2006-32-0008 / 20066508

Governor System for General Purpose Engine

Using Adaptive Control Theory
Tomoki Fukushima, Hayato Matsuda, Yoshihisa Shinogi and Yoichi Taniguchi
Honda R&D Co.,Ltd.

Copyright © 2006 SAE International and Copyright © 2006 SAE Japan

ABSTRACT the throttle valve shaft using a motor and converge

engine speed to a target value by PID control, etc.
General purpose engines are  required to keep the However, as a governor for general purpose engines
engine speed constant, and are therefore equipped with where dynamic characteristics of the controlled object
governor mechanisms. However, the engines are applied change, due to the fact that the engines are used for
to various applications, and the dynamic characteristics several different applications, and the environmental use
of the controlled engine changes according to different conditions such as temperature and pressure change, it
operating conditions. To enhance robustness, an is not sufficiently robust and gain adjustments adapted to
adaptive control system that uses a self-tuning regulator changes in dynamic characteristics are required. In the
has been constructed. Applying elliptical gears to the present research, an electronic robust governor using an
mechanism for driving the throttle valve, it was possible adaptive control theory has been developed, which has
(2),(3)
to realize both high resolution near the closed position used Self-tuning Regulator control (hereinafter, STR
and a reduction in operating time of the throttle valve. control) for changes to dynamic characteristics of the
controlled object in order to control the engine speed of
INTRODUCTION the small-single cylinder engines.

In automobiles and on motorcycles, people estimate

conditions using the speedometer and their five senses
and then use the throttle (accelerator pedal) for control.
In comparison, products with general purpose engines,
most notably the small single cylinder engines (in
generators, lawn mowers, tillers, snow throwers, water
pumps, etc.) have a mechanism that automatically adjust
the throttle opening of the carburetor, either because it is
not possible for a person to respond fast enough to
sudden load changes or for unattended operation. This is
a mechanism for keeping the engine speed constant.
Many products use mechanical feedback control which
applies James Watt's centrifugal force governor
(1)
mechanism such as the one shown in Fig. 1. This
mechanism detects changes in engine speed using the
centrifugal force of a counterweight, and a linkage
adjusts the throttle opening of the carburetor. The throttle
opening becomes steady at where the centrifugal force
and governor spring are balanced. However, there is
mechanically a difference in engine speed between idle
and when a load is applied.

In recent years, use of inexpensive high performance

microprocessors has enabled the introduction of
governors that are electronic (hereinafter; electronic
governors) as generators, instead of mechanical Fig. 1 Centrifugal type
governor mechanisms. The electronic governors drive
MAIN SECTION
4000 40

1. IMPLEMENTATION OF STR CONTROL

3500
35

Throttle opening angle (deg)

1.1 Engine Modeling

Engine speed (rpm)

3000 Engine speed
30
Fig. 2 shows a simplified engine model where throttle 2500
opening is used as an input. Considering the block 25
diagram of a general purpose base engine that uses a 2000

carburetor, mass air flow Ga and mass fuel flow Gf are 20

1500
determined by the throttle opening Tth and engine speed Throttle opening angle
NE when the air fuel ratio is fixed. A mean effective
1000 15
pressure Pmi generated by combustion of the intake 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
mixture is converted to engine speed by the crank Time (sec)

linkage system. The engine load characteristics,

Fig. 3 Step response
connected to this crank linkage system of general
purpose engines, differ with the engine application (for
generators, lawn mowers, tillers, snow throwers, water
pumps, etc.). Even when the engine is used on the same A(q 1 ) y (k ) q 1 B(q 1 )u (k )  w( k ) (1)
application, the load characteristics differ with the
moment of inertia of the attachment. In order to control
A(q 1 ) 1  a1q 1    an q  n (2)
an electronic governor, the throttle opening angle Tth is
selected as the input and engine speed NE selected as
the output, with the area surrounded by dashed lines is B(q 1 ) b0  b1q 1    bm q  m (3)
used as a single block model for the controlled object.
a1  a n , b0 bm  : Model Parameters
A step response of the engine speed relative to step
input of the throttle valve is shown in Fig. 3. With the w(k )   : White Noise
premise of performing adaptation control using the ARX
(4)
(Auto-Regressive Exogenous) model , a minimum
In Eq. (1), with the target engine speed defined as ym the
square model (equation 1), with throttle opening Tth as
output error is calculated using the following equation.
the input u and engine speed NE as the output y,
modeling was performed while focusing on the order and
e1 (k ) y m (k )  y ( k ) (4)
lag-type.

The control object is automatically adjusting the throttle

opening u, the input, allowing the engine speed y, the
output of the controlled object, to become equivalent to
Engine model
Engine
the target engine speed ym. Here, the load fluctuation is a
load primary unknown parameter. In addition, the whole
parameters of the engine combustion model, including
Ga
Pm i Crank
the load, are estimated as the unknown parameter by
Carburetor Combustion
model model
shaft sequential calculation.
T th Gf
model NE

NE ( E ngine sp eed ) 1.2 Controller Design

(5)
With the introduction of the Diophantine equation and
Fig. 2 Block diagram of engine model
configuring Eq. (1) in the following manner, variance of
the output error can be minimized, enabling achievement
of the control object.

1
u (k )
b0
^
y m (k  1)  T T ] (k ) ` (5)

Here,

TT >b b
1 m , h0  hn1 @ (6)

] (k ) >u (k  1)  u (k  m) , y (k )  y (k  n  1)@ (7)

However, in the actual system, as the parameter is
unknown, sequential estimation is performed using
parameter estimation law below. Middle gear
(Normal-driven)
 
T (k ) T (k  1)  3 (k  1)] (k  1)H 1 (k ) (8)
Middle gear
( Elliptical-drive) Motor pinion
(Normal-drive)
1
3 (k ) 3 (k  1)
O1 (k )
(9)
1 ª O2 (k )3 (k  1)] (k  1)] T ( k  1)3 (k  1) º Throttle control gear
 « »
O1 (k ) ¬ O1 (k )  O2 ( k )] T (k  1)3 (k  1)] (k  1) ¼ (Elliptical-driven) Throttle shaft
ECU cover Detail of gear train Throttle control motor

Here, ECU gromet

TT >b 0 ,T T @ (10)

Motor case
] T (k ) >u(k ) , ] (k )@ (11) ECU assembly
Motor pinion
(Normal-drive)
T
Middle gear
Here 0 < O1(k) d 1, 0 d O2(k) < O(k) ʌ(0)= ʌ (0)>0. If the (Normal-driven Throttle control gear
& elliptical-drive) (Elliptical-driven)
unknown parameter converges to the true value, the Throttle shaft
system becomes the minimum variance control using the
configuration of Eq. (5). Therefore, a robust controller for
a general purpose engine speed governor with respect to
dynamic characteristic fluctuations can be attained.

2. MECHANISM CHARACTERISTICS

An outline form of the electronic governor mechanism

installed on a carburetor is shown in Fig. 4. A Permanent
Magnet type stepper motor (hereinafter; PM type stepper
motor) has been selected for use in this mechanism as Fig. 4 Carburetor assembly
the actuator to control the throttle valve.

2.1 Non-linear Reduction Mechanism

2a
General purpose engines frequently have 0% to 100%
and 100% to 0% sudden load fluctuations. In order to
enhance the ability to minimize engine speed fluctuations
Am A th
during load fluctuations, it is necessary to increase the
throttle opening and closing speed. If the reduction gear m th
train is formed using normal gears and resolution is set m
th
2b

loosely, matching the requirements of a large throttle Om

Fm Fm F th O th F th
opening, resolution at slight opening is insufficient and
can cause hunting. On the other hand, if the resolution is
set fine to meet slight opening requirement
characteristics, throttle opening and closing speed is m th

reduced due to the stepper motor characteristics Pitch curve

involved.
L 0 (=2a)

In order to allow for these conflicting requirements,

(6)
elliptical gears have been utilized. Fig. 5 shows a
Fig. 5 Elliptical gear train
linkage that uses elliptical gears.

With Om, Oth, as the centers of the ellipses, and

respective focus Fm, F'm, Fth, and F'th, of gears of the
same shape with long diameter 2a, and short diameter
2b and with Fm and Fth as rotational axes, |AmFm| = Um,
|AthFth| = Uth and Tm, Tth as the rotation angles.
 r
Um (12)
1 H cos T m 14
Normal gear

Mass air flow rate (kg/sec)

12
r
U th (13)
1 H cos T th 10
8
U m  U th 2a (14)
6
Elliptical gear
However, 4
2
b2 a 2 b 2
r , H 0
a a
0 10 20 30 40 50 60 70 80 90
Motor step (pulse)
Therefore,
Fig. 7 Relationship between motor step and mass air flow rate
­ 1  H cos T m ˜ 2a  r  r ½
1
(Engine speed = 3600rpm)
T th cos ® ¾ (15)
¯ >2a ˜ 1  H cos T m  r @˜ H ¿

The relationship of Tm and Tth with H = 0.25, 0.425, and 3. INSTALLATION IN EQUIPMENT RESULTS
0.65 is shown in Fig. 6.
With a test engine A (Table 1) installed in a lawn mower,
The number of steps used for an elliptical gear Fig. 8 shows results comparing governor characteristics
mechanism is 35% less than the number used for a between its use in a conventional mechanical governor
normal gear. And so it is possible to increase the throttle and in an adaptive control type electronic governor. The
opening and closing speed. By using a non-linear conventional mechanical governor has steady state error,
resolution mechanism such as this, a linear relationship where the engine speed fluctuates depending on the
between motor step pulse and mass air flow Ga such as load. With respect to this point, when using an adaptive
shown in Fig. 7 is achieved. If the non-linear relationship control type electronic governor, it can be seen that
is corrected mechanically, linearization processing using engine speed is uniform, independent of the load.
the control system is no longer needed.

3.5

90
(deg)

3.0
80 WOT
= 0.25
th

70 2.5
Output power (kw)

60 = 0.425
Throttle opening angle

50 2.0
40
1.5 STR control
30
= 0.65
20 Mechanical
1.0
10
0 0.5
0 20 40 60 80 100 120 140 160
0.0
Drive gear angle m (deg)
1500 2000 2500 3000 3500 4000

Fig. 6 Characteristics of angle with difference in elliptical gear Engine speed (rpm)
eccentricity
Fig. 8 Dynamic characteristic of governor

In addition, a test engine A (Table 1) installed on a

cylindrical power generator was equipped with an
elliptical gear as shown in Fig. 5, and with a normal
circular gear, and their idle stability were compared. For
this comparison, the same STR control forming an
electronic governor was used, the electric load was set to
no load and the target engine speed set to 1400 rpm.
Results for the use of the elliptical gear mechanism are
shown in Fig. 9 and results where the normal circular
gear was used are shown in Fig. 10. Through the use of 3600
the elliptical gear mechanism, as compared to the use of Elliptical gear
3400
a normal circular gear mechanism, idle stability has been

Engine speed (rpm)

3200
enhanced. 3000
2800
2600 Target engine speed
1600 2400
2200
Engine speed (rpm)

1500 Load on Load off

2000
1400
0 1 2 3 4 5 6 7
1300
Time (sec)
1200
Elliptical gear Fig. 11 Dynamic performance with elliptical gear
1100 Target engine speed

1000
0 1 2 3 4 5
3600
Time (sec) Nomal gear
3400

Engine speed (rpm)

Fig. 9 Idle characteristic with elliptical gear 3200
3000
2800

1600
2600
Target engine speed
2400
Engine speed (rpm)

1500
2200 Load on Load off
1400
2000
1300 0 1 2 3 4 5 6 7
1200 Time (sec)
1100 Normal gear Target engine speed
Fig. 12 Dynamic performance with normal gear
1000
0 1 2 3 4 5

Time (sec)

Fig. 10 Idle characteristic with normal gear Table 1 Test engine specifications

Engine A B
The convergence capability of engine speed fluctuations Air-cooled, Air-cooled,
during rated load intermittent operation (from 100% to 4-stroke, 4-stroke,
Type
0% and 0% to 100%) is shown in Fig. 11 and Fig. 12. single-cylinder single-cylinder
gasoline (OHV) gasoline (OHC)
Results for the use of the elliptical gear mechanism are
shown in Fig. 11 and results where the normal circular Displacement (cm )
3
163 438
gear was used are shown in Fig. 12. Through the use of Dry weight (kg) 15 39
the elliptical gear mechanism, as compared to the use of Bore Stroke (mm) 68.0 45.0 88.0 72.1
a normal circular gear mechanism, the convergence Max. power (kW / rpm) 4.1 / 3600 11.2 / 3600
capability of engine speed has been enhanced. Both
stability of engine speed for no loads and convergence of
engine speed during load fluctuations have been
achieved. (7)
A test engine B (Table 1) is applied an adaptive control
type electronic governor system. With this engine
installed on a cylindrical power generator, the
convergence capability of engine speed fluctuations
during rated load intermittent operation (from 100% to
0% and 0% to 100%) is shown in Fig. 13. Furthermore,
an adaptive control type electronic governor was installed
in commercialized products (lawn mowers, snow
throwers, pressure washers, etc.) to perform practical
durability testing for confirmation. Tuning was not
required for the individual products where favorable
operation characteristics were obtained from the
beginning through to the end of the durability testing REFERENCES
verifying the validity of this system.
1. Gomi, T.: Nainen Kikan, p.214-215 (1985) (in
Japanese)
2. Terao, M., Kanai, K.: Robust Adaptive Control, p.
3600
Target engine speed 109-113 (1993)
3400
3. Omatsu, S., Yamamoto, T.: Self Tuning Control, p.
Engine speed (rpm)

3200
3-4 (1996)
3000 4. Adachi, S.: Seigyo no tameno System Dotei, p. 55-
2800 64 (1996) (in Japanese)
2600
Engine speed
5. Goodwin, G. C., Long, R. S. 㧦 Generalization of
2400 Results on Multivariable Adaptive Control, IEEE
2200 Load off Load on Trans., AC-24-6, p. 1241-1245 (1980)
2000 6. Katori, H.: Hienkei Haguruma no Sekkei Seisaku to
0 1 2 3 4 5 6 7 8 Ouyou, p. 7-34 (2001) (in Japanese)
Time (sec) 7. Ito, K., Honda, S., Saito, T., Kurata, M., Naoe, G.:
Development of Electronically Controlled Multi-
Fig. 13 Dynamic performance of governor
purpose Engine iGX440, Honda R&D Technical
Review, Vol. 17, No. 2 (2005)

CONCLUSION CONTACT

Through applying adaptive control and a non-linear gear Honda R&D Co.,Ltd. Power Products R&D Center
mechanism to the governor of a general purpose engine, Department 3, Development Division
the following features have been achieved.
E-mail tomoki.fukushima@h.rd.honda.co.jp
1. A robust governor relative to fluctuations of dynamic
characteristic of the engine, the controlled object,
has been developed, allowing use in a general
purpose engine, for which applications are unlimited.

2. The realization of both a high resolution near the

closed position and a reduction in operating time of
the throttle valve made it possible to control the
engine from idle condition to sudden load change
condition.

3. Through linearization of the relationship between

motor step and mass air flow, linearization of the
input signal in control calculations becomes
unnecessary, leading to a simplified control system.