Unity Feedback PD Controller Design for an Electronic Throttle Body

2006 ERNST & SAPUTRA
Unity Feedback PD ControllerUnity Feedback PD ControllerUnity Feedback PD ControllerUnity Feedback PD Controller
Design for anDesign for anDesign for anDesign for an ElectronicElectronicElectronicElectronic
Throttle BodyThrottle BodyThrottle BodyThrottle Body

1.0.0. Abstract
his project report examines the design of an electronic throttle body and applies a control
system to stabilize and control the response. This design can be broken up into four primary
categories. The initial stage is to obtain information about the system and organize the
material in a manner useful for control development (identifying the transfer function). This involves
developing the frequency-domain block diagram for the system. This is done by analyzing the
equations of motion and implementing them into the current system. Additionally, the transfer function
equation is obtained from the block diagram to be used for design and modeling.
Once the necessary information has been obtained from the system, the development of a controller
can begin. Using the transfer function obtained from the block diagram, the use of software analysis
(such as MATLAB) can be used to identify the characteristics of the existing system. This can allow a
controls engineer to encounter any points of instability within the system that may have been
overlooked. In addition to identifying points of concern within the system (ie: oscillation from poles on
the jù axis), the software application can be used to identify what type of control system, whether it is
P, PD, PI, or PID, will and will not be a reasonable means for their application. From there, a
controller with general specifications can be chosen.
The next stage in the process of developing a closed loop feedback control system for an electronic
throttle body is to simulate an open loop system model of the plant without additional control. This
allows you to account for any unforeseen problems that the system might encounter. This stage is
crucial for the fact that you identify the limitations of your model (ie: the min to max position of the
plate angle). An open loop system model will allow the controls engineer an opportunity to identify
additional elements that may be necessary in the final stages of development for their controller.
Now that the stability of your system is identified in a static and dynamic atmosphere, the final design
can be developed. The final design would be a closed loop feedback control system. After including
the controller to the system, the system characteristics (ie: rise time, overshoot) may not be at the
desired level. Because of this, adjustments must be made in order to meet the specifications of the
consumer. Once the controller has been tuned to obtain the desired result, the actual implementation
onto the electronic throttle body would begin.
2.0.0. Introduction
n the early 1980s, electronic throttle body was introduced as a transition technology to fully
electronic port injection. The electronic throttle body (ETB) has no linkage connection
between the throttle pedal and ETB is required the use of an electric actuator motor. The
throttle body is a component within the engine that controls the amount of air into the induction
system. It also opens and closes the control device of the accelerator pedal effort. For several years,
there have been numerous commercial industries, such as the automotive industry, that has a large
interest in applying control system technology to this application. The increase in interest for this
application can be contributed to the opportunity to provide a state-of-the-art engine management
system that helps satisfy governmental regulations as well as customer demands.
The primary purpose of an electronic throttle body is to control the amount of airflow into the engine.
As part of the throttle body, a butterfly valve is used to open and close the passage into the intake
manifold in order to increase/decrease the volume of the air entering the engine. Our task is to
develop a control system to limit the amount of airflow allowed to enter the engine by adjusting the
position of the plate within the electronic throttle body. The control system will be required to obtain
the desired output rating while meeting the customer specifications for the rise time (<50 ms), settling
time (<250 ms), and overshoot (<25%) of the step response to the overall system. The specifications
for our specific controller design are: <25% overshoot, a settling time of <250ms, and a rise time of <
50ms.

3.0.0. Model Description
3.1.0 The original system model
Components Name Description
Current Input
An Ideal controlled input used to supply power to
electric components in the system.
DC Motor
Electrical to rotational conversion unit used to
create an angular velocity that is sent to the gear
shaft.
Angular Velocity -> Angle
Converts the angular velocity to an angle. Angular
velocity is the derivative of orientation with respect
to time.
Gear / Gear Ratio
A toothed wheel designed to transmit and adjust
torque (valued at 59.0E-03).
Plate Inertia
The tendency of the plate at rest to remain at rest,
and of an object in motion to remain in motion.
Rotational Spring
A flexible elastic object used to store mechanical
energy based upon the position of the plate.
Rotational Reference
A static connection between points used to identify
dynamic motion in a rotational form.
Each of the components shown above is used in developing the original functional model
representation of a simple electronic throttle body.

3.2.0 The modified model system model
Components Name Description
Voltage Pulse
An non-ideal controlled input used to
supply power to electric components in
the system.
DC motor
Electrical to rotational conversion unit
used to create an angular velocity that is
sent to the gear shaft.
Gear / Gear Ratio
A toothed wheel designed to transmit and
adjust torque (valued at 59.0E-03).
Stop Plate
Used to restrict the range of rotational
motion (0° - 90°).
Rotational Spring
A flexible elastic object used to store
mechanical energy based upon the
position of the plate.
Angle –to-Voltage
Converter
Conversion unit used to change a
measured input from an angular value into
voltage.
Rotational Reference
A static connection between points used
to identify dynamic motion in a rotational
form.
Proportional Derivative
(PD) Controller
A component of a system that makes the
system operate within desired limits (ie.
customer specifications).
Each of the components shown above is used in developing the modified functional model
representation of a simple electronic throttle body with a controller and feedback.

4.0.0. Design Approach and Analysis & Results
4.1.1. Design Approach – Part 1
When we examined the above schematic, we first derived the frequency-domain block
diagram which followed by the resultant transfer function. To create this block diagram,
we applied all the rules of conservation of energy, momentum, and torque to develop
the relevant equations of motion (EOM). From the EOM we created a block diagram of
the system by using the given important values of the model: i, tK ,r , spK , mJ , pJ ,θ.
1. p
m
J
J J
r
= + 2. ( )
1 ( ) ( )
TK G sOut
In G s H s
+
=
+
3. ( )
( )
T
s
K
i s
τ
= 4. ( ) 1
( ) p
m
s
Js
J
r
θ
τ
=
+
5. 2
( ) 1
( )
s
s s
θ
θ
=
4.1.2. Analysis and Results – Part 1
From the EOM, we analyzed the system to determine the appropriate block diagram
and transfer function. Below our block diagram is the resultant transfer function.
The block diagram:
r
K
s
r
J
J
K
spp
m
t
++
=
2
)(
i(s)
Theta(s) or
sppm
t
KsJrJ
rK
++
= 2
)(i(s)
Theta(s) ,
where 17
059.
1
≈=r
To design a control system, our first step was to perform an analysis of the plant
transfer function and obtain the results of a time response to a unit step input via
MATLAB.
Steps taken to design a control system:
1. Perform the analysis of the plant transfer function whiling obtaining the results to
a time response from a unit step input via MATLAB. Identify whether the plant
transfer function is stable, unstable, or oscillatory.
2. Perform a root locus analysis in MATLAB, apply a proportional controller, and
analyze the plants behavior as the gain varies.
3. Identify the appropriate controller for the system.
4. Include the controller to the plant and perform the time analysis.

5. Simulate the controller while apply a sweep of gain values.
We performed an analysis of the plant transfer function and a time response to a unit
step input by using MATLAB.
The root locus shown above demonstrates how the system is expected to design
when the gain is varied. In other words, if you were to include a proportional controller
and change the K value of it, you will notice how the system changes. According to our
representation of the system, the poles will never leave the jω axis and therefore will
remain oscillatory regards of the proportional gain that is included into the system. This
can be seen in the image to the right, where the time response continues to oscillate
around 0.5. This response identifies a P controller as not the ideal controller this
application.
It can be seen in the time response that the plant is oscillatory. The throttle plate
inertia and dc motor inertia are the two components of the plant that cause the
oscillation to occur. Oscillation occurs when a second (or higher) order system is
introduced into the transfer function. From the transfer function, the combination of Jm
and Jp are what determine whether or not the system results in a second order
characteristic equation. When (Jm + Jp/r) becomes zero, the characteristic equation is
no longer second order. Therefore, the dc motor and the throttle plate are the two
physical components of the plant that cause it to behave this way.
Applying a proportional controller will not work because for any value of ‘k’ the poles of
the system will remain on the jω axis. In order for our controller to work more
effectively, we need to add a zero to our system.
We chose to use a PD (Proportional Derivative) controller. We chose a PD controller
because when including a derivative term, the poles will be located would be on the
LHP (Left Half Plane). Therefore, they will not remain on the jω axis as the gain is
varied and the system will no longer oscillate. PD Controller: (KDs + KP). Someone
could include a PID (Proportional Integral Derivative) controller as well. When looking
at the root locus, a PID controller places all the poles on the LHP. A PI (Proportional
Integral) controller would not work because it causes the poles of the system to result
in the RHP (Right Half Plane) which will make the system unstable.
After performing an analysis, we put the transfer function into MATLAB and
manipulated our zero that we added the following to our result: PD Controller: (0.233*s
+ 233). With this zero included into our MATLAB simulation, we were able to achieve
the specification of the customers.
Plant Transfer Function Analysis: Time Response to a Unit Step Input:
sys=tf([-.0187],[(-4.0295*10^-6) 0 -.003182]);
rltool(sys)
(additional option with rltool)

Root Locus Editor Step Response
PD Controller: (KDs + KP)
The next controller we chose to look into is a proportional/derivate PD controller. When
using such a controller, it includes a pole to existing system. This is ideal for our
application because when the zero is place into the appropriate location, it will cause
the root locus lines to converge into the LHP and therefore increasing the stability of
our model.
After a location was found for the pole, we looked at the step response to identify the
system’s characteristics. With an overshoot of 14%, a rise time of 3.8 ms. and a settle
time of 25 ms, adding a pole at our desired location should exceed the specifications
from the customer. Below are three examples different attempts our group ran through
to end up learning the characteristics of the PD controller. The root locus editor
displays that result. Choosing gains for the controller and then simulates it. If you
adjust the value of Kp and Kt properly, you will be able to the customer specifications.
With Kd = .5 and Kp = .5* 10 = 5 With Kd = .005 and Kp = .005* 10 = 5
Transfer function:
0.5358 s + 5.358
--------------------------------
4.03e-006 s^2 + 0.5358 s + 5.361
Transfer function:
0.005358 s + 0.05358
------------------------------------
4.03e-006 s^2 + 0.005358 s + 0.05676
With Kd = .00005 and Kp = .00005* 10 = 5

Transfer function:
5.358e-005 s + 0.0005358
---------------------------------------
4.03e-006 s^2 + 5.358e-005 s + 0.003718
As shown in the diagrams above, when increasing the derivative constant of your
controller, the settling time and rise time decreases, but the overshoot dramatically
increases. On the other hand, the increase in the overshoot can be compensated by
lowering the proportional gain constant. With this combination, a PD controller can be
tuned to the desired specifications.
Now that our basic system model as well as a controller has been developed to meet
the customer’s specifications, our group continued onto the next stage of our design.
When looking at our electronic throttle body system on a real time basis, there are
additional elements in the model that are unaccounted for. The non-linear components
add additional poles and zeros to the system which in return can cause instability.
Fortunately, the use of System Vision software accounts for the dynamic behavior the
system will encounter allowing us to take this into consideration. With the use of
System Vision, we developed an open loop system model to determine the response
characteristics.
In order to do simulate the electronic throttle body, additional modifications were
required to allow the system to be accurately modeled. The ideal current source is
replaced with a voltage pulse at 12v. Rather than applying an angular velocity motor
and later changing the angular velocity to angle, we install a motor that outputs the

angle thus eliminating the previously shown conversion block. This motor contains the
following specifications: D=0, Winding Resistance = 2.8, Inertia = 4E-6, Inductance =
1.1E-3, and KT = 0.0187.
An additional modification is a rotational reference stop. This allows the system to
mimic the actual application into a System Vision simulation with better accuracy. The
final stage of our modification to our block diagram of the system was to ignore the
affects of the plate inertia. When looking into the original
equation,
r
K
s
r
J
J
K
spp
m
t
++
=
2
)(
i(s)
Theta(s)
you will notice that the inertia from the plate,
Jp, is far less significant than the inertia from the motor. Because of the fact
that 17
059.
1
≈=r , Jp can be ignored without viewing any significant difference in our
system. The reason for ignoring the additional component of our system is due to the
processing capabilities of our software (System Vision). Every time an additional
component is included, the software creates a sweep of every part in relation to the
other parts in the system. There every time an additional part is implemented, the
system has more to processing sweeps to account for.
Since System Vision accounts for the non-ideal situation, we can not duplicate the
oscillatory behavior shown previously in MATLAB. The ideal simulation in MATLAB
(root locus plot) demonstrates how the poles lie upon the jω axis. In the non-ideal
situation, this would not be the case. The pole would be drawn more into the left hand
plane (LHP), thus causing the oscillatory behavior to be reduced.
When variations of the input parameters where for the motor are changed, you can
notice a significant change in the how the plate reacts. Adjusting the magnitude, for
example, you will notice the overshoot response to act accordingly (a rise in the
magnitude will result in a rise in the overshoot).
Angular Velocity vs. Time Plot Bode Plots (Magnitude and Phase)
When replacing the voltage source with the previously used ideal current source, the
oscillatory behavior returns. The characteristics of the ideal current source cause the
system to behave more as expected. Adding the more realistic voltage source is
essentially the same as adding a zero on the LHP. A zero would cause the root locus
line to converge more into the LHP, therefore increasing the system’s stability. The
inductive contribution from the motor could also be an additional factor in the
contribution of stabilizing the system.

Now that our basic system model and controller has been created as well as modeled,
we can begin the final stage of developing a closed loop feedback controller system.
As shown in the second stage of our design, a PD and PID controller are both feasible
options to obtain our desired results. We have chosen to implement a PD controller
and model the characteristics via System Vision.
Our design involved an angle to signal (Q) sensor, a signal to voltage sensor, a
differential block, a summation block, a proportional controller, and a derivative
controller. The first three devices mentioned were used to tie back the resultant output
to the input causing unity feedback. The additional three devices where used to
develop the PD control.
From adding a pole to the system in our MATLAB analysis, we selected one of the
many possible points of stabilization for our controller; we have chosen our PD
controller to be (0.233s + 233). After including this controller design to our system, the
resultant rise time and settling time met the customer specifications. However, the
overshoot from the response was not with the acceptable range. Therefore, (knowing
of the effects of a proportional controller) we choose to lower our proportional constant
from 233 to 20. This put our P/D ratio from 100 to 10.
Our electronic throttle body with the unity feedback and control (0.233s + 20) gives a
time response with the following characteristics: overshoot = 7.4699%, settling time =
2.3333 ms, rise time = 1.1137 ms all of which lye well into the range of the customer
specifications.
Step Response of the electronic throttle body with our PD controller (PD Controller: 0.233s + 20)

Conclusions
From the development of a system model to the controller selecting and testing, this project
encompassed a large variety of aspects/techniques used in the industry. We began with deriving the
frequency-domain block diagram from the model of a widely used mechanical/electrical element.
From our block diagram, we develop the resultant transfer function so we can design a control system
with the assistance of such software as MATLAB and System Vision. Additionally, we included and
replaced some components as requested, such as replacing the ideal current source to the voltage
pulse component at 12v, using the angle output motor to eliminate the conversion component, and
adding the inductance and the stops. As a result from the process, we have developed a PD
controller that exceeds the specifications:
Customer
Specifications
PD Controller
Output Response
Overshoot (%OS) < 25 % 7.4699 %
Rise Time (TR) < 0.05 sec 0.001137 sec
Settling Time (TS) < 0.25 sec 0.0023333 sec
These objectives have been met by the following PD Controller: KD*s + KP = ( 0.233*s + 20 )

6.0.0 Appendix
6.1.1 Questions & Answers
Questions Answers
Perform analysis of the plant transfer function itself in
MATLAB. Is the plant stable, unstable, or oscillatory?
The plant is oscillatory. The throttle plate inertia and dc
motor inertia are the two components of the plant that cause
the oscillation to occur. Oscillation occurs when a second
(or higher) order system is produced. From the transfer
function, the combination of Jm and Jp are what deplict
whether or not the system results in a second order
characteristic equation. When (Jm + Jp/r) becomes zero, the
characteristic equation is no longer second order. Therefore,
the dc motor and the throttle plate are the two physical
components of the plant that cause it to behave this way.
Perform a root locus analysis in MATLAB. This applies a
gain to the system, a proportional controller, and analyzes
the plants behavior for varying gains. Will a proportional
controller work for this system? Why? If not, what must your
controller add to work more effectively? HINT: Examine the
pole locations.
No, a proportional controller will not work because for any
value of ‘k’ the poles of the system will remain on the jω
axis. In order for our controller to work more effectively, we
need to add a zero to our system.
Pick a controller. Given the above analysis, which
controllers should work? Why? HINT: Examine what the
controllers add to the loop, these are the “knobs” you can
turn to affect performance. What does each knob affect?
We chose to use a PD (Proportional Derivative) controller.
We chose a PD controller because when including a
derivative term, the poles will be located would be on the
LHP (Left Half Plane). Therefore, they will not remain on the
jω axis as the gain is varied and the system will no longer
oscillate. PD Controller: (KDs + KP). Someone could include
a PID (Proportional Integral Derivative) controller as well.
When looking at the root locus, a PID controller places all
the poles on the LHP. A PI (Proportional Integral) controller
would not work because it causes the poles of the system to
result in the RHP (Right Half Plane) which will make the
system unstable.
Attach your controller to the plant and again perform time
analysis.
After performing an analysis, we put the transfer function
into MATLAB and manipulated our zero that we added to
the following result: PD Controller .233*s + 233
With this zero, we were able to achieve the specification of
the customers.
(Please see Math Analysis for this question)
Choose some gains for your controller and simulate. How
does it perform? Are you able to meet customer
specifications? Why or why not? What physical components
of the plant are directly affecting your controller? HINT:
Examine the pole locations symbolically. Which values are
the most affective? Physically, why is this so?
Please see: 4.2.2. Analysis and Results – Part 2

The following are Step Response Curves from System Vision demonstrating the effects of our closed loop
feedback controller design.
Step Response with the Initial PD Controller: (0.233s + 233)
Time Response with the Finalized PD Controller: (0.233S + 20)

Below is the output code used when running the simulation of our finalized PD controller.
=====> Saved and checked schematic : theschematic.1
VHDL-AMS netlisting succeeded.
Generating Spice with command c:mentorgraphicsSystemVision4.2wvwin32binsvspice.exe -_ -h -
kc:mentorgraphicsSystemVision4.2standardwspice.cfg -gtheschematic.tempfile theschematic
Wirelisting theschematic into file genhdltheschematictheschematic.cir.
Warning: No ground node (Label a net GND)
Post-Processing...
0 error(s) and 1 warning(s) in file theschematic.cir.
Netlisting completed : theschematic
Simulating the design theschematic with the library Z:MyProjectsim_admstheschematicWORK_AMS41
---------------------------------------
c:mentorgraphicsSystemVision4.2simsystemvisionwin32/adms/v4.1_1.1/bin/vasetlib -prod pr
Z:MyProjectsim_admstheschematicWORK_AMS41
Modifying adms.ini
Modifying modelsim.ini
** Warning: vmap will not overwrite local modelsim.ini.
c:mentorgraphicsSystemVision4.2simsystemvisionwin32/adms/v4.1_1.1/bin/vamap -prod pr WORK_AMS41
Z:MyProjectsim_admstheschematicWORK_AMS41
Modifying adms.ini
Adding logical reference "WORK_AMS41" to directory "Z:MYPROJECTSIM_ADMSTHESCHEMATICWORK_AMS41"
Modifying adms.ini
c:mentorgraphicsSystemVision4.2simsystemvisionwin32/adms/v4.1_1.1/bin/vamap -prod pr FUNDAMENTALS_VDA
c:/mentorgraphics/SystemVision4.2/sim/systemvision/win32/Libraries/Fundamentals_VDA/lib/v4.1_1.1/Fundamentals_VDA
Modifying adms.ini
Adding logical reference "FUNDAMENTALS_VDA" to directory
"C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32LIBRARIESFUNDAMENTALS_VDALIBV4.1_1.1
FUNDAMENTALS_VDA"
c:mentorgraphicsSystemVision4.2simsystemvisionwin32/adms/v4.1_1.1/bin/vamap -prod pr SPICE2VHD
c:/mentorgraphics/SystemVision4.2/sim/systemvision/win32/Libraries/Spice2VHD/lib/v4.1_1.1/Spice2VHD
Modifying adms.ini
Adding logical reference "SPICE2VHD" to directory
"C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32LIBRARIESSPICE2VHDLIBV4.1_1.1SPICE2V
HD"
Compilation not required : theschematic
Simulating using cmd file : Z:/MyProject/sim_adms/theschematic/expt1.cmd
Including spice file : Z:MyProjectgenhdltheschematictheschematic.cir
Software under License
Copyright Mentor Graphics Corporation
***** ANALYSIS ....
***** 0 error(s).
***** 0 warning(s).
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32ADMSV4.1_1.1LIBSSTD.standard
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32ADMSV4.1_1.1LIBSIEEE.math_real
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32ADMSV4.1_1.1LIBSIEEE.fundamental_constants
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32ADMSV4.1_1.1LIBSIEEE.electrical_systems
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32ADMSV4.1_1.1LIBSIEEE.mechanical_systems
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.gear_r(ideal)
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.spring_r(linear)

Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.stop_r(ideal)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.dcmotor_r(basic)
Loading C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.v_pulse(ideal)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.q_from_angle(ideal)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.q_to_voltage(ideal)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.e_difference(behavioral
)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.e_deriv(s_dmn)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.e_gain(behavioral)
Loading
C:MENTORGRAPHICSSYSTEMVISION4.2SIMSYSTEMVISIONWIN32EDULIBV4.1_1.1EDULIB.e_sum(behavioral)
***** GENERATION ...
Warning 113: NODE "ELECTRICAL_REF": Not connected to any element.
This node has been removed from the netlist.
Warning 113: NODE "ROTATIONAL_REF": Not connected to any element.
This node has been removed from the netlist.
***** 0 error(s).
***** 2 warning(s).
INFORMATION ABOUT COMPILATION...
Memory space allocated (bytes): 361066
11 elements
8 nodes
0 input signals
EldoHDL VERSION : ELDO v6.4_1.1 (Production version) Tue Jun 14 16:32:26 GMT 2005
*** DATE: 02-Dec-2005 01:10:26
*** TITLE: * Command file for design: theschematic
TEMPERATURE : 27.000000 degrees C
Searching Operating Point between -1.000000e+013V and
1.000000e+013V
Performing DC analysis...
--> Partitioning circuit...
***> DC CPU TIME 0s 000ms <***
DC:1 iterations FOR DC analysis
ERNST_SAPUTRA 0.0
FEEDBACK 0.0
INPUT 0.0
N1N37 0.0
N1N65 0.0
N1N67 0.0
N1N69 0.0
N1N83 0.0
EldoHDL NEWTON: VNTOL=1.000000e-007 RELTOL=5.000000e-005
Compute from 0.000000 Nano to 2.500000E+007 Nano
***>Current simulation completed
SIMULATION INFORMATION
memory size allocated in bytes 738947
Latency: 0.000000%

average number of iterations: 1.000000
nb of components: 11
nb of nodes: 8
nb of MOS or BIP calls: 0
Number of steps computed: 10666
***>CPU TIME 1s 360ms <***
--- Simulation finished at time 25 ms
--- Nb of transactions 3
--- Nb of events 3
Simulation results stored in theschematic.2

Unity Feedback PD Controller Design for an Electronic Throttle Body

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