Anti swing tracking control for 2D overhead crane using double layer fuzzy logic controllers

In this paper, a simple and efficient technique to control overhead crane based on fuzzy logic inferrence system is proposed. A second order fuzzy logic controller (DLFLC) is proposed to track the desire position, aliminate the payload swing and resist unknown dirturbance exerted on the system.

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ANTI-SWING TRACKING CONTROL FOR 2D OVERHEAD CRANE USING DOUBLE LAYER FUZZY LOGIC CONTROLLERS

Vu ThiThuy Nga1, Le Xuan Hai1,*, Le Viet Anh1, Ta Van Truong1,

Hoang Nghia Hiep1, Ha Thi Kim Duyen2, Phan Xuan Minh1

Abstract: In this paper, a simple and efficient technique to control overhead

crane based on fuzzy logic inferrence system is proposed A second order fuzzy logic controller (DLFLC) is proposed to track the desire position, aliminate the payload swing and resist unknown dirturbance exerted on the system The simulation and experiment results show that the improvement of proposed control

scheme for example smaller swing, improved accuratly position

Keywords: Tracking Control, Payload Anti-swing, Fuzzy Logic Controller (FLC), Overhead Crane, Double

Layer Fuzzy Logic Controller (DLFLC)

1 INTRODUCTION

Overhead cranes are essential load and unload equipment, widely used in many areas such as at construction sites , factories and harbors Modelling of crane belong to a class of underactuated mechanical systems, with one control input (a trolley driving force) and two system variables to be controlled (a trolley position and a load swing angle) That leads to the unexpected swing of payload in operation process Therefore, the control principle of the crane is to move trolley on the desire path and make the payload oscillation smaller as possible Researching on increasing the control quality of crane system is always considered and developed by many researchers Various attempts for control of overhead crane have been proposed For many years, the anti-swing trajectory tracking control methods for cranes mainly included non-linear, adaptive, sliding mode control technique For example, the papers [1] and [2] presented non-linear control laws based on feedback linearization method and Lyapunov stability theory, or in the papers [3] and [4], sliding mode control was used Nevertheless, this control structure is relatively complex, so applied it to microcontroller is not really simple That is the main reason for improving the control design with fuzzy logic system due to its applicability on digital controller

In [5], Benhjdjeb et al constructed a fuzzy logic controller, and it is a effective method

in comparison to other traditional methods presented before That scheme have been

developed in some works [6], [7], [8] Nearly, Wang et al [9] proposed a new control

structure, with double fuzzy controller in order to seperate tracking control task and antiswing control task However, the experimental results are not presented in [9] In [10], [11], adaptive fuzzy controllers are used for overhead crane, output scaling factor of that fuzzy controller is updated according to the process trend by a fuzzy gain modifier The controllers guarantee the good performances for overhead crane despite of system uncertainties However, the swing of the angle still high Some other methods combined fuzzy logic system in some different structures, to enhence the quality of system [12],[13],[14],[15]

In this paper, a double layer fuzzy logic controller (DLFLC) is proposed to solve effectively the problem for overhead crane system This control structure contains three fuzzy logic controllers in two layers, which have a serial connection Two fuzzy controllers belong to the first layer, to solve two separate problems, achieve the expected location of crane and confine the swing of crane as small as possible The second layer has one controller, is designed combining the effectiveness of first layers’s controllers The

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Research

Journal of Military Science and Technology, No 48A, 5 - 2017 69

fuzzy logic system is used with inference rules are chosen by experience expert to make a

ideal control method

This paper is divided into six parts: Introduction, Overhead Crane Dynamic model,

Construction of Double Layer Fuzzy Logic Controller, Simulation Results, Experiment

Results and Conclusion

2 OVERHEAD CRANE DYNAMIC MODEL

Figure 1 shows the schema of a 2D overhead crane, that includes trolley and load The

following notation are defined as: mc, ml , l , u are the weight of trolley, the weight of

load, the length of cable and impact force, respectively Trolley and load are considered

like moving on Oxy plane

Figure 1 Overhead crane model

The dynamic equations are constructed based on Lagrange type II:

*

i

dtq  q   q  

   (1)

Where: Qi* is generalized force, T is kinetic energy,  is potential energy, qi is

generalized coordinate

The kinetic energy and potential energy of the crane system are described by:

2 c l 2 l l

T  m m x  m l m lx  (2)

cos

l

m gl 

   (3)

2

*

x

T

m m x m l x

d T

m m x m l m l

dt x

T

Q u



 

 



 







2

( mc m x m ll)   l  cos   m ll  sin   u

(4)

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accurately Moreover, a number of parameters such as the payload, tension of cable wire also very susceptible to change during operation In such conditions, the fuzzy logic controller has advantage because this control law is constr

not depend on precise knowledge about model

separate task, track the desired path of trolley and d

laws are designed by Takagi

controllers and each solves one problem Ouputs of two controllers in the first layer are the inputs of the second layer This layer ha

interaction between two control tasks to provide the appropriate control signal u for the system The diagram of DLFLC is shown in Figure 2

3.1 Design FLCs for the first layer

variables and one output variable FLC1 with input variables

u1is designed to

e

design, each input variable contains three fuzzy sets with triangular membership functions

From equations (4) and (5), dynamic model of overhead crane is obtained as followed:

From (6), it is noticed that the parameters of model are

In this paper, three fuzzy controllers in two layers are used, in order to achieve two separate task, track the desired path of trolley and d

These two fuzzy controllers (FLC1 and FLC2) have same structure, including two input variables and one output variable FLC1 with input variables

is designed to

e, output variable

is designed to

output variable







is designed to

output variable

From equations (4) and (5), dynamic model of overhead crane is obtained as

(m c m x m l l) l cos m l l sin u

l x  g 





 

is designed to

output variable

d T dt



(m c m x m l l) l cos m l l sin u

l x  g 





  

is designed to achieve the expected location of trolley

output variable

T

d T dt





 

 

 



l x  g 

 

3 DOUBLE LAYER FUZZY LOGIC CONTROLLER

achieve the expected location of trolley output variable

T

m l m lx

d T dt





 

 



 



 From equations (4) and (5), dynamic model of overhead crane is obtained as

l x  g 



achieve the expected location of trolley

output variable u2, decreases

2

m l m lx

d T





 

 



 



l  x  g 

l x  g 



achieve the expected location of trolley , decreases

2

sin ; sin ; 0

m l m lx

d T

m l m lx m lx



 

 

 

 



l    x    g 

Figure

2

sin ; sin ; 0

m l m lx

m l m lx m lx



cos sin

l     x    g 

laws are designed by Takagi-Sugeno fuzzy model [16] The first layer contains two controllers and each solves one problem Ouputs of two controllers in the first layer are the inputs of the second layer This layer ha

Figure

2

cos

sin ; sin ; 0

m l m lx

m l m lx m lx



cos sin

l   x     g 

m m x m l  m l  u

Sugeno fuzzy model [16] The first layer contains two controllers and each solves one problem Ouputs of two controllers in the first layer are the inputs of the second layer This layer ha

Figure

cos

sin ; sin ; 0

m l m lx

m l m lx m lx

T



  

cos sin

l   x     g 

(m c m x m l l) lcos m l l sin u

Figure 2 The diagram of DLFLC

the payload’s swing angle design, each input variable contains three fuzzy sets with triangular membership functions

cos cos sin

sin ; sin ; 0

m l m lx m lx

T

  

cos sin

l   x    g 

2

(m cm x m l l)  lcosm l l sin u

The diagram of DLFLC

cos cos sin

sin ; sin ; 0

m l m lx m lx

  

cos sin

l   x    g 

2

(m m x m l)  cosm l sin u

cos sin

sin ; sin ; 0

m l m lx m lx

  



cos sin

l  x  g 

(m m x m l)  cosm l sin u

cos sin

sin ; sin ; 0

m l m lx m lx

  



cos sin

(m m x m l)  cosm l sin u

Sugeno fuzzy model [16] The first layer contains two controllers and each solves one problem Ouputs of two controllers in the first layer are the inputs of the second layer This layer has only one controller, which combines interaction between two control tasks to provide the appropriate control signal u for the system The diagram of DLFLC is shown in Figure 2

cos sin

sin ; sin ; 0

m l m lx m lx

  



m m x m l m l u

In this paper, three fuzzy controllers in two layers are used, in order to achieve two separate task, track the desired path of trolley and decrease the swing of payload Control

Sugeno fuzzy model [16] The first layer contains two controllers and each solves one problem Ouputs of two controllers in the first layer are

s only one controller, which combines interaction between two control tasks to provide the appropriate control signal u for the system The diagram of DLFLC is shown in Figure 2

cos sin

sin ; sin ; 0

m l m lx m lx

  

In this paper, three fuzzy controllers in two layers are used, in order to achieve two

ecrease the swing of payload Control Sugeno fuzzy model [16] The first layer contains two controllers and each solves one problem Ouputs of two controllers in the first layer are

s only one controller, which combines interaction between two control tasks to provide the appropriate control signal u for the

*

cos sin

sin ; sin ; 0

accurately Moreover, a number of parameters such as the payload, tension of cable wire also very susceptible to change during operation In such conditions, the fuzzy logic controller has advantage because this control law is constructed based on experience and

FLC2 with input variables the payload’s swing angle

sin ; sin ; 0

accurately Moreover, a number of parameters such as the payload, tension of cable wire also very susceptible to change during operation In such conditions, the fuzzy logic

ucted based on experience and

The diagram of DLFLC

FLC2 with input variables the payload’s swing angle

sin ; sin ; 0

accurately Moreover, a number of parameters such as the payload, tension of cable wire also very susceptible to change during operation In such conditions, the fuzzy logic

These two fuzzy controllers (FLC1 and FLC2) have same structure, including two input variables and one output variable FLC1 with input variables e x

FLC2 with input variables the payload’s swing angle In order to simplify the design, each input variable contains three fuzzy sets with triangular membership functions

From (6), it is noticed that the parameters of model are difficult to determine accurately Moreover, a number of parameters such as the payload, tension of cable wire also very susceptible to change during operation In such conditions, the fuzzy logic

These two fuzzy controllers (FLC1 and FLC2) have same structure, including two input

x

e and

FLC2 with input variables

In order to simplify the design, each input variable contains three fuzzy sets with triangular membership functions

difficult to determine accurately Moreover, a number of parameters such as the payload, tension of cable wire also very susceptible to change during operation In such conditions, the fuzzy logic

e and e

FLC2 with input variables

x

e, FLC2 with input variables

x

e output variabl FLC2 with input variables

output variabl FLC2 with input variables

output variabl

FLC2 with input variables eand

(5) From equations (4) and (5), dynamic model of overhead crane is obtained as

(6)

output variable

eand

(5)

(6)

e and

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(A k1 =NS, A k2 =ZE, A k3 =PS; k=1,2), and the basic domain is [-1, +1] Output variable

contains five constants (c1 c2 c3 c4 c5) = (-2, -1, 0, 1, 2), the basic domain is [-2,+2] The

establishment of the input of the triangular membership function is shown in Figure 3 The

IF-THEN rules of the fuzzy controllers are designed as shown in Table 1

Figure 3 The membership function of input variables

Table 1 The IF-THEN rules

1

u

( )

x

e e

NS ZE PS

(e )

x

e 

PS 0 1 2

ZE -1 0 1

NS -2 -1 0

The output signal u i (i=1,2) is determined as the formula of Takagi-Sugeno [14]

9

1

i i i

i i

h c u

h





(7)

Where:

1 ( ) 2 ( )

h  e  e

  ;i 1, 2, 9; (8)

Here, je x(je x) 1, 2,3 is the index of fuzzy sets

9

1

i i i

i i

h c u

h





(9)

1 ( ) 2 ( )

   



  ;i 1, 2, 9; (10)

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Here, je(je)1, 2,3is the index of fuzzy sets

3.2 Design FLC for the second layer

The second layer has one FLC with two input variables u1andu2, output variable is

control signal u Each input variable includes five fuzzy sets (A k1 =NM, A k2 =NS, A k3 =ZE,

A k4 =PS, A k5 =PM; k=1,2) with the basic domain is [-2,+2] The establishment of the input

of the triangular membership function is shown in Figure 4 The constants for output’s

variable is chosen by (c1 c2 c3 c4 c5 c6 c7 c8 c9) =(-4 -3 -2 -1 0 1 2 3 4) and the basic domain

is [100,+100] The IF-THEN rules of the fuzzy controllers are shown in Tab 2

Figure 4 The membership function of input variable

Table 2 The IF-THEN rules

u

1

u

NM NS ZE PS PM

2

u

PM 0 1 2 3 4

PS -1 0 1 2 3

ZE -2 -1 0 1 2

NS -3 -2 -1 0 1

NM -4 -3 -2 -1 0

The control signal u is determined as the formula of Takagi-Sugeno [14]

25

1 25

1

i i i

i i

h c u

h





(11)

Where:

1 1(u ).1 2 2(u )2

Here, ju ju1( 2)1, 2,3, 4,5is the index of fuzzy sets

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4 SIMULATION RESULTS

To verify the performances of the proposed proposed control structure the simulation is done for overhead crane systemwith the following parameters:

Table 3 The parameters of overhead crane system

Specification Value Trolley mass (m c) 20 (kg) Payload mass (m l) 5 (kg) Cable length (l) 1 (m) Gravitational (g) 9.81 (

2

/

m s )

4.1 Simulation without disturbance affect

Simulations are executed with Matlab-Simulink software The simulation results are shown in Figure 5 Figure 5a performances displacement trolley, Figure 5b performances tracking error, Figure 5c, 5d show the sway angle of payload and control signal, respectively From the simulation results, it can be seen that the trolley arrived at the desired position in nearly 6 seconds, and swing angle is less than 0.1 (rad)

Figure 5 Simulation results without disturbance effect

4.2 Simulation with disturbance affect

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The disturbance is added from 1(s) to 1.1(s) The position of trolley, tracking error, control signal and swing angle are shown in Figure 6a, 6b, 6c, 6d, respectively In this case, the proposed controller stills ensuring the quality of system, with trajectory tracking and reduction of load swing angle Hence, using the DLFLC for crane system is better to reduce disturbance

Figure 6 Simulation results with disturbance effect

5 EXPERIMENTAL RESULTS

Based on the simulation result, experimentation is setup to identify the effectiveness of the proposed controller The hardware system is structured based on the system presented

in [17] The controller is programed on Atmega32 microcontroller chip, communicates with computer via port RS232, human machine interface is designed by C# Window Form and sampling time is 25 miliseconds

Figure 7 descibes the overhead crane model in laboratory.In which, the system

comprises a cart of mass mc moving on a rail of mass ml.Below the trolley is a winch

which yields a force u to tune the length l of the suspended rope Furthermore, the system

includes 3 three-phase asynchronous motors connected with the inverter and encoder; this makes the whole system similar to that in industry The three-phase deceleration motor with a breaking system is controlled by the inverter OMRON 3G3JX due to its compact size and easy use This inverter is simple but satisfies the requirement The incremental optical encoder used in the experiment is Rotary Encoder E40S6-1024-3-T-24 with voltage of 12V DC – 24V DC

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Research

Journal of

desired position is 1m Experiment results show the applicability of the proposed controller in the real time system The overhead crane arrived at the expected position in ne

it decreases to 0

layer fuzzy logic controller Not only have simpl

Research

Journal of

Figure 8

desired position is 1m Experiment results show the applicability of the proposed controller in the real time system The overhead crane arrived at the expected position in nearly 20 seconds and the angle of the load is less than 0.1 degrees in absolute value, and

it decreases to 0

This paper presented a control scheme for 2

Research

Journal of

Figure 8

desired position is 1m Experiment results show the applicability of the proposed controller in the real time system The overhead crane arrived at the expected position in arly 20 seconds and the angle of the load is less than 0.1 degrees in absolute value, and

it decreases to 0

Research

Journal of Military

Figure 8

it decreases to 0

Military

Figure 8 includes the position of trolley control signal and swing angle of payload with

it decreases to 0

Military

includes the position of trolley control signal and swing angle of payload with desired position is 1m Experiment results show the applicability of the proposed controller in the real time system The overhead crane arrived at the expected position in arly 20 seconds and the angle of the load is less than 0.1 degrees in absolute value, and

it decreases to 0

Military Science and Technology, No

Science and Technology, No

Figure

Figure 7

7 The 3D overhead crane in laboratory

Figure 8.

The 3D overhead crane in laboratory

Figure 8.

5 CONCLUSION

Figure 8 Experiment

5 CONCLUSION

Experiment

5 CONCLUSION

Science and Technology, No 48A

Experiment

5 CONCLUSION

This paper presented a control scheme for

2-layer fuzzy logic controller Not only have simpl

48A,

Experiment

5 CONCLUSION

-D overhead crane system by using double layer fuzzy logic controller Not only have simple structure, easy to be installed in digital

5 -

Experimental

5 CONCLUSION

D overhead crane system by using double

e structure, easy to be installed in digital

2017

result

5 CONCLUSION

2017

results

s

The 3D overhead crane in laboratory.

75

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technology, the presented controller also doesn’t require accurately knowledge about system Both simulation and experiment results show that the controller is effective to move the trolley with lower payload oscillation and perfectly capable of using in industry applications

ACKNOWLEDGEMENT: This research is funded by the Hanoi University of

Science and Technology (HUST) under project number T2016-PC- 107

REFERENCES

[1] J Yu, F.L Lewis, T Huang, “Nonlinear feedback control of a gantry crane”,

American Control Conference, Proceedings of the 1995, Jun 1995

[2] Park H., Chwa D and Hong K S.,“A feedback linearization control of container cranes: Varying rope length”, Int J Control Autom Syst 5 (4), pp 379 – 387, Aug

2007

[3] W Wang, J Q Yi, D B Zhao, D T Liu,“Anti-swing control of overhead cranes based on sliding-mode method”, Control theory and Applications, pp1013-1016,

Sep.2004

[4] H Lee, Y Liang, and D Segura, “A sliding-mode antiswing trajectory control for overhead cranes with high-speed load hoisting”, Trans ASME, J Dyn Syst Meas

Control, vol 128, no 4, pp 842–845, Dec 2006

[5] Benhidjeb A, Gissinger GL, “Fuzzy control of an overhead crane performance

comparison with classic control”, Control EngPract,pg 1687-1696, Volume 3, Issue

12, Dec 1995

[6] M Mahfouf, C H Kee, M F Abbod and D A Linkens, “Fuzzy Logic Based Anti-Sway Control Design for Overhead Cranes”, Neural Computing &Applications,

Volume 9, Issue 1, pp 38–43, May 2000

[7] Nalley Michael J., Trabia Mohamed B., “Control of overhead cranes using a fuzzy logic controller“, Journal of Intelligent and Fuzzy Systems, vol 8, no 1, pp 1-18,

2000

[8] Cheng-Yuan Chang, “Adaptive Fuzzy Controller of the Overhead Cranes With

Nonlinear Disturbance”, IEEE Transactions on Industrial Informatics, pg 164 - 172,

May 2007

[9] Lifu Wang, Hongbo Zhang, Zhi Kong, “Anti-swing Control of Overhead Crane Based on Double Fuzzy Controllers”, The 27th Chinese Control and Decision

Conference , pp 981 – 986, May 2015

[10] A K Pal, R K Mudi, “An Adaptive Fuzzy Controller for Overhead Crane”, IEEE

International Conference on Advanced Communication Control and Computing Technologies (ICACCCT), Aug 2012

[11] Cheng-Yuan Chang, “Adaptive Fuzzy Controller of the Overhead Cranes With

Nonlinear Disturbance”, IEEE Transactions on Industrial Informatics, vol 3, no 2,

pp 164-172, May 2007

[12] Leila Ranjbari, Amir H Shirdel, M Aslahi-Shahri, S Anbari, A Ebrahimi, M

Darvishi, M Alizadeh, RasoulRahmani, M Seyedmahmoudian, “Designing precision fuzzy controller for load swing of an overhead crane”, Neural Comput&Applic,

Volume 26, Issue 7, pp 1555–1560, Oct 2015

[13] Liu D, Yi J, Zhao D, Wang W,“Adaptive sliding mode fuzzy control for a two-dimensional overhead crane”, Mechatronics 15(5):505–522, Mar 2005

[14] M S Park, D Chwa, and S.K Hong, “Antisway tracking control of overhead cranes with system uncertainty and actuator nonlinearity using an adaptive fuzzy

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sliding-Research

mode control”, IEEE Trans Ind Electron., vol 55, no 11, pp 1677–1684, Nov

2008

[15] X Li, W Yu, “Anti-Swing Control For An Overhead Crane With Fuzzy

Compensation”, Intelligent Automation & Soft Computing, pp.1-11, Mar 2013 [16] Tomohiro Takagi, MichioSugeno,“Fuzzy identification of systems and its

applications to modeling and control”, IEEE Transactions on Systems, Man, and

Cybernetics, Volume: SMC-15, Issue: 1, pp 116 - 132, Sep 1985

“Implementation of a laboratory overhead crane control”, Journal of military

scientific research and technology, No14, Aug 2016

TÓM TẮT

ĐIỀU KHIỂN BÁM QUỸ ĐẠO VÀ CHỐNG RUNG LẮC CHO CẦN CẨU TREO 2D

BẰNG BỘ ĐIỀU KHIỂN MỜ HAI LỚP

Bài báo đề xuất một phương pháp điều khiển mới đơn giản và hiệu quả cho cần cẩu treodựa trên cơ sở hệ logic mờ Một bộ điều khiển mờ hai lớp được đề xuất nhằm đảm bảo bám vị trí đặt của xe,đồng thời giảm thiểu rung lắc cho tải và khắc phục được nhiễu tác động vào hệ thống Kết quả mô phỏng và thực nghiệm đều cho thấy hiệu quả bộ điều khiển được đề xuất, xe đẩy bám vị trí đặt nhanh và giảm góc lắc của tải ngay cả khi có nhiễu tác động

Từ khóa: Position Control, Payload Anti-swing, Fuzzy Logic Controller (FLC), Overhead Crane, Double

layer Fuzzy Logic Controller (DLFLC)

Author affiliations:

1

Department of Automatic Control, Hanoi University of Science and Technology;

2

Department of Electronics, Hanoi University of Industry ;

*Correspondingauthor: xhaicuwc.edu.vn@gmail.com

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