2009-01-0370

Optimization of PID Control for Engine Electronic Throttle System Using Iterative
Feedback Tuning
Shugang Jiang, Michael H. Smith and James Kitchen
A&D Technology Inc.

Copyright © 2009 SAE International

ABSTRACTThe Electronic Throttle Control (ETC) system is more
and more used and increasingly becoming a standard
part of the engine. It controls the amount of air intake
into the cylinders by precisely positioning the throttle
plate at the desired opening. An ETC system provides
the possibility of improving the overall engine andvehicle performance because with such a mechanism,
the engine controller can decide and set the throttle
position not only based on driver intention, but also
taking into consideration the specific engine operation
mode information, such as safety factors, emission
constraints, etc.
After the throttle position target is determined, therequirement for the ETC system is that the throttle plateshould achieve the commanded position as accurately
and as quickly as possible. In many cases the controller
is designed by first establishing a model of the electronic
throttle system using experimental identification.
However, due to such nonlinear effects as static friction,
dynamic friction, and nonlinear return springs etc.,
identification of a model for the electronic throttle systemsometimes does not give good results. This makes acontroller design based on the model far from optimal.
Iterative Feedback Tuning (IFT) is a method for directly
tuning the controller parameters based on the data ofclosed loop experiments without the need for an explicit
model of the system. This property makes IFT an
attractive method for ETC design. In this paper a TwoDegree-of-Freedom(2-DOF)
Proportional-IntegralDerivative (PID) controller for an engine electronic
throttle system is designed and the PID control gains are

optimized using IFT. The application shows that the IFT
method gives very good performance for controller
tuning.

INTRODUCTION
The ETC system has gained success in high volume
applications and is becoming a standard part of theengine [1-3]. By precisely positioning the throttle plate at
the commanded opening, an ETC system controls theamount of air intake into the cylinders, and consequently
the engine operation. Compared with the traditional
throttle system that has direct mechanical connection
with the acceleration pedal, an ETC system provides thepossibility of improving the overall engine and vehicle
performance because this mechanism allows the engine
controller to decide and set the throttle position not only
based on driver intention (the acceleration pedal
behavior), but also taking into consideration the specificengine operation mode information, including safety
factors and emission constraints etc. This helps toimprove the air fuel ratio regulation in transients, andcatalyst thermal management etc. An ETC system also
makes it possible to integrate such functions as idle
speed control, traction control, and cruise control etc.
with a single controller/actuator, which provides
significant benefits for the OEMs.
After the engine controller determines the throttle
position target, an ETC system should achieve thecommanded throttle position as accurately and as
quickly as possible. Usually a comprehensive ETC
strategy consists of a PID feedback controller andnonlinear compensators that handle such nonlinear

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effects as static and dynamic friction, and limp-homeeffects [4-8]. While a lot of emphasis has been placed on
the nonlinear strategy design, a PID feedback control
that mainly handles the linear operating mode of thesystem plays an important role in the overall strategy.
Good design and implementation of the PID feedback
control is the basis for good performance of anelectronic throttle system. This paper focuses on the
optimization of the PID feedback control for ETC system.

system and the rapid prototyping controller used for the
study. Section 2 describes the PID controller structure
adopted. Formulae for implementing IFT of the controller
are obtained. In Section 3, application of the method on
an electronic throttle system is performed. Results are
given and analyzed. Section 4 summarizes the paper.

To produce good control performance, usually sets ofdifferent PID control gains are obtained for different
regions of the whole operating range of the throttle [1-8,
10-12]. Several approaches might be used for obtaining
the PID control gains. With the most commonly usedmethod, first a linear process model for the throttle
system is obtained through identification experiment,
then the control gains are designed based on theprocess model [4-6, 9-10]. In [11] the gains are initiallyobtained by direct hardware testing, and subsequently
improved by the guidance using frequency response
analysis. These methods require the establishment of aprocess model. In [12] the method involves tuning the
PID gains on-line using sequential quadratic
programming.

Figure 1 shows the hardware of an ETC system. The
electronic throttle body consists of a brushed DC motor,
gearbox, throttle plate, dual opposing return springs, andthrottle position sensor (usually two outputs) which uses
potentiometers. The controller samples the acceleration
pedal sensor signals, and together with other related
engine information, determines the required throttle
opening. Based on the throttle position target and themeasured real throttle position, the controller determines
the Pulse Width Modulation (PWM) signal parameters,
sends out the signals to an H-bridge driver to control theoperation of the motor, and consequently the opening of
the throttle plate. By using an H-bridge driver, the motor
and the throttle plate can rotate in either direction. The
motor torque is balanced by the return springs, which
are opposing to each other so that the plate is put into its
default position, which is called the limp-home position,in the case of power supply failure or other system
malfunction.

For the methods that require a process model, however,experimental identification might not provide a goodresult due to nonlinearity of the throttle system. This
makes a controller design based on the model far from
optimal. Iterative Feedback Tuning is a method for
directly tuning the controller parameters based on thedata of closed loop experiments without the need for an
explicit model of the system [13-15]. Since its
appearance in 1994 [13], IFT has been applied in thetuning of various controllers with good results. Manyadvances have been made, for example, the method
has developed from the control of single input single
output linear time invariant systems, to the control oflinear multiple input multiple output systems [16-17] andthe control of systems containing nonlinearities [18-21].
Many aspects of the method, such as stability,
robustness, gradient estimation, optimal prefiltering, andvarious numerical simulations and experiments etc. havebeen reported [22-30].
IFT tunes the controller parameters iteratively along thegradient direction of a given criterion function. A modelof the system, as well as knowledge of disturbances is
not required. Since this design method is not based on
the plant model, it inherently avoids the problems
caused by deviation between the model and the plant.
This makes it an attractive approach for ETC design. In
this paper a 2-DOF PID controller is implemented tomainly handle the linear operating mode of an engine
throttle system and the IFT method is used to optimize
the PID control gains. The application shows that the IFT
method is very effective for controller tuning.
The paper is organized as follows. Section 1 provides abrief description of the engine electronic throttle control

ENGINE ELECTRONIC THROTTLE CONTROLSYSTEM

Figure 1. ETC Hardware
A rapid prototyping controller is used for this study.
Figure 2 shows the hardware framework of thiscontroller. It has a dual CPU architecture, using aPentiumM processor for high-speed control, and aRenesas SH4 processor for running the human-machineinterface, including color touch-screen LCD, function
keys, and Ethernet communication with the host PC. A
bus controller on the active back plane handles the datatransfer between the function boards and the CPUs.
Various function boards can be selected and integrated
in the controller as required.
For ETC implementation, an analog input board isincluded in the controller for sampling acceleration pedal
position and throttle position, and a PWM board isincluded for motor control. Model-based development
methodology is used. Control logic is designed on thehost PC using MATLAB®/Simulink®/Stateflow®, taking
the form of block diagrams. The S-functions for system
hardware and function modules are developed andintegrated in the block diagram. Real-Time Workshop®
converts the block diagram into C code, which is thencompiled, linked, and downloaded automatically to therapid prototyping hardware platform for real-time
execution under the RT-Linux operating system. Agraphical user interface software is used which enables
the arrangement of various screen elements on the host
PC and on the color touch-screen LCD. These screen
elements are associated with the variables orparameters of the Simulink® model, enabling real-timeparameter setting, signal monitoring and data logging.

response, or called reference. y is the measurement of
the plant variable to be controlled. e is the error. G1
and G2 comprise the controller. GP represents theplant. u is the control. It is obvious:u = G1r − (G1 + G2 ) y
y = GPu(1)(2)
The criterion function is chosen to be the integrated
squared error between the desired response and theachieved response:
Tf

1
J (ρ ) =e 2 (t , ρ )dt∫
2T f 0where T f

(3)

is the time to reach equilibrium, andρ

represents the controller parameters to be optimized.
The control design objective is to minimize this criterion
function. The gradient of this function with respect to thecontroller parameters is:
Tf∂J ( ρ ) 1∂e(t , ρ )=e(t , ρ )
dt
∫
∂ρ
Tf 0
∂ρ

(4)

The iterative tuning of the controller parameters can be
carried out by:ρ (k + 1) = ρ (k ) − γ k H k−1
Figure 2. Hardware Architecture of the Rapid
Prototyping Controller∂J ( ρ )
(k )
∂ρ

(5)

where γ is the step size, and H is the Hessian of J for
which the following approximation is used:
Tf

∂e ∂e
1
( )( )T dt
H=∫
T f 0 ∂ρ ∂ρ

(6)2-DOF PID CONTROLLER AND IFT

It is evident that to implement this tuning process, theIn this section the structure of the PID controller adopted
for this study is shown, and the IFT formulae for thisstructure are derived.

key is to obtain the term

Thorough introductions to the IFT method can be foundin [13-15]. In this study, the feedback type 2-DOF
controller structure shown in Figure 3 is used. This is avariation of the structure used in the above mentioned
literatures. This structure is more straightforward forunderstanding the influence of the controller
components, which will be shown later in this section.

∂e. While in IFT, this is done
∂ρby performing some closed loop experiments.
For succinctness,∂is denoted by ′ in the following∂ρformulae. Taking derivative of (1) and (2) with respect tothe controller parameters leads to:u ' = G1 ' r − (G1 '+G2 ' ) y − (G1 + G2 ) y 'y ' = GPu '

(7)
(8)

Rewrite (7) as follows:u ' = G1 (G1 'G '+G2 'r− 1y ) − (G1 + G2 ) y '
G1
G1

(9)

It can be seen that the pair of equations (9) and (8) has
exactly the same format as the pair of equations (1) and
Figure 3. 2-DOF Controller Structure
The IFT formulae for this controller structure are
obtained as follows. In Figure 3, r is the desired

G1 'G '+G2 'r− 1y ) is used as
G1
G1
reference, the output from the plant will be y ' . This is(2). This means if (shown in Figure 4.

the essence of the IFT method. Something thatdeserves note is that (11) shows e' and e are notuncorrelated, which makes the estimation of the gradientof the criterion function shown in (4) biased. To takecare of this, the y in (11) should be replaced by theoutput from a third experiment which is conducted
exactly the same as the normal experiment shown in
Figure 3. Another thing deserving notice is that
Figure 4. Illustration of Pair of Equations (9) and (8)This reference is a combination of r and y . To obtain
the output y ' , experiments that use r (called normal
experiment) and y (called gradient experiment) as
references need be performed [15]. The normal
experiment is shown in Figure 3. Figure 5 shows the
scenario of the gradient experiment, in which y * , e *and u * are used to denote the output of the plant, theerror and the control of this case.

G1 '+G2 'G1 'andin (11) might be non-causal.
G1
G1
However, since the normal experiment and gradientexperiment are carried out alternately and their data iscollected and processed batch-wise, the calculation ofe' can be performed. One can also add proper filters toplace extra pole(s) to these transfer functions for thecausality purpose. With e' obtained from the experimentdata, iterative tuning of the controller parameters can
now be implemented using (4) (5) (6).
For this study the specific format of the 2-DOF PID
control is chosen as:

KI
s
KDs
G2 ( ρ ) =100(0.001s + 1)
with ρ1 = K P , ρ 2 = K I , ρ 3 = K D .
G1 ( ρ ) = K P +Figure 5. Gradient Experiment
Since (G1 'G '+G2 'r− 1y ) is a combination of r and y ,G1
G1

considering the linearity from the reference to the output,
y ' can be obtained by the same combination of theplant outputs that use r and y as references, i.e., theoutputs of the normal experiment and gradientexperiment:

G1 'G '+G2 '
y− 1
y*
G1
G1
Because e' = r '− y ' = − y ' , it leads to:
G '+G2 'G'e' = 1y*− 1 y
G1
G1
y' =

(10)

(12)
(13)

This means the proportional and integral controls are on
the error and the derivative control is on the process
variable, with low pass filtering added. This design takes
care of the derivative kick encountered in conventional
one-degree-of-freedom controller, and provides good
performance for reference response and disturbancerejection. Based on experience, a constant number 100
is included in the format of G2 to make the gain K D in
about the same magnitude as gain K P and K I , which is
helpful for the numerical computation.
From (12) and (13) it is obtained:(11)

This is illustrated in Figure 6.

Figure 6. Calculation of ∂e / ∂ρ
Thus it can be seen that e' can be calculated using theoutputs of the normal and gradient experiments, which is

⎡
⎤
s
⎢
⎥
KPs + KI⎢⎥1 ∂ (G1 + G2 ) ⎢
1
⎥
=⎢
⎥
G1
∂ρ
KPs + KI⎢⎥s2⎢⎥⎢⎣100( K P s + K I )(0.001s + 1) ⎥⎦s⎤⎡⎢K s + K ⎥I
1 ∂G1 ⎢ P
⎥
=⎢
1
⎥
G1 ∂ρ
⎢ KPs + KI ⎥
⎥
⎢
0
⎦
⎣

(14)

(15)

Now all necessary formulae to perform the IFT study for
the ETC are obtained and the optimization of the control

-0.5
70

-0.25

0

60
Throttle Opening (deg)APPLICATION RESULTS AND ANALYSISThe control scenario is set to be a 30 degree stepcommand. Control loop time is set to be 1 millisecond.
Considering the commonly adopted specification for
ETC, e.g., throttle plate positioning within themeasurement resolution and step response settling timeof less than 100 millisecond, the 30 degree stepcommand is prefiltered with a first order low pass filter
which has a time constant of 30 millisecond, and its
output is used as the desired response. The initial gainsof the controller are obtained by doing Ziegler-Nichols
testing and their values are as follows:

0.25

0.5

0.75

40

15
Reference for GradientExperiment
12
Output of GradientExperiment
9

30

6

20

3

50

10

0
Motor Voltage

0
-0.5

-3
-0.25

0

0.25
Time (sec)

0.5

0.75

Figure 8. Results of Gradient Experiment

K P = 0.39 , K I = 8.55 , K D = 0.44
Results of the normal experiment with the above control
gains, including system response and motor voltage
etc., are shown in Figure 7. It is obvious the overshoot of
the response is large and the overall performance of thesystem is far from acceptable. The output of the normal
experiment is used as a reference and the gradientexperiment is carried out, the results of which are shownin Figure 8. By using the results of the normal
experiment, the gradient experiment, and a third
experiment the same as the normal experiment, thederivatives of the system error with respect to controller
parameters are calculated. Figure 9 (a through c) showsthese results. The Hessian, and the gradient of thecriterion function with respect to the controller
parameters can be subsequently calculated and the newgains are obtained.
-0.25

0

0.25

0.5

0.75

16

35

14

30

12
StepCommand
Desired Response
Initial Response

20

10
8

15

6

10

4

5

Figure 9(b).

∂e / ∂ρ 2 for the First Iteration

2
Motor Voltage

0-0.5∂e / ∂ρ1 for the First Iteration

1
18

40

25

Figure 9(a).

Motor Voltage (V)Throttle Opening (deg)

-0.5

-0.25

0

0.25
0.5
Time (sec)

0.75

Figure 7. Results of Normal Experiment

0
-2
1

1
18

-6
1

Motor Voltage (V)parameters can be implemented using the rapid control
prototyping system.

and the criterion function is 1.7344. Figure 11 shows thesystem response of all the iterations for comparison
purpose. It shows clearly the improvement of the system
performance during the IFT process.
Thus the IFT method is successfully implemented in the
optimization of 2-DOF PID control for the ETC and thesystem realizes very excellent control performance.
-0.5
35

-0.25

0

0.25

0.5

0.75

∂e / ∂ρ3 for the First Iteration

For the first iteration, the criterion function decreases
from 4.0847 to 2.8161, and the system response
improves. More iterations are carried out and the resultsof the whole IFT process are summarized in Table 1.
Results of the last iteration are shown in Figure 10. It
can be seen that after this iteration, the performance ofthe control is pretty good and the requirement is wellfulfilled. The final control parameters are obtained asfollows:

12
Step Command
Desired Response
Third Iteration

25
20

10
8

15

6

10

4

5

2
Motor Voltage

0
-0.5

-0.25

0

0.25
0.5
Time (sec)

0.75

0
-2
1

Figure 10. Results of the Last Iteration

K P = 0.7292 , K I = 7.4019 , K D = 0.7824
Table 1.
IterationStarting Gains[ K P K I K D ]′1

⎡0.3900⎤⎢8.5500⎥⎥⎢⎢⎣0.4400⎥⎦

2

3

Final

⎡0.4813⎤⎢7.1662⎥⎥⎢⎢⎣0.5159⎥⎦⎡0.6442⎤⎢6.9179⎥⎥⎢⎢⎣ 0.6671⎥⎦⎡0.7292⎤⎢7.4019⎥⎥⎢⎢⎣0.7824⎥⎦

J

Results of the IFT Process for ETC Optimization∂J ( ρ ) / ∂ρHγ

New Gains[ KP

4.08472.81611.9813

1.7344

K I K D ]′⎡− 11.5777⎤⎢ 0.2542 ⎥⎥⎢⎢⎣ − 2.0895 ⎥⎦⎡ 140.2929 − 0.0699 − 17.4669⎤⎢ − 0.0699 0.1059− 1.3342 ⎥⎥⎢⎢⎣− 17.4669 − 1.3342 24.2001 ⎥⎦1.00⎡0.4813⎤⎢7.1662⎥⎥⎢⎢⎣0.5159⎥⎦⎡ − 5.7344⎤⎢ 0.0740 ⎥⎥⎢⎢⎣− 0.1777⎥⎦⎡ − 2.2871⎤⎢ 0.0232 ⎥⎥⎢⎢⎣− 0.5034⎥⎦⎡ 42.1881⎢− 0.0198⎢⎢⎣− 7.5738⎡ 19.1583⎢− 0.0094⎢⎢⎣ − 4.1641− 0.0198 − 7.5738⎤
0.0432 − 0.3975⎥⎥− 0.3975 8.6862 ⎥⎦1.00− 0.0094 − 4.1641⎤
0.0191 − 0.1739⎥⎥− 0.1739 5.9831 ⎥⎦0.50⎡0.6442⎤⎢6.9179⎥⎥⎢⎢⎣ 0.6671⎥⎦⎡0.7292⎤⎢7.4019⎥⎥⎢⎢⎣0.7824⎥⎦

Motor Voltage (V)Figure 9(c).

Throttle Opening (deg)

30

1
14

45
40

Throttle Opening (deg)

35
30
25

Step Command
20

Desired Response

15

InitialFirst Iteration

10

Second Iteration
5

Third (Final) Iteration

0
-5
-0.5

-0.25

0

0.25
Time (sec)

0.5

0.75

1

Figure 11. Comparison of the Responses of All
Iterations

CONCLUSION
Because of nonlinearity of the engine electronic throttle
system, experimental identification of a plant model
might not give a good result and consequently acontroller design based on the plant model might notprovide good control performance. Iterative Feedback
Tuning directly tunes the controller parameters based on
the data of closed loop experiments without the need foran explicit model of the system, which makes it adesirable method for ETC design. In this paper a 2-DOF
PID controller is implemented for engine electronic
throttle system. IFT formulae for the controller structure
are obtained. Optimization of the PID control parameters
is successfully performed. The application shows that
this method provides excellent performance for thecontroller tuning.

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CONTACT
Dr. Shugang Jiang
Technical Specialist
A&D Technology Inc.
4622 Runway Blvd., Ann Arbor, MI 48108 USA
Email: sjiang@aanddtech.com

DEFINITIONS, ACRONYMS, ABBREVIATIONS
2-DOF: Two-Degree-of-Freedom
ETC: Electronic Throttle Control
Iterative Feedback Tuning
IFT:
PID:
Proportional-Integral-Derivative
PWM: Pulse Width Modulation