IEEJ International Workshop on Sensing, Actuation, and Motion Control

Vertical Velocity Control of Electric Airplanes by Using PropellerSlipstream for Safe Landing

Nobukatsu Konishi∗a) Student Member, Hiroshi Fujimoto∗ Senior Member

Yasumasa Watanabe∗ Non-member, Kojiro Suzuki∗ Non-member

Hiroshi Kobayashi∗∗ Member, Akira Nishizawa∗∗ Non-member

Aircrafts are desired to be more energy efficient and safer due to the increasing demand for air transportations. How-ever, generally speaking, nowadays commercial airplanes tend to loss stability under wind disturbances, especiallyduring landing. On the other hand, electric airplanes (EAs) are believed to satisfy the two demands because electricmotors are used for the propulsion. Especially, as the actuators, electric motors can improve the control performancesof EAs compared with internal combustion engines (ICEs). In this paper, by utilizing electric motors’ advantages, ver-tical velocity control method using propeller slipstream is proposed for safe landing, which might be a key technologyto innovate the design of EAs. Moreover, simulations and experiments are conducted to verify the effectiveness of theproposed method.

Keywords: Electric Airplane, Vertical velocity control, Propeller, Slipstream, Motor

1. Introduction

1.1 Background Considering the increase of de-mand for air transportation, aircrafts are desired to be moreenergy efficient and safer. Electric airplanes (EAs) can sat-isfy these demands, because electric motors are used forpropulsion (1)∼ (4). Compared with internal combustion en-gines (ICEs), motors have the following remarkable advan-tages (5).• Response of motor torque is much faster than that of in-

ternal combustion engines (over 100 times).•Distributed installation and independent control are easy.•Motor torque can be measured precisely from the cur-

rent.There are some studies on safety and efficiency control forEAs by utilizing these advantages and it is widely recognizedthat EAs will have multiple motors and propellers (6) (7).

1.2 Objective Although nowadays airplanes includ-ing EAs are designed to have higher stability and control-lability, over 60 % accidents of light airplanes were occurredduring approaching and landing (4) (8). Besides, landing weightof EAs is larger than that of a normal airplane, because theweight of battery-powered EAs is not decreased during theflight. Solving this problem is challenging, and current worksfocus on making temporary lift. Some studies control a highlift device as a powered high-lift system (?) (9), and another hasto employ plasma actuators (10). These solutions, however,need extra devices to increase the weight and the response

a) Correspondence to: konishi@hflab.k.u-tokyo.ac.jp∗ The University of Tokyo

5–1–5, Kashiwanoha, Kashiwa, Chiba, Japan, 227–8561∗∗ Institute of Aeronautical Technology Japan Aerospace Explo-

ration Agency6–13–1, Osawa, Chofu, Tokyo, Japan, 181–0015

Fig. 1. Physics of propeller cross section.

of these devices are not fast enough for safety improvement.In order to solve the problem, this paper proposes a verti-

cal velocity control method that uses the propeller slipstream,and the fast response of motors can therefore be utilized. Theproposed method will be verified by simulations and experi-ments.

2. Modeling of Multiple Propellers Electric Air-plane

In this section, the dynamics for an airplane with multiplepropellers is explained.

2.1 Propeller Dynamics (11) Figure 1 shows the crosssection of a propeller blade at distance r from hub. Duringflying, the propeller cross section moves as a compositionof rotation and forward motion. Therefore, the cross sectionmoves as a spiral. Assume the airflow is parallel to the axisof propeller. Airspeed Vx is the relative velocity between theair and airplane. Counter torque R is generated by the bladeof propeller, and R can be resolved into the direction of themotion of the airplane “thrust” F and the direction of pro-peller revolution “counter torque” Q. Assume the air densityis ρ, the propeller whose diameter Dp rotates at the propeller

c© 2015 The Institute of Electrical Engineers of Japan. 1

Vertical Velocity Control of Electric Airplanes (Nobukatsu Konishi et al.)

VxVP

VS

PR

PF

P∞ P∞

Airspeed Slipstream

Pressure

Front Rear

position

Fig. 2. Propeller slipstream diagram.

revolution speed n, and generates the thrust F and the countertorque Q which can be express as

F = CF(J)ρn2Dp4, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (1)

Q = CQ(J)ρn2Dp5, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (2)

where CF is propeller thrust coefficient, and CQ is propellercounter-torque coefficient. Generally, each of them is a func-tion of advance ratio J which is defined as

J =Vx

nDp, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (3)

2.2 Propeller Slipstream When a propeller rotatesand makes thrust, propeller slipstream is amplified with theincrease of airspeed. Figure 2 illustrates the diagram betweenairspeed and propeller slipstream. Vx is airspeed, Vp is windspeed through propeller, and Vs is propeller slipstream. P∞is the pressure outside propeller stream, PF is the pressureof the front face of propeller, and PR is that of the rear face.Eq. (4) is realized from infinite direction ahead to the frontface of the propeller, and Eq. (5) is realized from the reardace of the propeller to infinite direction of back, based onBernoulli’s theorem.

12ρVx

2 + P∞ =12ρVp

2 + PF , · · · · · · · · · · · · · · · · · · · · (4)

12ρVp

2 + PR =12ρVs

2 + P∞. · · · · · · · · · · · · · · · · · · · · (5)

Because thrust is basically the force on a propeller caused bythe pressure difference between front face and rear face of thepropeller, Eq. (6) is obtained as propeller thrust by multiply-ing the disk-area of the propeller and the pressure difference,

F =π

4Dp

2(PR − PF). · · · · · · · · · · · · · · · · · · · · · · · · · · · · (6)

From Eq. (4) ∼ Eq. (6) are reformulated as Eq. (7).

F =π

4Dp

2 ρ

2(Vs

2 − Vx2)

=π

8ρVx

2Dp2

(Vs

Vx

)2

− 1

. · · · · · · · · · · · · · · · · · · · · (7)

By reformulating Eq. 7, slipstream Vs is obtained as

Vs = Vx

√

1 +8π

CF(J)(

nDp

Vx

)2

. · · · · · · · · · · · · · · · · · · · (8)

2.3 Aerodynamic Force of Wing When an airplanehas N propellers, some propellers are on the right wing, andthe others are on the left wing, and the subscript j representsjth propeller. S is wing area, S sj is area which slipstream of apropeller blows against, and S a is area which airspeed blows

J-CQ Function

J-CF Function

Advanced Ratio

1s

Thrust Function

Drag Function

VE

Vwind

+−

+ +−−

Fj

Tj*

Qj

ω j nj

nj

J j

CQj

CFj

njnj

Fj

Propeller Model

Plane Model

Blocks with rounded cornersrepresent non-liner blocks

1Jω js

12π

Counter Torque Function

Sum Propeller Thrust

1M

ax

CQjρnj

2Dpj5

CFjρnj

2Dpj4

12CDρSsVs

2

++

V 1+ 8πCFj

njDpj

V⎛⎝⎜

⎞⎠⎟

2

Slipstream Function

12CLρSsVs

2

Sum Lift

Lj+ +

1s

1M

az Vz

Lift FunctionWing Model

Sum Drag

Fall

Dall

Ds

Db

Ls

Lb

Lj

Dj

Lall

Vsj

Vsj

VsjDj

Vx

Vx

Vx

Vx

j=1

N

∑

j=1

N

∑

j=1

N

∑

VxnDp

Vx

12CDρSaV

2

12CLρSaV

2

−+

Mg

Lall−+

Dz

Fig. 3. Model block of plane with multiple propellers.

against. Wing area can be expressed in short as

S =N∑

j=1

S sj + S a. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (9)

CL is lift coefficient and CD is drag coefficient. Total lift Lallis a summation of lift Lsj by each propeller slipstream and liftLa by airspeed as Eq. (10). In the same way, total drag Dall isa total of drag Dsj by each propeller slipstream and drag Daby airspeed as Eq. (11).

Lall =

N∑

j=1

Lsj + La

=12ρCL

N∑

j=1

S sj Vs2 +

12ρCLS aVx

2, · · · · · · · · · (10)

Dall =

N∑

j=1

Dsj + Da

=12ρCD

N∑

j=1

S sj Vs2 +

12ρCDS aVx

2. · · · · · · · · · (11)

It is assumed that propeller slipstream is not interfered witheach other and the slipstream speed Vsj is spread over theslipstream area S sj .

2.4 Motion Equation of Plane When the airplanewith N propellers moves straight at airspeed V and acceler-ates at ax and az, the equations of plane dynamics on horizon

2

Vertical Velocity Control of Electric Airplanes (Nobukatsu Konishi et al.)

G CP PlantP Controller

Vxn,n

+-

+-+ +

-

Q

T*nFB*

n

Plane

2π Jω sLPF+-

DOB

n*

CFF

CPI

FF Controller

PI Controller

Vx

nFF*

Vz*

Gdif

affine differential

Vz

Vz

Fig. 4. Vertical velocity controller for each propeller.

j=3

j=1 j=2

N=3 propellers airplane image

Fig. 5. Plane with 3 propellers

0.2 0.4 0.6 0.8 1 1.2 1.40

0.05

0.1

0.15

0.2

Advance Ratio [ï]

Prop

elle

r coe

ffici

ent [ï]

measured(CF)quadratic(CF)measured(CQ)quadratic(CQ)

Fig. 6. Propeller characteristics.

axis is expressed as Eq. (12) and the equation on vertical axisis expressed as Eq. (13).

Max = Fall − Dx, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (12)Maz = Lall − Dz − Mg. · · · · · · · · · · · · · · · · · · · · · · · · · (13)

The relationship among airspeed Vx, ground speed VE , and awind speed Vwind is Eq. (14).

Vx = VE − Vwind. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14)

The model of airplane with multiple propellers can be ex-pressed as Fig. 3. In this paper, Vwind is ignored, and Vx isequal to VE .

3. Designing of Vertical Velocity ControlIn this chapter, designing Vertical velocity control by slip-

stream is explained as a proposed method. The controller hasa disturbance observer (DOB) to compensate for propellercounter torque which is regarded as disturbance, a propellerrevolution speed controller CP at the inner loop, and a verticalvelocity controller CPI at the outer loop.

3.1 Designing of Propeller Counter Torque Observerand Revolution Speed Controller In this part, countertorque observer (CTO) and revolution controller are designedin a doted line box on Fig. 4.

The propeller counter torque can be expressed as

Q = T − 2πJωn. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15)

Therefore, if motor torque T and revolution speed n is de-tected, propeller counter torque Q can be estimated with a

Table 1. Parameter in simulation.air density ρ 1.23 kg/m3

gross weight M 0.700 kgwing area S 0.0963 m2

lift coefficient CL 1.01drag coefficient CD 0.149

propeller diameter Dp 254 mmnominal propeller inertia Jω 5.06×10−5 kg ·m

cut-off frequency ωc -200 rad/sproposed revolution controller pole ωn -50.0 rad/s

vertical velocity controller pole ωV -5.0 rad/sreference model pole ωg -50.0 rad/s

affine differential frequency ωdi f -5.00 rad/s

propeller counter torque observer as shown in a doted linebox on Fig. 4. In this paper, it is assumed that the currentcontroller is adequately fast to use motor torque reference T ∗for estimation, By adding the estimated value to the torquecommand, the plant is nominalized as Eq. (16) at frequencyranges below the cut-off frequency ωc of the low pass filterof the CTO.

Pnom =1

2πJωs. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (16)

The revolution speed control is done by proportional con-troller. The gain CP of the controller is decided by placingthe pole at ωn. Here, the plant is assumed to be the nominalplant as shown in Eq. (16).

The transfer function from n∗ to n is expressed as Eq. (17)and is defined Gn.

nn∗=ωn

s + ωn= Gn. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (17)

Therefore, ωn becomes as

ωn =Kp

2πJω. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18)

3.2 Designing of Vertical Velocity Controller Inthis part, the vertical velocity controller is designed. The con-troller is designed as a two-degree-of-freedom controller asshown in Fig. 4. CF can be quadratically approximated usingcoefficients aCF , bCF , and cCF as

CF = aCF J2 + bCF J2 + cCF . · · · · · · · · · · · · · · · · · · · · (19)

From Eq. (10), Dz is considered to be negligibly small, andvertical acceleration az was expressed as

az =L − Mg

M· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (20)

= αVn2 + βVn + γV = g(n), · · · · · · · · · · · · · · · · · · (21)

where

αV =4CLρ

∑Nj=1 S sj cCF Dp

2

πM, · · · · · · · · · · · · · · · · · · · (22)

βV =4CLρ

∑Nj=1 S sj bCF DpVx

πM, · · · · · · · · · · · · · · · · · · (23)

γV =4CLρ

∑Nj=1 S sj aCF Vx

2

πM+

CLρS Vx2

2M− g. · · · · (24)

Feed forward controller CFF is designed as follows. Definefunction f as a function between revolution speed n∗ and az

3

Vertical Velocity Control of Electric Airplanes (Nobukatsu Konishi et al.)

0 2 4 6 8 10−2

−1

0

1

2

Time [s]

Ver

tical

Vel

ocity

[m/s]

CaliculationReference

(a) Vertical velocity.

0 2 4 6 8 106.5

7

7.5

8

8.5

9

Time [s]

Lift

[N]

(b) Lift.

0 2 4 6 8 108

10

12

14

16

18

20

Time [s]

Spee

d [m

/s]

SlipstreamAirspeed

(c) Slipstream & Airspeed

0 2 4 6 8 103000

4000

5000

6000

7000

Time [s]

Prop

elle

r Rev

olut

ion

[rpm

]

(d) Propeller revolution.

Fig. 7. Simulation results of a step vertical velocity reference.

0 5 10 15 20−5

0

5

10

15

20

25

30

Time [s]

Hei

ght [

m]

CaliculationReference

(a) Height.

0 5 10 15 20−2

−1

0

1

2

Time [s]

Ver

tical

Vel

ocity

[m/s]

CaliculationReference

(b) Vertical velocity.

0 5 10 15 206

6.5

7

7.5

8

Time [s]

Lift

[N]

(c) Lift

0 5 10 15 203000

4000

5000

6000

7000

Time [s]

Prop

elle

r Rev

olut

ion

[rpm

]

(d) Propeller revolution.

Fig. 8. Simulation results of a landing situation.

as

az = g(Gn · n∗). · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (25)

Therefore,

n∗ = Gn−1 · g−1(az) =

s + ωn

ωng−1(az) · · · · · · · · · · · · (26)

Eq. (26) is non-proper, so feed forward controller CFF isdesigned using reference model Gg(s) as Eq. (27) and affinedifferential from vertical velocity to vertical acceleration Gdifas Eq. (28).

Gg(s) =ωg

s + ωg· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (27)

Gdif(s) =sωdif

s + ωdif· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (28)

n∗ = g−1(Gdif · Vz) ·Gn−1 ·Gg(s) · · · · · · · · · · · · (29)

Here, ωV is the pole of the reference model. Feed forwardcontroller CFF is a nonlinear variable controller as shown inEq. (29), because g−1(Gdif · Vz) varies by V and is nonlinear.

Next, feedback controller CPI is designed as follows. Feed-back reference Vz

∗ is created by multiplying the referencemodel Gv(s) and the affine differential Gdiv(s) to Vz

∗ asVzFB

∗ = Gg(s) ·Gdif(s)Vz∗. By using Taylor series at feed for-

ward controller CFF output nFF∗, g(n) can be approximated to

its first order as Eq. (30)

az ≈ 2αVn + βV · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (30)

The revolution speed controller is assumed to be fast enoughso n∗ = n. The feedback controller uses the difference of thereference and output, so when βV is regard as a constant, Eq.(31) can be obtained as a transfer function GV from n∗ to Vz.

GV =∆az

∆n∗=∆az

∆n= 2αV · · · · · · · · · · · · · · · · · · · · · · · (31)

The vertical velocity control uses an integral and proportion

the 1st floor

the 2nd floor

15.5 m

1.5 m1.6 m

motor

8 m

(a) Gettingen Wind tunnel diagram. (b) Experimental airplane.

Fig. 9. Wind tunnel overview.

controller, and the gain KPI is designed by placing the pole atωV while the plant is assumed to be GV .

Vz

Vz∗ =

ωV2

(s + ωV )2 . · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (32)

Therefore, the PI controller gains become as

KP =2ωV

2αVnFF + βV· · · · · · · · · · · · · · · · · · · · · · · · · · · · (33)

KI =ωV

2

2αVnFF + βV· · · · · · · · · · · · · · · · · · · · · · · · · · · · (34)

Here, KP and KI are functions of nFF and Vx, so the feedbackcontroller CI is variable.

3.3 Controller Design Concept In this part, con-troller design concept on this paper was explained. Assumethat N = 3 propellers airplane shown in Fig. 5. 2 propellerson wing are controlled by the proposed method. A propelleron head is used for airspeed control to keep airspeed constantby compensating thrust addition of the proposed method fora future work by referring (6).

4. Simulation of Vertical Velocity ControlVertical velocity control method was verified by some sim-

ulations.4.1 Simulation Condition The simulation model

uses the parameters of the APC10×10 E model propeller. TheJ–CF and J–CQ curves are shown in Fig. 6. The parameter

4

Vertical Velocity Control of Electric Airplanes (Nobukatsu Konishi et al.)

Strain gaugeWire

Dleft

Dright

Lleft

Lright

Lrear

45°

45°

Counter weight

CH2

CH1CH3

CH4

CH5

Handle

α

(a) Wire balance measuring method.

−5 0 5 10 15−0.5

0

0.5

1

1.5

Attack angle [deg]Ae

rody

nam

ic c

oeffi

cien

t [−]

CLCD

(b) Model airplane lift and drag coeffi-cient.

Fig. 10. Measuring aerodynamic.

Plant(Experimental

equipment)

L 1Ms

Mg-Dz

+-PC

T* VerticalVelocityController

Vz

Fig. 11. Experimental block diagram.

including the airplane constants and the poles of each con-troller are as listed in Table. 1.

4.2 Vertical Velocity Control Simulation for Step Re-sponse Step response simulation was conducted to thevertical velocity controller. The airspeed was changed by thepropeller thrust, and a step reference was given. When theairspeed Vx was set at Vx = 10 m/s, the simulation startedat a steady state of Vz = −1.0 m/s. At t = 0.0 s, the refer-ence changed from −1.0 m/s to 0.0 m/s. This simulation isregarded as one of the touch down patterns.

The simulation results are shown in Fig. 7. Figure 7(a)shows vertical velocity Vz and Fig. 7(b) shows Lall. At 5.0s,lift is enlarged instantaneously to respond the vertical veloc-ity step reference. The cause of the overshoot in Fig. 7(a)is considered from the feed forward controller and the mo-tor torque limitation. Figure 7(c) shows the airspeed Vx andthe propeller slipstream Vs which is depend on the propellerrevolution in Fig. 7(d).

There is a delay between the vertical velocity and the stepreference because the cause of the overshoot. From the view-point of the safe landing, Vz = 0 m/s command when touch-ing down is not suitable. But the vertical velocity at touchdown is abled to be reduced by the step reference of the pro-posed method, so it will be succeed in safe landing.

4.3 Vertical Velocity Control Simulation for LandingSituation In this part, landing situation was simulated byvertical velocity control. Landing path was decided as Vz = 0when an airplane touched down shown in Fig. 8(a). Verticalvelocity was made a cubic function path from 15 m heightto ground shown in Fig. 8(b). From the simulation results,vertical velocity can be controlled as reference. Figure 8(c)and (d) showed Lift and propeller revolution. Propeller revo-lution was changing depending on velocity reference to gen-erate lift.

Compared to Chapter 4.2, vertical velocity referencechanges gradually, so there is no delay between response andreference. It is accomplished Vz = 0 m/s when touchingdown. This simulation is verified that vertical velocity con-trol is effective for the safe landing.

Table 2. Model airplane parameter.wing area S 0.0963 m2

gross weight M 0.700 kgspan 1.07 m

maximum lift coefficient CL 1.01drag coefficient (when CL is max) CD 0.149

PropellerMotor

Wind gauge Model airplane

Fig. 12. Experimental equipment.

5. Experiment of Vertical Velocity ControlVertical velocity control method was verified by some ex-

periments.5.1 Experimental Setup and Method The experi-

mental units for this research are explained. Located in theaerospace engineering department at the University of Tokyo,one part of the units is a Goettingen type wind tunnel shownin Fig. 9(a) with a 1.5 m diameter of the opening. First, theairplane was supported by wires and the wires kept tensionby counterweights as shown in Fig. 9(b). And then the wireswere connected to strain gages to measure the difference ten-sion as lift and drag. Lift and drag were calculated from Eq.(35) and Eq. (36).

L = Lright + Lleft + Lrear, · · · · · · · · · · · · · · · · · · · · · · · (35)D = Dright + Dleft. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (36)

Lift was occurred to upside of airplane, so the model airplanewas supported to be upside down to keep wires tension. Itis able to change the attack angle of airplane by moving theposition of strain gage CH3.

From the lift information, vertical velocity was calculatedas Eq. 13 and integrator. Vertical drag Dz was calculated as

Dz = D sin(arctan

(Vz

Vx

)). · · · · · · · · · · · · · · · · · · · · · · (37)

In this paper, the vertical velocity was calculated and used forthe feedback controller as Fig. 11 under arctan

(VzVx

)≈ 0

The model airplane specification is Table. 2, and lift coeffi-cient CL and drag coefficient CD were measured as shown inFig. 10(b). Two motors and two propellers are placed abovethe wing whose location is in propeller slipstream in Fig. 12.

5.2 Vertical Velocity Control Experiment for Step Re-sponse In this part, in order to confirm the vertical veloc-ity control proposed method, experiment was carried out insame condition as the simulation. The airspeed was fixed bythe wind tunnel and step reference was given.

When the airspeed Vx was set at Vx = 10 m/s, the experi-ment started at vertical velocity reference Vz = −1.0 m/s. Att = 5.0 s, vertical velocity reference changed to 0.0 m/s insame condition as the simulation.

The results were shown in Fig. 13. Figure 13(a) and Fig.13(b) is the response of vertical velocity and total lift on wingrespectively. At t = 5.0 s, propeller revolution was enlarged

5

Vertical Velocity Control of Electric Airplanes (Nobukatsu Konishi et al.)

0 5 10−2

−1

0

1

2

Time [s]

Ver

tical

Vel

ocity

[m/s]

MeasuredReference

(a) Vertical velocity.

0 5 106

7

8

9

Time [s]

Lift

[N]

(b) Lift.

0 5 108

10

12

14

16

18

20

Time [s]

Spee

d [m

/s]

SlipstreamAirspeed

(c) Slipstream&Airspeed.

0 5 102000

3000

4000

5000

6000

7000

Time [s]

Prop

elle

r Rev

olut

ion

[rpm

]

(d) Propeller revolution.

Fig. 13. Experimental results of step response by vertical velocity control.

0 5 10 15 20

0

10

20

30

Time [s]

Hei

ght [

m]

MeasuredReference

(a) Height.

0 5 10 15 20−2

−1

0

1

2

Time [s]

Ver

tical

Vel

ocity

[m/s]

MeasuredReference

(b) Vertical velocity.

0 5 10 15 206

6.5

7

7.5

8

Time [s]

Lift

[N]

(c) Lift.

0 5 10 15 202000

3000

4000

5000

6000

7000

Time [s]

Prop

elle

r Rev

olut

ion

[rpm

]

(d) Propeller revolution.

Fig. 14. Experimental results of landing by vertical velocity control.

depend on step reference, and the slipstream was increasedin Fig. 13(c). Figure 13(d) is the propeller revolution. Ver-tical velocity response was delay from the reference. Mainreason of the difference is considered that the slipstream wasoccurred with 0.2 s delay from the propeller revolution re-sponse and the motors have torque limitation. In order tokeep velocity and lift, the propeller revolution was changedactively and slipstream was varied depending on the propellerrevolution.

5.3 Vertical Velocity Control Experiment for LandingSituation In order to confirm the safe landing by the pro-posed method, experiments was carried out in same conditionas the simulation. Figure 14 is experimental results. Therewas no delay between the vertical velocity response and thereference in this situation from Fig. 14(a) and (b). Lift andpropeller revolution were same response as the simulation.Propeller revolution was blurred because of lift measuringmethod. From these results, vertical velocity control was ef-fective for the safe landing.

6. ConclusionThis paper aimed at landing safety improvement by con-

trolling motors and propellers. In order to achieve the aim,the propeller slipstream was modeled and then used for thevertical velocity control. The effectiveness of the proposedmethod was verified by simulations and experiments.

The proposed method can improve the response speed andlanding accuracy, compared to the conventional approachingand landing methods like powered lift system and flaring.The proposed method can be a key technology for a landingassist in the future.

Future works are to consider about the airplanes attitudeand disturbance robustness. Moreover, to enhance the per-formance of the proposed method, it is desirable to includeairspeed control by using extra propellers.

AcknowleagementThis research was partly supported by the Ministry of Edu-

cation, Culture, Sports, Science, and Technology grant (BasicResearch A, number: 26249061).

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