# Modeling and simulation of a vehicle with automatic transmission

The role of a vehicle’s transmission is to adapt the traction performance of the engine (motor) to the road load and acceleration demand of the driver. In a vehicle with automatic transmission (AT), the decision to change the gear and the actuation of the gears are done independently of the driver.

In this article we are going to simulate the longitudinal dynamics of a vehicle together with the control logic for gear shifting. As example, we are going to simulate a Mercedes CL 500, equipped with a 5.0L V8 petrol (gasoline) engine and a 7-speed automatic transmission (7G-tronic).

This model can be used for several purposes, some of them being:

• evaluation of vehicle performance: maximum speed and 0-100 kph acceleration
• evaluation of the impact of the gear ratios on the traction performance of the vehicle
• evaluation of different gearshift patterns on the performance of the vehicle
• evaluation of the road load and vehicle aerodynamics on the vehicle performance
• evaluation of the engine parameters on the overall vehicle dynamic performance

The article is structured in several chapters, each one of the chapters focusing on particular aspects:

1. Introduction: gives an overview of the control schematic, plant (vehicle) modeling and top level Xcos block diagram
2. Plant model: Driver & Environment: setups the acceleration, braking profile of the vehicle as well as the road slope
3. Plant model: Engine: gives details about the mathematical model of the engine
4. Plant model: Automatic Transmission: gives details about the mathematical model of the transmission, including torque converter and gearbox
5. Plant model: Vehicle: gives details about the mathematical model of the vehicle, including the road loads and traction force limit
6. Controller: TCU: gives details about the shift lines and dynamic corrections
7. Simulation results: gives details about the vehicle dynamic performance during: acceleration, braking and hill climb

### 1. Introduction

The electronic control unit of the automatic transmission, often called Transmission Control Unit (TCU), decides when to shift gears and also controls the electrohydraulic actuators of the clutches and brakes.

The simulation model consists of a Plant and a Controller. The Plant consists of an internal combustion engine (ICE), an automatic transmission (AT) and a vehicle. The external inputs in the Plant model are the accelerator pedal position, the brake pedal position and the slope (gradient) of the road. The Controller is the Transmission Control Unit (TCU). It has the accelerator pedal position and vehicle speed as inputs and outputs the gear number.

The basic information which is used by the TCU to change gears are the vehicle speed and the engine load. The vehicle speed information is usually measured by wheel sensors or output shaft sensors in the transmission. The engine load is measured differently, depending on the type of engine (petrol/gasoline or diesel). For a diesel engine, the load is given by the total mass of fuel injected into the cylinders. For a gasoline/petrol engine, the engine load is determined by the air pressure in the intake manifold, which is directly dependant on the throttle position.

Since the engine load is mostly dependant on the accelerator pedal position, we are going to use accelerator pedal position as input.

The Plant model contains a lumped inertia for the engine and a lumped mass for the vehicle. The connections between the two lumped parameters is done through the torque converter performance/torque ratios and the gearbox ratios.

where:
Te [Nm] – engine torque
Je [kg·m2] – engine and impeller inertia
lTC [-] – torque converter performance coefficient
kTC [-] – torque converter torque coefficient
ix [-] – gearbox ratio
i0 [-] – final drive ratio
mv [-] – vehicle mass
vv [-] – vehicle speed

Between the engine inertia and the vehicle mass there is no mechanical link. The torque which goes into the transmission, the turbine torque, is calculated based on the torque converter speed ratio and the gear ratio. Having this kinematic link only allows us to treat the engine as a rotational body and the vehicle as a translational body.

The Controller is the Transmission Control Unit (TCU). Based on the vehicle speed and accelerator pedal position decides in what gear the transmission should be in. It contains two static gearshift decision maps, one for upshift and another one for downshift, and some dynamic corrections for accelerator pedal movement, minimum time in gear and engine braking (overrun).

The top level Xcos block diagram of the simulation of the longitudinal dynamics of a vehicle together with the control logic for gear shifting is in the picture below.

The exchange of information (signals) are abbreviated using the keywords defined in AUTOSAR . This way we can keep consistency on the signal names and parameters, which allows the user to easily understand the content of a signal just by reading its name.

There are two types of signals in the simulation:

• variables: their value can change during the simulation, e.g. engine speed, gearbox torque
• parameters: they are constant during the simulation, e.g engine inertia, vehicle mass

The signal definition follows a specific rule:

PhysicalMeaning_Unit_[Type]

The physical meaning is made up of several keyword defining what is the content of the signal. For example:

• AccrPedlPosn – which means accelerator pedal position
• EngMaxN – which means engine maximum speed
• VehDragCoeff – which means vehicle’s aerodynamic drag coefficient

The unit, represent the unit of measurement of the signal. For example:

• s – seconds
• kg – kilograms
• prc – percent [%]
• z – no unit

The type is not used in the naming of the variables, it is use to represent the type of parameter. For example:

• C – scalar parameter (calibratable), can be changed function of vehicle model
• X – array parameter, used as axis for interpolation
• Y – array parameter, used as axis for interpolation
• Z – array parameter, used as map for interpolation

All the parameters are defines in an `*.sce` file are loaded in the Scilab workspace before the simulation. After the simulation, the main variables are saves into the Scilab workspace and post-processed (plotted) using Silab scripts. The general simulation parameters are defined in the table below:

Parameters

 Name Value Description tf 50 Final simulation time [s] dt 0.01 Sample time [s]

We’ll now dive into detailed description of each subsystem (component) of the top level simulation model.