# A2 Coursework: Design of an Automotive Control System to Follow a Drive Cycle

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¶ … Automotive Control System to Follow a Drive Cycle.

Automotive control is a driving force within the automotive innovation. To lower fuel consumption, improved safety and lower exhaustive consumption as well as enhancing convenience and comfort function, there is a need to apply automotive control. Automotive control system is fundamental principles used for successful design of automobile automatic control systems.

The goal of this report is to "Design an Automotive Control System to Follow a Drive Cycle" and this report is organized in three parts. The first part demonstrates the strategy to implement an engine stimulation and dynamometer. The second part demonstrates the strategy to add control system and the third part provides the implementation of a drive cycle.

First Part

: Simulation of an engine and dynamometer

This part demonstrates the stimulation of engine and dynamometer. To enhance the greater understanding of the stimulation, the report demonstrates the steps in building a mathematical model of engine. The report reveals how the results work correctly and the report implements all parts, which include inertia, friction, throttle accurately. The paper uses the Excel software and JavaScript for the stimulation. Dynamometer is a device used to measure moment of force, force and power. The power produced by the motor, engine and other rotating prime mover could be calculated using rotational speed (RPM) and speed. A dynamometer is also used to determine power and torque required to operate a driven machine.

1.2: "Steps to Build a Mathematical Model of an Engine"

A mathematical model that governs the performance of an engine generally expresses fuel consumption, power and torque, and the model generally governs the function of engine speed at zero torque. The mathematical model could predict the fuel quantity that determines the engine speed. (Harris, & Pearce, 1990). Engine performances could be predicted using a simulation program. This section provides steps in modeling the engine using a mathematical model. The approach to use is to decompose the system to minimum number of parameter which assists in revealing the operation of an engine. This is achieved by considering all the moving components using Newtonian mechanics to demonstrate the dynamic operation of an engine. The system provides desired output using the necessary functional blocks. This report also demonstrates the construction of model of an engine using a simple diagram revealing simple input parameters, which will have some effect on the system operation and outputs representing the particular state of the system. Typically, the output of the engine is demonstrated by its speed, which determines the quantity of fuel to fill in the engine. The diagram in Fig 1 provides the simplistic model of an engine:

Fig 1: Outlining the System indicating Input and Output of an Engine

Fuel (0-100%) Speed (rpm)

Analysis of the diagram in Fig 1 reveals the purpose of the system; however, the diagram does not explain the process that occurs within the engine. Thus, there is a need to build a mathematical model to describe the input of fuel in relation to the output of the engine speed. An engine is a complex structure, however, the engine fiction and rotation inertia as well as its applied torque due to fiction could be simplified using mathematical model. Thus, the mechanical of the system is described using a mathematical model. (Golten, & Verwer, 2003). The following diagram illustrates a simplified engine as well as forces that act upon it.

Fig 2: Illustration of Physical System of an Engine

T

Frictional Angular

Torque (Nm) Displacement Acceleration

Applied torque (Nm) Moment of inertialJ (kg m2) (rad) Angular Velocity rad/s2

(rad/s)

The diagram in Fig 2 reveals the single rotating mass equivalent to all the moving components within the engine. Typically, the applied torque is being generated directly from the combustion of fuel, which is working on the pistons. On the other hand, the frictional torque occurs due to the interface between components of moving engine and is being dictated from specific lubricated regime. Using the mathematical model, the report demonstrates the parameter of the diagram in Fig 2.

Generally, the torque demonstrates the rate of change of an angular momentum in the same process that acts as a force to provide rate of change within linear momentum. The following equation demonstrates the torque:

T= dL= d (JO)

dt dt

The J. is defined as the mass distribution on the axis rotation. However, J is constant with the moment of inertia.

Then

T=JO

On the other hand, F=ma is the analogous of a force acting on mass. However, the report considers the retardation from fiction, which is associated with the fiction of the engine. The equation is as follows:

T -- TF = JO (1.1)

Where T. serves as frictional torque

Using mathematical inspection, the report provides the following relations:

dt (1.2)

and =?

dt

The next process is to define T. And TF to complete all the equation necessary to define the process.

The fiction between components of the engine is considered with the result of a shearing stress based on the lubricating interface of the moving components. The result is proportional to the square of angular velocity that can be derived from dimensional analysis. Thus, the frictional torque is defined as follows:

TF=k1?2 (1.3)

From the equation, k serves as the constant proportionality. Typically, torque has been approximated by the proportion of fuel consumed. Thus,

T=k2F (1.4)

F represents the total fuel supplied to the engine represented as the (0-100%) where K. is constant.

The equations 1, 2, 3 and 4 are used to provide the simplified model of an engine. The diagram in Fig 2 is used to present the visual model of the engine, and the block represents relation variables in Fig 3. To fully define the model, there is a need to define the model dependant and their variables and their interdependent. From Fig 3, the block reveals the unidirectional inputs on the left and the output on the rights, which represents the transfer of functions from one variable to the other.

Fig 3: A Typical Block

RC

With C= GR, it is often convenient to represent the block in matrix notation to demonstrate the interrelationships of the block, where R. And C. are column vector which generally contains input/output variables respectively.( for example an N. x1 matrix where N. represents the number of input and output variables). Moreover, G represents the transfer function between each of the input/output combination (represented by an NxN matrix). With inputs (R1 and R2) and (C1 and C2), the system could be represented by the following equations:

C1= G11 R1 + G12 R2

C2= G21 R1 + G22R2

The equation could also be represented by the following matrix:

[ C1 ] = [ G11 G. 12] [R ] or Simply C=GR

[ C2 ] [ C21 G22 ] [ R2]

Based on the above equation the next step is to construct the block diagram

Contracting a Block Diagram

The block diagram in Fig 4 revealing the system diagram representing the engine model, which reveals the output speed of the engine using the equation I, 2,3, and 4 and the block diagram in Fig 2. The block diagram also reveals the correlation of fuel supplied with the engine speed.

Fig 4: System Diagram for Model of the Engine

T + TN

F ?(rpm)

Thus, the description of the flow of the diagram in Fig 4 is as follows:

1. The first functional block at the left hand side operates for the fuel input. When F. is multiplied with k2, it delivers applied torque, T as being revealed in Fig 4.

2. The second element in the block diagram is to produced a summing function that delivers applied Torque T. As well as frictional torque, TF, which produces an output TN= T- TF. The +/- sign at the summing block of the inputs indicates whether the inputs is to add and subtract.

3. The next is step is to take the sum and divide it by the moment of inertial, J, of the Engine as being revealed in the equation 1 in order to obtain the angular acceleration at the engine output level.

4. The report determines the angular velocity of the output of the engine and this is achieved by integrating the angular acceleration using Equation 2 .

5. The block output of the angular velocity is in radian/second using rpm. The final operation of the blocks is performed with following conversion factor:

Rev = [ 60] radians min [2?] sec

6.The final step is to define TF using the summing function. Typically, Equation 3 reveals that TF is proportional to ?2 . Thus, the ? system variable is used to create a branch in the block. Thus, the operation in the block is k1( )2, where the brackets in the block contains the input variables.

1.3: Stimulation of the Engine System

The report provides the stimulation of the system in Fig 4, and the stimulation is implemented using Excel and JavaScript. The stimulation of…
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