AG Overall model

MONOCAB OWL is supported by:

WG Management

Info about the working group AG Overall Model


The basis for carrying out simulations and analytical calculations are models that mathematically represent the physical behavior of the MonoCab. An important finding from the simulations is, among other things, the dimensioning of the components (drives, mechanics, ...). Errors in the modeling would significantly endanger the operation and project success in case of a wrong dimensioning. Therefore, several modeling approaches are deliberately pursued in the project and compared with each other in order to identify and avoid errors. The methods used in the project and the resulting models are summarized below.

Analytical models


System modeling is an extremely important part of the control system design process. An accurate model of a dynamic system provides a better understanding of the physical system and facilitates the analysis and design of controllers. The behavior of dynamic systems is described by differential equations. One of the first steps in the design process is to derive these equations from physical laws. There are several methods for deriving the dynamic equations. For mechanical systems, two common approaches are Lagrangian mechanics and Newtonian mechanics.
Based on the Lagrangian formalism, an analytical model of the presented multibody system of MonoCab (see Figure 1) was derived taking into account all degrees of freedom. In this modeling, the frame vehicle is assumed to be an inverse pendulum with corresponding physical properties.
The system consists of three bodies, the frame vehicle (inverse pendulum), the moving mass and the gyroscopes. In terms of a Lagrangian approach to modeling the overall system, the kinetic and potential energies are calculated and thus Lagrangian differential equations are set up and the equations of motion are determined.


Figure 1: Schematic representation of the bodies for mapping the vertical dynamics.

Numerical multibody models


In order to calculate and analyze the dynamics of complex systems, multi-body simulation can be used. Here, the modeling of the systems is carried out by bodies with mass and by massless connecting elements, such as joints and force elements. The dynamics of the system is described as a mathematical model via equations of motion in the form of differential equations. Solving these equations provides the forces, velocities, accelerations and contacts of the bodies as the result of the simulation.

As part of the multibody simulation, numerical multibody models of the MonoCab were created using the Simpack and Simscape tools (see Figure 2). In the models, all relevant bodies of the vehicle, such as vehicle body, chassis, stabilization, cabin, battery, electric motors, etc., are taken into account with their mass and inertia properties. The kinematics of the overall system results from the coupling of the individual bodies via various joints. For the models in Simpack, special focus is placed on the chassis and wheel-rail contact. Accordingly, the kinematics of the chassis (swing arm), the elastic chassis components such as springs, dampers and rubber bearings as well as the non-linear wheel-rail contact are represented. The models contain all degrees of freedom of the real vehicle.

Figure 2: Multibody model of the MonoCab in Simpack

Simulation tools and studies

The developed models allow a multitude of simulations and related investigations as well as designs of systems and algorithms. An orderly approach and use of the tools is important here, so that an interpretation of the results is possible at all. When using a complex overall model with all occurring effects, occurring misbehavior can otherwise hardly be interpreted and differentiated. The use of partial models (e.g. exclusively vertical dynamics) and different simulation tools allows a targeted and step-by-step approach. The applied methods as well as the related investigations are explained in the following.

Offline simulations and analytical calculations

On the basis of the analytical models, further calculations can be carried out to better understand and interpret the relationships. For example, analytical calculations were used to investigate how the gyro systems and the displaceable mass in the MonoCab must be fundamentally designed and what conditions are associated with them. Furthermore, analytical calculations form the basis for controller design, which plays a decisive role for stabilization control in particular. However, the complexity of the overall system does not allow a purely analytical consideration of all effects and interrelationships. This is where numerical simulation comes in.

Offline simulation is understood here as the computer-aided simulation of the vehicle (e.g. as a controlled system) together with the algorithms of the control units (e.g. as a controller) in a coherent simulation setup. For this purpose, the tool Mathworks Simulink® is used. In addition to simulation, the tool offers the advantage that the developed ECU software can be directly compiled and uploaded to the ECUs (rapid control prototyping), see also HIL simulation.

The offline simulation represents the basic first stage for the investigations. Here, the sub-areas of vertical dynamics and longitudinal dynamics are considered separately as well as overall models (e.g. via Simscape). The investigations include:

  • General commissioning and sequence controls
  • Analysis of the main functions developed, including stabilization control, longitudinal controls, automated driving functions and orientation detection
  • Dynamic and static effects of actuation, sensing and communication, including quantization, noise, bandwidth, latencies, compliance, backlash and friction.
  • Design (operating limits) of actuators and mechanics with regard to torque, speed and position limitations
  • Influence of vertical dynamics due to disturbances, such as uneven loading, crosswinds and lateral acceleration in curved runs.
  • Influence of longitudinal dynamics due to alignment-related influences as well as slip, wind and friction.
  • Energy consumption (range) during operation
  • Detection of faults as well as triggering and testing of reaction mechanisms

HIL simulation

The HIL simulation takes place with the help of hardware from the company dSPACE. Figure 3 shows the structure of the hardware used for the HIL simulation.


Figure 3: HIL setup with real hardware

The lower part mainly contains a multiprocessor board on which models of the MonoCab's dynamics are simulated. In addition to that, an interface board is installed there, which has 4 CAN ports.

The upper body, made of aluminum profiles, is equipped with 4 control units of the type MicroAutoBox II, MABX for short. These are used for rapid control prototyping and are installed identically in the MonoCab. They run the same software as later in the vehicle, e.g. control algorithms for the vertical stabilization and the traction drives, sequence controls for commissioning and disassembly of the MonoCab, etc. Each of these boxes is also equipped with 4 CAN buses. Each of these boxes also has 4 CAN connections, as well as further analog and digital inputs and outputs.

All 4 MABX and the multiprocessor board are coupled via Ethernet with a switch and via this with a PC. This PC is used to load the software onto the individual control units and the simulator. During the simulation, it is possible to intervene in the software and record measured values.

In addition, a receiver unit of a remote control is connected to the HIL (not shown in Figure 1). This was connected to the Driving_ECU via CAN. Thus, the modeled MonoCab can already be controlled by remote control and the integration of the remote control into the overall concept can be tested.
The structure is shown schematically in Fig. 4 with all the important connections.

Figure 4: Structural design of the HIL simulation

Various simulations are performed with the help of this setup:

  1. Model-based design and test of the stabilization control of the MonoCab
    The control and associated functions such as observers are executed on the redundant Stab1_ECU and Stab2_ECU control units. The manipulated variables are transmitted via a private CAN to the model of the vehicle vertical dynamics on the HIL simulator. The model calculates the actual variables (torques, velocities and positions,...) and writes them again to the Private CAN.
  2. Model-based design and test of the acceleration control of the MonoCab.
    The control code runs on the Central_ECU. Via Public CAN, the calculated manipulated variable is transmitted in the form of a torque to the model of the vehicle longitudinal dynamics on the HIL simulator. The model calculates the actual variables (acceleration, velocity and position of the MonoCab) and writes these in turn to the Public CAN.
  3. Model-based design and test of the speed and position control of the MonoCab.
    The code for the position and speed controls runs on the Driving_ECU. Both controls determine a target acceleration. This is transmitted to the Central_ECU via the Public CAN together with a driving step (specifies whether the MonoCab should stop, move forward or reverse). The control gets the actual speed and actual position from the vehicle longitudinal model on the HIL simulator. The same code runs on the Central_ECU and the HIL simulator as in the first attempt.
  4. Testing the integration of the remote control into the overall control concept.
    The receiver unit of the remote control is connected to the Driving_ECU via Private CAN. This unit processes the received switch positions of the remote control and converts them into an acceleration setpoint and a desired speed step. These two values are written to the Public CAN, where they can be read by the Central_ECU and the HIL simulator. The same code runs on the HIL simulator and the Central_ECU as in the other two experiments.
  5. Testing of the developed safety functions
    With a large number of control units, converters, actuators and sensors, the overall system is highly complex. In addition, the vehicle is exposed to different ambient conditions and stimuli (vibrations, track position errors). Under these aspects, special attention must be paid to the fault reaction of the vehicle in the event of a component failure or cable break. Within the scope of the HIL setup, faults can be provoked and the reaction of the vehicle can be tested safely.


Video 1 shows the HIL simulation of the MonoCab. The measurement data from the HIL simulator is used for the animation. Starting from the parking position (switched-off state with support via the tertiary stabilization), the vehicle is switched on and straightened with the aid of the stabilization. The vehicle is then ready to drive and accelerates up to a target speed of 60 km/h. The vehicle is then turned off and supported by the tertiary stabilization. In the arc, the vehicle tilts so that the lateral acceleration is balanced.


Video 1: Animation of the vehicle in dSPACE MotionDesk

CO simulation

Co-simulations are performed to analyze the overall system. The co-simulations include on the one hand the mechanical model of the vehicle in the form of the multi-body simulation model in the tool Simpack and on the other hand the model of the stabilization control in the tool Mathworks Simulink®.

Co-simulation ensures the functionality of the MonoCab concept numerically at an early stage of the project, as it allows the complete dynamic behavior of the vehicle as an overall system to be investigated. For this purpose, analyses are carried out with regard to driving safety and ride comfort. A closer look is taken at running stability, crosswind, derailment safety, encounter traffic and the dynamics and limits of stabilization.

Similarly, the multibody model is used in conjunction with the co-simulation as part of the structural design of the chassis to determine the stiffness, damping and dimensions of the chassis with regard to driving safety and ride comfort using parameter variations. The parameters are in turn used as the basis for researching and procuring suitable components, such as suspension struts for the chassis.

Video 2 shows a CO simulation of the MonoCab. At the beginning of the video, the stabilization is already active and the vehicle is traveling at a target speed of 60 km/h. Due to simulated track position errors, the stabilization systems are actively engaged.


Video 2: CO simulation of a MonoCab with track position errors


  • Georg Klepp, Guido Langer: Monorail Flow Patterns and Vehicle Drag. In: Aerovehicles 4-Fourth International Conference in Numerical and Experimental Aerodynamics of Road Vehicles and Trains, Berlin, August 2021.
  • Martin Griese, Fabian Kottmeier, Thomas Schulte: Vertical control of a self-stabilizing monorail vehicle. In: IECON 2021-47th Annual Conference of the IEEE Industrial Electronics Society. 13-16 October 2021.
  • Martin Griese, Seyed Davood Mousavi, Thomas Schulte: Modeling the vertical dynamics of a self-stabilizing monorail vehicle. In: ICCMA 2021- 9th International Conference on Control, Mechatronics and Automation. 11-14 November 2021.

Working group team

  • Seyed Davood Mousavi

    Research associate - vertical dynamics - safety functions, modeling, multibody simulation with Simscape, HIL simulation

  • Raphael Hanselle

    Research Associate- Longitudinal Dynamics - Control, Safety and Modeling, HIL Simulation.

  • Dominic Stork

    Research associate - multibody simulation with Simpack; focus: chassis and wheel-rail contact

  • Magnus Droste

    Research assistant - vertical dynamics - safety functions, HIL simulation