Artificial Intelligence Applied into Pneumatic Flexible Manipulator

Juan-Manuel Ramos-Arreguin1, Jesus Carlos Pedraza Ortega2, Efren Gorrostieta3 and Rene de Jesus Romero-Troncoso4

1 Universidad Tecnológica de San Juan del Río; jramos@mecamex.net

2 Universidad Autónoma de Querétaro, Facultad de Informática; e-mail: efren.hurtado@usa.net 3 Facultad de Ingeniería Mecánica, Eléctrica y Electrónica; e-mail:

troncoso@salamanca.ugto.mx 5 Universidad Autónoma de Querétaro, Facultad de Informática; e-mail:caryoko@yahoo.com

Abstract

Several researches with flexible manipulator robot had been developed using an electrical actuator while other research works deal with pneumatic control, but both investigation lines had been used in separate way. Our goal is simulate the control position angle for the flexible arm, limited to one degree of freedom. We propose an interaction between the pneumatic control and the flexible manipulator robot, being this, the original part of the present work. In this proposal, a speed feedback is used for control position, taken from the pneumatic actuator displacement. We use a fuzzy logic algorithm to adjust the control values, getting a fuzzy algorithm with better results than classic control PID. The project is focused to the engineering application in pneumatic control and flexible manipulators. Result shows a soft movement behavior when speed feedback is used, combined with fuzzy logic, let us to get better results than the classic control approach. Keywords: Fuzzy control, PID, flexible manipulator, adaptive process, pneumatic actuator. 1. Introduction

In principle, a flexible manipulator robot with pneumatic actuator is light, cheap, and has the advantage to handle a higher power-weight, with respect to robots with electric actuators [1]. The modeling of the flexible manipulators has been made for almost 35 years [2] [3], where almost all the works use electrical or hydraulic actuators, and those of pneumatic type are less used due to their non linear nature. Later, an analytical method was used to

examine the performance of a flexible manipulator, using a high-torque stepper motor. Then, a modeling and control was developed for a two-link flexible robot arm [4], without actuator, just simulation. Moreover, a position control was developed using fuzzy neuronal algorithm [5]. Also, a robust control was developed for one-link flexible robot [6], where the actuator is a DC motor and a non linear control was developed using a motor shaft [7]. Finally, an artificial intelligent control was implemented in a single-link flexible robot arm, driven by a permanent magnet (PM) synchronous servo motor [4]. Along this research line, a Thermo-mechanical model has been developed and a dynamic model analysis was developed [9], but these works are not considering a pneumatic control for an actuator applied in a flexible manipulator robot, and this work is focused in it.

Based on this type of works, a flexible manipulator with pneumatic actuator was developed, where a mechanical system and pneumatic behavior are involved, to give a flexible arm movement [9], which leads to the Thermo-Mechanical model. From the point of view of the control engineering, this model allows to predict the behavior of different variables that take part in the physical process to control. 2. Thermo-mechanical model

Figure 1(a) shows a diagram of the pneumatic actuator, where X , X� , X�� are the position of the piston actuator, the speed and the acceleration of the piston rod with respect to the cylinder, respectively; additionally we have the internal pressures Pa1, Pc1, Pc2 and Pa2, that appear at the left side pad of the cylinder, in the chamber of the piston at the left side of the rod, the chamber at the right side rod, and at the

2008 Seventh Mexican International Conference on Artificial Intelligence

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DOI 10.1109/MICAI.2008.76

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pad of right side of the cylinder, respectively; the actuator force Fa; A1, A2 and A3 are the free air flow area of the valves at the left side of the cylinder, at the right side of the cylinder and the air return; a 5/2 valve is used. Although the model needs the three valves, and we use only two, considering the valves A1 and A2 with the same value, due to the fact that when the rod comes down, the valve enabled is A2 and when it goes up, A1 is enabled, therefore the used configuration is like the one shown on figure 1(b).

L alvL alp

LX, X , X

m c1

p a1

p c1 p c2

m c2

pa2 F a

m a1 m a2

A1 A2A3

5/2 Valve

(a)

A1 A3

5/2Electro-

Valve

(b)

Figure 1. Diagram of a pneumatic piston with damping on both sides. (a) The three valves needed for the mathematical model. (b) Using only two valves for simulation and practice process, where A1 = A2.

The set of equations (1) shows the Thermo-

Mechanical model, which describes the dynamics of the pneumatic actuator. The model calculates the changes of the internal pressures of the cylinder; Pa1, Pa2, Pc1 and Pc2, depending of the cylinder’s rod position. Due to the effects generated by the damping pads at the ends of the cylinder, it is necessary to divide the Thermo-Mechanical model in three intervals; pad of the piston side (0 � X < Lalp), middle (Lalp � X < L - Lalv), and the pad of the piston rod side (L - Lalv � X � L), as observed in the equation set (1).

For the interval 0 � X � L:

Xdtd

X �� (1a)

Xdt

dXD 2

2

�� (1b)

For the interval 0 � X � Lalp:

��

���

���

���

� ��

� DXPRT

Amm

A

AXA

kRTP a

apca

ap

pap

a 10

110

1 ��� (1c)

� �� �

��

���

� DXP

RT

AAm

XAAkRT

P capp

capp

c 10

10

1 �� (1d)

For the interval Lalp < X � L:

� � ��

���

��� DXP

RT

Am

XA

kRTP a

pa

pa 1

01

01 �� (1e)

� � ��

���

��� DXP

RT

Am

XA

kRTP c

pc

pc 1

01

01 �� (1f)

For the interval 0 � X < (L – Lalv):

� �� �� �

��

���

�

��� DXP

RT

AAm

XLAAkRT

P cvp

cvp

c 20

20

2 �� (1g)

� �� �

� ���

���

�

��� DXP

RT

AAm

XLAAkRT

P avp

avp

a 20

20

2 �� (1h)

For the interval (L – Lalv) � X � L:

� �� �� �

��

���

�

� DXP

RT

AAm

XLAAkRT

P cvp

cvp

c 20

20

2 �� (1i)

��

���

�

�

��

0

22202 RT

DXPAAmm

AA

AXL

kRTP a

vav

ca

vav

pa

��� (1j)

Where Ap, Av, Aav and Aap, are the free air flow area

from the outside inwards of the cylinder’s left side, from the outside inwards of the right side of the cylinder, at the left pad, and at the right pad of the cylinder, respectively.

3. Fuzzy control system

On figure 3, the block diagram of the control proposal is shown. In this diagram a PID control is involved by using a feedback, where an adjustment is carried out on the control parameters. The details will be explained in next section. As we can observe on figure 3, �p is the set point, � is the current position, u is the vector of control variables formed by the free air flow on the valves, as shown in the equation (2). Also, e is the position error in the output angle of the

340

mechanism at the time Tk, and it includes the proportional error ep, integral error ei, and derivative error ed, as observed in the equations (3) to (5), then �V is the speed difference at two intervals of time defined in the equation (6), and finally K is the set of control values for the PID controller (7).

u(k )TPlant

F uzzy sets Rule-base

Fuzzy P rocess

e(k )Tsp(k )T

+

-

�(k )TC ontrolle rX

Kv�V

K

K , K , K3 v p

Actuator+

+

Figure 3. Diagram to blocks of the fuzzy control for the

Thermo-Mechanical model.

� �321 ,, AAAu � (2)

Where A1, A2 and A3, are the areas of the external valves, used by the controller, as shown in the figure 1(a). The valve A3 is the pressure input, and the valves A1 and A2 are the air return to the atmosphere. In the next section we will talk more about it.

�� � pkp Te )( (3)

)()()()( 21 ��� kkkki TeTeTeTe (4)

)()( 1� kkd TeTee (5)

)()( 1�� kk TVTVV (6)

]K,,,[ vidp KKKK � (7)

The K vector represents the fuzzy adaptation process for the proportionality, derivative, integral and speed constants, obtained by a fuzzy logic algorithm to improve the behavior of the system. In this control scheme, the feedback of the speed changes is important, due to the fact that a better behavior at the plant output was obtained; avoiding abrupt changes in the displacement speed generated by the pneumatic actuator, as well as the angular speed behavior of the plant, and therefore a vibration problem in the system is avoided. The control equation that defines the air free flow area is defined in the equation (8).

)()(

)()()( 0

kvkddj

kiijkppjjkj

TVKTeK

TeKTeKATA

��

���� (8)

Where Tk represents the sample time, considered of

50 ms; j represents the valve which is controlled; Kp, Kd, and Ki, are the constants of the law of the PID

control, and Kv is the speed change constant. The K vector values are obtained using a fuzzy logic algorithm, which will be explained in the next section.

4. Fuzzy control algorithm

Due to the fact that a combination of high non linearity of the pneumatic system and the thermo-mechanical model complexity, a single rule set can not be used. When the rod goes up, it has a particular behavior, but when it goes down a different behavior (hysteresis) occurs, very close to one of the cylinder sides where a damping effect is present. Therefore, the use an individual fuzzy set for each control parameter and different set of rules is necessary. In this section we talk about how we get the fuzzy sets to the flexible manipulator control and the application in the equation (8).

The fuzzy process considers several inputs signals: like the error (ep), the set point (�p), and the output angle (�). The outputs are the Kp, Ki, Kd and Kv signals applied to the control equation (8). As starting point, a system characterization is performed in a hand-tuning way, to get an idea about the intervals we need to use, and later the intervals were modified to get an improved performance. We are using the direct Mamdani method (Kazuo, 1997), and the defuzzification method is the centroid. To perform the control evaluation, we are using the MATLAB software with the Fuzzy Logic Toolbox, and we use the thermo-mechanical model as the plant.

To find the fuzzy sets needed to control the system, first we consider Kv, K3, Ki and Kd equal to zero, and only apply the fuzzy process to Kp. Once we get a good response, a fuzzy process is applied to Ki, later to Kd, Kv, and finally to K3. Next, we must do a few changes in order to obtain a better system behavior. Now, we explain the fuzzy sets and rules applied to each control parameter. 4.1. The Kp parameter

The fuzzy process for Kp needs three inputs and one output, as shown in figure 4. The fuzzy sets for all inputs and outputs use a triangular shape membership functions for each class. The classes for the input theta are extreme, low and positive. The classes for the input error are; negative big, negative half, negative small, zero, positive small, positive half and positive big. The classes for the input set point are; set point 1, and set point 2. The classes for the output are; small, half, big and very big. This parameter defines the system speed. The complete fuzzy rules set are shown in table 1.

341

Figure 4. Fuzzy sets for Kp control constant.

Table 1. Rules used for Kp.

Rule 1 If e is NSmall then Kp is Big Rule 2 If �p is SP1 then Kp is Big

If � is not Extreme and e is Zero then Kp is Small

Rule 4 If � is not Positive and e is PSmall then Kp is Small

Rule 5 If � is not Positive and e is PHalf then Kp is VBig

Rule 6 If � is not Positive and e is PBig then Kp is Big

Rule 7 If � is Positive and e is PSmall then Kp is Big

4.2. The Kv parameter

The fuzzy process for Kv has the same inputs than parameter Kp, as show in figure 5, using triangular membership functions for each class. The classes for the theta input are; low and high. The classes for the input error are; negative and positive. The classes for the input set point are; negative 5, negative 4, negative 3, negative 2, negative 1 and positive. The classes for the output are; zero, very small, small, half, regular and high. The Kv parameter helps us to avoid an abrupt change of the speed in the system movement. The complete set of fuzzy rules are shown in table 2. 4.3. The K3 parameter

The fuzzy process for K3 needs only one input and one output, use triangular membership functions for each class as shown in figure 6. The classes for the input set point are; very down, negative down, regular down, down and up. The classes for the output are; very few, few, half, high, very high and all. This parameter helps to control the flow air input of the system, and due to this effect, it is important to

minimize the overshoot at the output variable, �. Then, the fuzzy rules are shown in table 3.

Figure 5. Fuzzy sets for Kv control constant.

Table 2. Rules used for Kv.

Rule 1

If � is Low or e is Negative and �p is Positive then Kv is Small

Rule 2

If � is High and e is Positive and �p is Neg1 then Kv is Regular

Rule 3

If � is High and e is Positive and �p is Neg2 then Kv is Half

Rule 4

If � is High and e is Positive and �p is Neg3 then Kv is VSmall

Rule 5

If � is High and e is Positive and �p is Neg4 then Kv is Half

Rule 6

If � is High and e is Positive and �p is Neg5 then Kv is High

Fig. 6: Fuzzy sets for K3 control constant.

Table 3. Rules used on Fuzzy2.

Rule 1 If �p is Up then K3 is All Rule 2 If �p is Down then K3 is VHigh Rule 3 If �p is RDown then K3 is Half Rule 4 If �p is NDown then K3 is Few Rule 5 If �p is VDown then K3 is VFew

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4.4. The Kd and Ki parameters

The optimal value of those parameters happens to be zero. To obtain this optimal value, the control parameters Kd and Ki are not used in control equation (8). We conclude it by hand-tuning method applied to the simulation process. 4.5. The final control equation

The equation (9) shows the final control equation. The values of the valves represent a percentage of the aperture, where 0 means totally closed and 1 is totally open. The valve A2 is equal to the A1, because in practice it is the same valve, but the mathematical model needs the three values. The value of A3 depends of A1, we only need to control the air return of the system, to get a better behavior; this valve is important to stop the piston displacement when the arm is close to the set point.

)()()()(

)()()(

133

12

101

kk

kk

kvkppk

TAKTA

TATA

TVKTeKATA

��

���� (9)

4.6. Experimental description

The figure 7 shows the flexible manipulator prototype simulation with pneumatic actuator, where the arm is made of PVC material. Remember that on figure 1 we have a scheme that shows the air flow in both directions, and the air return is controlled by two independent proportional valves. Then, these valves are used to avoid that some of the cameras remains without pressure, generating a braking effect to the advance of the piston. 5. Results

Due to the high non-linearity of the system, the hand-tuning method is used to set the member ship intervals used in the fuzzy process for each input and output. First, the integral, derivative and speed parameter (Ki, Kd and Kv), are setting 0, and K3 is equal to 1. The Kp value start in 0.1 and is increased until an oscillation is present. As second step, K3 is decreased until the output has a behavior without an oscillation. The third step is to adjust the Kv to avoid the vibration problem on the system, getting a behavior without a fast speed changes. This procedure is used with different set points to test all interval of � for the

arm. The K3 value is important because is the pneumatic brake for the system and depends of the reference, in other words, the major problem to control the system, is when the reference is negative, due to the gravity and the mechanical characteristics, as much negative is the reference, K3 is close to zero. The Error input is used to know if the arm goes up or goes down. The Ki and Kp are not necessary to get a nice system behavior.

Figure 7. Flexible manipulator robot prototype with

pneumatic actuator.

The reference values used to test the control are: 60º, 12º, -72º, 25º and 79º. The results are shown in figure 9, including a comparison of results between classic control and fuzzy control. In the figure 9 (a), we can see the rod movement. The system needs 1.9 seconds to go from 0 m to the 63.2% of 0.02 m, with a slope of 0.5263 seg-1. The response arrives to the 98% of the final value in 5 seconds. The figure 9 (b) shows the angle of the flexible arm, also by observation we can see that when the angle � is greater than 0, the system has a different behavior when � is smaller than 0. When � is greater than 0, the system needs 5 seconds to arrive at 98% of set point, when is going down and 2 seconds when it goes up. When � is smaller than 0, the systems needs 6 seconds to get a 98% of set point going in down direction, and 3 seconds in up direction. The figure 9(c) is a comparison between the PID control and fuzzy control response. The figure 9(c) shows a better control behavior when the fuzzy algorithm is used than the PID control algorithm, especially when the set point is close to -80º. At this point, the rod position is close to 0.1 m, and the rod is close to the damping area, and it must support the inertial forces generated by the mechanism weight.

343

0 10 20 30 40 50 60 70 80 90 1000

0.02

0.04

0.06

0.08

0.1

0.12Rod position relative to the cylinder

x [m

]

t [s]

ReferenceResult of control

(a)

0 10 20 30 40 50 60 70 80 90 100-80

-60

-40

-20

0

20

40

60

80

100Flexible Manipulator Arm Angle

Thet

a [º

]

t [s]

ReferenceResult of control

(b)

0 10 20 30 40 50 60 70 80 90 1000

0.02

0.04

0.06

0.08

0.1

0.12Rod position relative to the cylinder

x [m

]

t [s]

Without FuzzyWith Fuzzy

(c)

Figure 9. Control results of the flexible manipulator robot and comparison between fuzzy control and PID control. (a)

Rod displacement; (b) Output angle behavior, �; (c) Comparison between a PID control and Fuzzy control.

By trying to use the Kd and Ki parameters, a small

oscillation is present in the system, as shown in figure 10. For that, we are not using these parameters.

0 10 20 30 40 50 60 70 80 90 1000

0.02

0.04

0.06

0.08

0.1

0.12Rod position relative to the cylinder

x [m

]

t [s]

ReferenceResult of control

0 10 20 30 40 50 60 70 80 90 100-80

-60

-40

-20

0

20

40

60

80

100Flexible Manipulator Arm Angle

Thet

a [º

]

t [s]

ReferenceResult of control

Figure 10. System behavior when Ki and Kd are used.

6. CONCLUSIONS

The novelty of this work is in the establishment of the connection between the pneumatic control and flexible manipulating robots lines, when applying a pneumatic actuator as an element of force generation for its movement, instead of an actuator of electrical type. Taking the advantage of being a light and clean manipulator with a greater relation force-weight.

A control alternative is proposed, by means of an adaptive fuzzy system, making an adjustment to the control parameters, where the feedback of the speed differences remarkably improves the response of the system output. The feedback of the speed difference is a good option, when it works with nonlinear systems, and its speed behavior has too many variations that can cause vibrations in the final effector. If a classical PID control is used, to get a good behavior, the space work’s arm must be divided in several intervals, with different constant values, and movement direction is important, as shows in simulation Juan et al. (2006). For it, the PID control comes to be complex, and a Fuzzy control is easier to do an adjustment and a better result is obtained.

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Other reported techniques use systems with pneumatic servomechanisms to generate the movement, for example the proportional valves, nevertheless, they do not consider the rest of the system in the aspect of dynamics [11]. In this case, a complete system is considered, that is, a pneumatic actuator and the structure have been included in the Thermo-mechanical model of a manipulator with one degree of freedom, to obtain a position controller of the flexible arm.

This approach is successful to control the position angle of the flexible arm, having as result a smooth movement, besides to have started an interaction between the work of pneumatic control and flexible manipulator lines.

7. References [1] A.B. Smith, C.D. Jones, and E.F. Roberts, “Article Title”, Journal, Publisher, Location, Date, pp. 1-10. [2] Jones, C.D., A.B. Smith, and E.F. Roberts, Book Title, Publisher, Location, Date. [1] M. Constantinos. “Development of Advanced Actuators Using Shape Memory Allows and Electrorheological Fluids”, Research in Nondestructive Evaluation, Springer New york ISSN 0934-9847, 14, 1-32. 2002. [2] John M., “Automatic Feedback Control of a Vibrating Flexible Beam”. MS Thesis, Department of Mechanical Engineering, Massachussets Institute of Technology, 1972 [3] Book W.J., Daniel W.E., Paul L.M., “Design and Control Considerations for Industrial and Space Manipulators”, Proceedings of the Joint Automatic Control Conference, Austin, TX, 591-598, 1974

[4] Xuru D., Tzyh J.T., Antal K.B., “A Novel Approach to the Modeling and Control of Flexible Robot Arms”, 1988 [5] Yeon G.C., Han H.T., Chang G.K., “The Study on Position Control of a Flexible Robot Manipulator using Fuzzy Neural Networks”, Third International Conference on Knowledge-Based Intelligent Information Engineering Systems, Adelaide, Australia, 226-229, 1999. [6] Panu, C., David B., “A Case Study of Robust Control Experiment on One-link Flexible Robot Arm”, Proceedings of the 38th Conference on Decision and Control, Phoenix, Arizona USA, 4319-4324, 1999. [7] Hisseine D., Lohmann B., “Nonlinear Tracking Control for a Lightweight Flexible Robot”, IEEE International Conference on Systems, Man, and Cybernetics, Nashville, TN, USA, 5, 3360-3365, 2000. [8] Rong J.W., Meng C.L., “Intelligent Optimal Control of Single-Link Flexible Robot Arm”, IEEE Transactions on Industrial Electronics, 51, 201-220, 2004. [9] Fernando F.K.M., José E.V., “Dynamic Model Analysis of a Pneumatically Operated Flexible Arm”, WSEAS Transactions on Systems, 4, 49-54, 2005. [10] Juan M.R., Efrén G., José E.V., José C.P., René J.R., Bernardo R.P., “Pneumatic Cylinder Control for a Flexible Manipulator Robot”, International conference on Dynamics, Instrumentation and Control (CDIC’06), Querétaro, México, 2006. [11] Janiszowski K.B., “Adaptation, Modelling of Dynamic Drives and Controller Design in Servomechanism Pneumatic Systems”, IEE Control Theory and Applications, 151, 234-245, 2004.

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