velocity.
- Arbitration module: Inside this module, the electric current outputs of the abovementioned modules are collected and blended, and 4 damper current setpoints are calculated. The blending is done independently for each wheel, since the vertical dynamics, feed-forward, and minimal damping modules each calculate 4 damper currents (1 for each wheel).

#### 4.3. Design and Parametrization of the Prediction Model

#### 4.4. Generation of eFMI Algorithm Code Model Representations

- Startup for initialization of all internal and interface variables,
- Recalibrate for the computation of dependent parameters when values of tunable parameters are changed and
- DoStep for the computation of the block outputs at each sample time depending on the inputs and internal state variables.

#### 4.4.1. Algorithm Code of the Controller Model

block CriticalDamping | |

… | |

equation | |

der(x[1]) = (u − x[1]) * w; | |

… | |

end CriticalDamping; |

method DoStep | |||

… | |||

algorithm | |||

… | |||

self.‘vertDyn.criticalDamping[2].x[1]’: = | |||

(self.‘vertDyn.criticalDamping[2].x[1]’ + | |||

(self.‘discrete.stepSize’ * | |||

self.‘derivative(vertDyn.criticalDamping[2].x[1])’)); | |||

… | |||

self.‘derivative(vertDyn.criticalDamping[2].x[1])’: = | |||

((self.‘vertDyn.multiplex2.u1[2]’ – | |||

self.‘vertDyn.criticalDamping[2].x[1]’) * | |||

self.‘vertDyn.criticalDamping[2].w’); | |||

… | |||

end DoStep; |

#### 4.4.2. Algorithm Code of the Prediction Model

#### 4.5. Generation of eFMI Production Code Model Representations

#### 4.6. Integration of eFMUs and Deployment on the ECU

#### 4.6.1. Integration of the eFMU into the Embedded Kalman Filter C-Library

#### 4.6.2. Assembly and Integration of the eFMUs

## 5. Results of Software and Hardware Tests

#### 5.1. Offline Open-Loop Tests

#### 5.1.1. Validation of the Controller eFMU

#### 5.1.2. Validation of the Kalman Filter Including the Prediction Model eFMU

#### 5.2. Real World Tests

## 6. Summary and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Diagram with a trade-off between comfort and road holding and its optimal Pareto front (adapted from [13]).

**Figure 2.**The eFMI workflow adapted from [11]. The highlighted path shows the workflow utilized in this work.

**Figure 3.**The vertical dynamics controller and prediction model design process using the eFMI workflow (adapted from [14]).

**Figure 4.**Overview of the full vehicle model and its various submodels in Modelica. The semi-active damper model is encircled.

**Figure 6.**Overview of the closed-loop high-fidelity Modelica model of a vehicle including a semi-active damping controller.

**Figure 7.**Nonlinear 2-mass system scheme (

**a**) adapted from [18] and its graphical representation in Modelica (

**b**).

**Figure 9.**Coupling of the controller eFMU and the state estimator containing an eFMU prediction model.

**Figure 10.**Test setup for open-loop tests to validate different parts of the eFMI workflow. The high-fidelity model described in Section 4.1 was used to create the synthetic excitation data.

**Figure 11.**Results of comparing original Modelica simulations with the run of eFMI Production C code (Software in the Loop) in the 64-bit and 32-bit variants of the semi-active damping controller.

**Figure 12.**Results from open-loop tests of the original Modelica model and the complete controller eFMU executed on the ECU. Electric currents (u_damper) for the rear left (RL) damper.

**Figure 13.**Results for the estimated velocity of the body ${\dot{x}}_{\mathrm{b}}$ and wheel ${\dot{x}}_{\mathrm{w}}$ from the simulation in TargetLink (blue) and the reference trajectory (red).

**Figure 16.**Comparison: Logged controller output during a test drive (eFMU on ECU) and the simulated controller with test drive excitation for the Modelica and eFMI production code (eFMU SiL) controller version. Rear left (RL) damper current (u_damper).

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**MDPI and ACS Style**

Ultsch, J.; Ruggaber, J.; Pfeiffer, A.; Schreppel, C.; Tobolář, J.; Brembeck, J.; Baumgartner, D.
Advanced Controller Development Based on eFMI with Applications to Automotive Vertical Dynamics Control. *Actuators* **2021**, *10*, 301.
https://doi.org/10.3390/act10110301

**AMA Style**

Ultsch J, Ruggaber J, Pfeiffer A, Schreppel C, Tobolář J, Brembeck J, Baumgartner D.
Advanced Controller Development Based on eFMI with Applications to Automotive Vertical Dynamics Control. *Actuators*. 2021; 10(11):301.
https://doi.org/10.3390/act10110301

**Chicago/Turabian Style**

Ultsch, Johannes, Julian Ruggaber, Andreas Pfeiffer, Christina Schreppel, Jakub Tobolář, Jonathan Brembeck, and Daniel Baumgartner.
2021. "Advanced Controller Development Based on eFMI with Applications to Automotive Vertical Dynamics Control" *Actuators* 10, no. 11: 301.
https://doi.org/10.3390/act10110301