M.Sc. Martin Griese
Line, vertical dynamics - overall concept and stabilization control
Line, vertical dynamics - overall concept and stabilization control
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.
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.
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
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.
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:
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:
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-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
Research associate - vertical dynamics - safety functions, modeling, multibody simulation with Simscape, HIL simulation
Research Associate- Longitudinal Dynamics - Control, Safety and Modeling, HIL Simulation.
Research associate - multibody simulation with Simpack; focus: chassis and wheel-rail contact
Research assistant - vertical dynamics - safety functions, HIL simulation