DSpace at VNU: Online tuning gain scheduling MIMO neural PID control of the 2-axes pneumatic artificial muscle (PAM) robot arm

Online tuning gain scheduling MIMO neural PID control of the 2-axespneumatic artiﬁcial muscle PAM robot arm Faculty of Electrical and Electronic Engineering, Ho Chi Minh City University

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Online tuning gain scheduling MIMO neural PID control of the 2-axes

pneumatic artiﬁcial muscle (PAM) robot arm

Faculty of Electrical and Electronic Engineering, Ho Chi Minh City University of Technology, Ho Chi Minh City, Viet Nam

a r t i c l e i n f o

Keywords:

Pneumatic artiﬁcial muscle (PAM)

Highly nonlinear PAM robot arm

Proposed online tuning gain scheduling

MIMO dynamic neural PID controller

(MIMO DNN-PID)

Real-time joint angle position control

Fast online tuning back propagation (BP)

algorithm

a b s t r a c t

This paper presents a detailed study to investigate the possibility of applying the online tuning gain scheduling MIMO neural dynamic DNN-PID control architecture to a nonlinear 2-axes pneumatic artiﬁ-cial muscle (PAM) robot arm so as to improve its joint angle position output performance The proposed controller was implemented as a subsystem to control the real-time 2-axes PAM robot-arm system so as

to control precisely the joint angle position of the 2-axes PAM robot arm when subjected to system inter-nal interactions and load variations The results of the experiment have demonstrated the feasibility and beneﬁts of the novel proposed control approach in comparison with the traditional PID control strategy The proposed gain scheduling neural MIMO DNN-PID control scheme forced both joint angle outputs of 2-axes PAM robot arm to track those of the reference simultaneously under changes of the load and sys-tem coupled internal interactions The performance of this novel proposed controller was found to be outperforming in comparison with conventional PID These results can be applied to control other highly nonlinear systems

1 Introduction

The development of compliant manipulator aimed to replace

monotonous and dangerous tasks, which has motivated lots of

researchers to develop more and more sophisticated and

intelli-gent controllers for human-friendly industrial manipulators Due

to uncertainties, it is difﬁcult to obtain an accurate mathematical

model for robot manipulators Thus, conventional control

method-ologies ﬁnd it difﬁcult or impossible to handle un-modeled

dynam-ics of a robot manipulator Furthermore, most of conventional

control methods, for example PID controllers, are based on

mathe-matical and statistical procedures for modeling the system and

estimation of optimal controller parameters In practice, such

manipulator to be controlled is often highly nonlinear and a

math-ematical model may be difﬁcult to derive Consequently, to

accom-modate system uncertainties and variations, learning methods and

adaptive intelligent techniques must be incorporated

Furthermore, the orientation of industrial robotics toward

applications needing greater proximity between the robot and

the human operator has recently led researchers to develop novel

actuator sharing some analogous features with natural skeletal

muscle The PAM actuator now has been achieving increased

pop-ularity by providing advantages such as high power/weight ratio,

full of hygiene, easiness in preservation and especially the capacity

of human compliance which is the most important requirement in medical and human welfare ﬁeld Thus, PAM actuator has been re-garded during the recent years as an interesting alternative to hydraulic and electric actuators However, the air compressibility and the lack of damping ability of the PAM manipulator bring the dynamic disturbance of the pressure response and cause the oscillatory motion Therefore, it is not easy to realize the perfor-mance of transient response with high speed and with respect to various external inertia loads in order to realize a human-friendly therapy robot Numerous intelligent control methods have been devised to solve complicated problems of industrial manipulators

in general and of PAM manipulators in particular Neo and Er (1996) and Lilly, Chan, Repperger, and Berlin (2003)improved

fuz-zy controllers to PAM manipulators A Kohonen-type neural net-work for the position control of robot arm is applied in Hesselroth, Sarkar, Patrick van der Smagt, and Schulten (1994) Forwardly, the authors have developed a feed-forward neural net-work controller (Patrick van der Smagt, Groen, & Schulten, 1996) Caldwell et al applied an adaptive controller and the error is better than ±0.5° (Caldwell, Bowler, & Medrano-Cerda, 1996) Carbonell

et al applied successfully sliding mode to control PAM actuator (Carbonell, Jiang, & Repperger, 2001) Applied fuzzy and PID con-trol to PAM system (Balasubramanian & Rattan, 2003a) Forwardly, authors improved fuzzy feed-forward control to PAM system ( Bal-asubramanian & Rattan, 2003b) Ahn et al developed Hinﬁnity con-trol to a 6-DOF manipulator (Ahn, Lee, & Yang, 2003) Gini, Folgheraiter, Perkowski, and Pivtoraiko (2003) proposed an

* Tel.: +84 08 39490415.

E-mail address: hphanh@hcmut.edu.vn

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Expert Systems with Applications

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / e s w a

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adaptive controller based on the neural network applied to the

artiﬁcial hand, which is composed of the PAM Nil et al developed

a hybrid fuzzy neural network to control a 3-DOF robot

manipula-tor (Nil, Yuzgec, & Kakir, 2006) Recently, inAhn and Thanh (2006),

Ahn et al have applied magneto-rheological (MR) brake combining

LVQNN to control the 1-link PAM manipulator Forwardly, Ahn and

Anh have successfully identiﬁed the highly nonlinear PAM

manip-ulator using neural NARX model (Ahn & Anh, 2007) and GA-based

fuzzy NARX model (Ahn & Anh, 2009) for improving the control

performance of the 1-link PAM manipulator

Though these control systems were partially successful in

obtaining smooth actuator motion in response to input signals,

the manipulator must be controlled slowly in order to get stable

and accurate position control Furthermore, the external inertia

load was also assumed to be constant or slowly varying It is

be-cause PAM manipulators are multivariable nonlinear coupled

sys-tems and frequently subjected to structured and/or unstructured

uncertainties even in a well-structured setting for industrial use

or human-friendly applications as well Assuming that PAM

manipulator is applied as an elbow and wrist rehabilitation robot

in future, which is the ﬁnal purpose of our study, it is necessary

to realize fast response, even if the external inertia load changes

severely At the same time, the external inertia loads can always

be varied and not be known exactly Therefore, it is necessary to

propose a new control algorithm, which is applicable to a highly

nonlinear PAM system with various loads

To overcome these drawbacks, the proposed online tuning

MIMO DNN-PID algorithm in this paper is a newly developed

algo-rithm that has the following good features such as highly simple

and dynamic self-organizing structure, fast learning speed, good

generalization and ﬂexibility in learning The proposed online

tun-ing MIMO DNN-PID controller is employed to compensate for

envi-ronmental variations such as payload mass and time-varying

parameters during the operation process By virtue of online train-ing by BP learntrain-ing algorithm and then auto-tuned gain schedultrain-ing

K and PID weighting values Kp, Kiand Kd, it is able to learn the 2-axes PAM robot-arm dynamics and make control decisions simul-taneously In effect, it offers an exciting online estimation scheme

of the plant

The outline of this paper composes Section1for introducing re-lated works in PAM robot-arm control Section2presents proce-dure of design an online tuning gain scheduling MIMO DNN-PID controller for the 2-axes PAM robot arm Section3presents and analyses experiment studies and results Finally, the conclusion is given in Section4

2 Control system 2.1 Controller design Many efforts have been made to compensate the coupled effect and nonlinear features of n-DOF PAM actuators Since the simplic-ity and efﬁciency of the feedback PID controller in closed-loop sys-tem is a commonly used technique and has been proven to be more stable, this scheme is used in this paper In the feedback PID con-troller system design, the proposed online tuning gain scheduling MIMO DNN-PID of the 2-axes PAM robot arm is updated online

to learn as close as possible the dynamic features of nonlinear 2-axes PAM robot arm This online tuning gain scheduling MIMO DNN-PID controller is to increase the accuracy for the two-joint po-sition control of the 2-axes PAM robot arm The block diagram of the proposed controller is shown inFig 1

The structure of the newly proposed online tuning MIMO DNN-PID control algorithm using MLFNN is shown inFig 2 This control algorithm is a new one and has the characteristics such as simple

1

−

Δ

z T

T

z

Δ

− −1 1

Neural PID Controller Joint 1

2-Axes PAM Manipulator

Online Tuning Gain Scheduling

MLFNN Network

Y1 (k) U1 (k)

e P (k)

e I (k)

e d (k) +

+

-

-1

−

Δ

z T

T

z

Δ

− −1 1

Neural PID Controller Joint 2

Online Tuning Gain Scheduling

MLFNN Network

Y2 (k) U2 (k)

e P (k)

e I (k)

e d (k) +

+

-

Trang 3

-structure, little computation time and more robust control,

com-pared with the previous neural network controller (Thanh & Ahn,

2006)

FromFigs 1 and 2, a control input u applied to the two-joints of

the 2-axes PAM manipulator can be obtained from the following

equation

where x is input of hyperbolic tangent function f() which is

pre-sented in Eq.(2), K and Bhare the bias weighting values of input

layer and hidden layer, respectively The hyperbolic tangent

func-tion f() has a nonlinear relafunc-tionship as explained in the following

equation

f ðxÞ ¼ð1 e

xÞ

The block diagram of proposed online tuning gain scheduling

MIMO DNN-PID control based on Multi-Layer Feed-Forward

Neu-ral Network (MLFNN) composed of three-layers is shown in

Fig 2 In this ﬁgure, K, Kp, Kiand Kd, are scheduling, proportional,

integral and derivative gain while ep, eiand edare system error

be-tween desired set-point output and output of joint of the PAM

manipulator, integral of the system error and the difference of

the system error, respectively

MLFNN is trained online by the fast learning back propagation

(FLBP) algorithm as to minimize the system error between desired

set-point output and output of joint of the PAM manipulator

FromFig 2, the input signal of the hyperbolic tangent function

f() becomes

xðkÞ ¼ KpðkÞepðkÞ þ KiðkÞeiðkÞ þ KdðkÞedðkÞ þ BiðkÞ

OðkÞ ¼ f ðxðkÞÞ

uðkÞ ¼ KðkÞOðkÞ þ BhðkÞ

ð3Þ

with

epðkÞ ¼ yREFðkÞ yðkÞ

eiðkÞ ¼ epðkÞ DT

edðkÞ ¼epðkÞð1 z

1Þ

DT

ð4Þ

whereDT is the sampling time, z is the operator of Z-transform, k is

the discrete sequence, yREF(k) and y(k) are the desired set-point

out-put and outout-put of joint of the PAM manipulator, respectively

Fur-thermore, Bi, Kp, Kiand Kdare weighting values of input layer, and

Bhand K are weighting values of hidden layer These weighting

val-ues will be tuned online by fast learning back propagation (FLBP)

algorithm

As to online tuning the gain scheduling K and PID parameters

Kp, Kiand Kd, the gradient descent method used in BP learning

algo-rithm using the following equations were applied

Kðk þ 1Þ ¼ KðkÞ g@EðkÞ

@K

Kpðk þ 1Þ ¼ KpðkÞ gp@EðkÞ

@Kp

Kiðk þ 1Þ ¼ KiðkÞ gi

@EðkÞ

@Ki

Kdðk þ 1Þ ¼ KdðkÞ gd@EðkÞ

@Kd

ð5Þ

and the bias weighting values Bi(k) and Bh(k) are updated as follows:

Biðk þ 1Þ ¼ BiðkÞ gB

i

@EðkÞ

@Bi

Bhðk þ 1Þ ¼ BhðkÞ gBh

@EðkÞ

@Bh

ð6Þ

whereg,gp,gi,gd,gB

iandgB

h are learning rate values determining the convergence speed of updated weighting values; E(k) is the error deﬁned by the gradient descent method as follows:

EðkÞ ¼1

Appling the chain rule with Eqs.(5) and (6), it leads to

@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@K

@EðkÞ

@Kp

¼@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@O

@OðkÞ

@x

@xðkÞ

@Kp

@EðkÞ

@Ki

¼@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@O

@OðkÞ

@x

@xðkÞ

@Ki

@EðkÞ

@Kd

¼@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@O

@OðkÞ

@x

@xðkÞ

@Kd

ð8Þ

and

@EðkÞ

@Bi

¼@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@O

@OðkÞ

@x

@xðkÞ

@Bi

@EðkÞ

@Bh

¼@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@Bh

ð9Þ

From Eqs.(1), (3), and (6), the following equations can be derived:

@EðkÞ

@y ¼ ðyREFðkÞ yðkÞÞ ¼ epðkÞ

@yðkÞ

Dy

Du¼

ðyðkÞ yðk 1ÞÞ ðuðkÞ uðk 1ÞÞ¼D

@uðkÞ

@O ¼ K

@OðkÞ

@x ¼ f

0ðxðkÞÞ

@xðkÞ

@Bi

¼ 1; @xðkÞ

@Kp

¼ epðkÞ; @xðkÞ

@Ki

¼ eiðkÞ; @xðkÞ

@Kd

¼ edðkÞ

@uðkÞ

@K ¼ OðkÞ;

@uðkÞ

@Bh

¼ 1

ð10Þ

e P (k)

e I (k)

e D (k)

1

Kd

Ki

Kp

Bi

Σ

K

MLFNN Network

Trang 4

From Eqs (8)–(10), the following resulting equations can be

derived:

@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@K ¼ epðkÞDOðkÞ

@EðkÞ

@Kp ¼@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@O

@OðkÞ

@x

@xðkÞ

@Kp ¼ epðkÞDKf0ðxðkÞÞepðkÞ

¼ DKf0ðxÞe2

pðkÞ

@EðkÞ

@Ki

¼@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@O

@OðkÞ

@x

@xðkÞ

@Ki

¼ epðkÞDKf0

ðxðkÞÞeiðkÞ

¼ DKf0ðxÞepðkÞeiðkÞ

@EðkÞ

@Kd ¼@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@O

@OðkÞ

@x

@xðkÞ

@Kd ¼ epðkÞDKf0ðxðkÞÞedðkÞ

¼ DKf0ðxÞepðkÞedðkÞ

ð11Þ

and

@EðkÞ

@Bi ¼@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@O

@OðkÞ

@x

@xðkÞ

@Bi

¼ epðkÞDKf0ðxðkÞÞ1 ¼ DKf0ðxÞepðkÞ

@EðkÞ

@Bh

¼@EðkÞ

@y

@yðkÞ

@u

@uðkÞ

@Bh

¼ epðkÞD1 ¼ DepðkÞ

ð12Þ

and with

f0ðxÞ ¼ 2 e

x

From Eqs.(5) and (6), the ﬁnal equations for online tuning gain scheduling K and PID parameters Kp, Kiand Kd are expressed as follows:

Kðk þ 1Þ ¼ KðkÞ þg epðkÞD OðkÞ

Kpðk þ 1Þ ¼ KpðkÞ þgp e2

pðkÞDK 2e

x

ð1 þ exÞ2

Kiðk þ 1Þ ¼ KiðkÞ þgi epðkÞeiðkÞDK 2e

x

ð1 þ exÞ2

Kdðk þ 1Þ ¼ KdðkÞ þgd epðkÞeiðkÞDK 2e

x

ð1 þ exÞ2

ð14Þ

and the bias weighting values Bi(k) and Bh(k) are updated as follows:

Biðk þ 1Þ ¼ BiðkÞ þgBi epðkÞDK 2e

x

ð1 þ exÞ2

Bhðk þ 1Þ ¼ BhðkÞ þg epðkÞD

ð15Þ

Fig 3 Working principle of the 2-axes PAM robot arm.

Fig 4 Photograph of the experimental 2-axes PAM robot arm.

Fig 5 Experimental set-up conﬁguration of the 2-axes PAM robot arm.

Trang 5

2.2 Experimental set-up

A general conﬁguration of the investigated 2-axes PAM

manip-ulator shown through the schematic diagram of the 2-axes PAM

robot arm and the photograph of the experimental apparatus

pre-sented inFigs 3 and 4, respectively

Fig 5presents the block diagram for joint angle position control

of the both joints of the 2-axes PAM robot arm using proposed

on-line tuning gain scheduling neural MIMO DNN-PID control scheme

The hardware includes an IBM compatible PC (Pentium

1.7 GHz) which sends the voltage signals u1(t) and u2(t) to control

the two proportional valves (FESTO, MPYE-5-1/8HF-710B), through

a D/A board (ADVANTECH, PCI 1720 card) which changes digital

signals from PC to analog voltage u1(t) and u2(t), respectively

The rotating torque is generated by the pneumatic pressure

differ-ence supplied from air-compressor between the antagonistic

arti-ﬁcial muscles Consequently, both joints of the 2-axes PAM robot

arm will be rotated to follow the desired joint angle references (Y

R-EF1(k) and YREF2(k)), respectively The joint angles, h1(°) and h2(°),

are detected by two rotary encoders (METRONIX, H40-8-3600ZO)

and fed back to the computer through a 32-bit counter board

(COMPUTING MEASUREMENT, PCI QUAD-4 card) which changes

digital pulse signals to joint angle values y(t) and y (t) The

pneumatic line is conducted under the pressure of 4 bar and the software control algorithm of the closed-loop system is coded in C-mex program code run in Real-Time Windows Target of MAT-LAB-SIMULINK environment Table 1 presents the conﬁguration

of the hardware set-up installed fromFig 5

3 Experimental results The performance of proposed online tuning gain scheduling MIMO DNN-PID control scheme is veriﬁed on joint angle position control of the both joints of the 2-axes PAM robot arm.Figs 3–5 describe the working diagram of this control scheme

Fig 6a presents the real-time SIMULINK diagram of proposed online tuning gain scheduling neural MIMO DNN-PID control algorithm which run in Real-time Windows Target In this novel control scheme, DYNAMIC_NEURAL_PID1 and DYNAMIC_NEU-RAL_PID2 are two subsystems programmed in C then compiled and run in real-time C-mex code Three initial PID parameters Kp,

Ki, Kdand gain scheduling K value are chosen by trial-and-error method and determined as K = 0.6, Kp= 0.089, Ki= 0.09, Kd= 0.07 for Joint 1 and K = 0.6, K = 0.089, K = 0.09, K = 0.05 for Joint 2

Table 1

Lists of the experimental hardware set-up.

error2

error1

Y1

XY Graph1

XY Graph

1/z Unit Delay8

z 1

Unit Delay5

z 1

Unit Delay4

1/z

Unit Delay3

z 1

Unit Delay2 z

1

Unit Delay1

Ucontrol2

Ucontrol1

Wpid1

To Workspace7

Ucontrol2

To Workspace6

error2

To Workspace5

error1

To Workspace4

Wpid2

To Workspace3

Y2

To Workspace2

REF2

To Workspace19

U1

To Workspace16

U2

To Workspace15

Ucontrol1

To Workspace13

Y1

To Workspace1

REF1

To Workspace

TRIANGLE

Reference2

TRIANGLE

Reference1

TRAPEZOID

Reference2

TRAPEZOID

Reference1

Sine Wave2

Sine Wave1

Saturation1 Saturation

Results

RECTANGLE

Reference2

RECTANGLE

Reference1

1/s Integrator1

1/s Integrator

[Wpid2]

Goto9

[error2]

Goto8

[error1]

Goto7

[Y2]

Goto6

[REF2]

Goto5

[Y1]

Goto4

[REF1]

Goto3

[Ucontrol1]

Goto2

[Wpid1]

Goto10

[Ucontrol2]

Goto1

0.025 Gain3

-0.025 Gain1

[Y2]

From9

[REF2]

From8

[Ucontrol2]

From7

[Ucontrol1]

From6

[error1]

From5

[Y1]

From4

[error2]

From3

[error1]

From2

[Wpid2]

From11

[error2]

From10

[Wpid1]

From1

[REF1]

From

Encoder Input Encoder Input2 Measurement Computing PCI-QUAD04 [auto]

Encoder Input Encoder Input1 Measurement Computing PCI-QUAD04 [auto]

du/dt Derivative1

du/dt Derivative

DYNAMIC_NEURAL_PID

DNN-PID2

DYNAMIC_NEURAL_PID

DNN-PID1

5 Constant2

5 Constant1

Analog

Analog Output2 Advantech PCI-1720 [auto]

Analog

Analog Output1 Advantech PCI-1720 [auto]

Fig 6a Experiment SIMULINK model of PAM robot-arm position control using proposed MIMO DNN-PID control.

Trang 6

Fig 6b presents the experiment SIMULINK diagram of 2-axes

PAM robot-arm position control using conventional PID controller

in order to compare as to demonstrate the superiority of proposed

control system Three PID parameters Kp, Ki, Kdand gain scheduling

K value of each PID controller are chosen by trial-and-error method

and determined as K = 0.6, Kp= 0.089, Ki= 0.09, Kd= 0.07 for Joint 1

and K = 0.6, Kp= 0.089, Ki= 0.09, Kd= 0.05 for Joint 2

Fig 7shows that the parameter conﬁguration of DYNAMIC_

NEURAL_PID subsystem composes seven parameters The ﬁrst

vec-tor parameter contains number of inputs and outputs of neural

DYNAMIC_NEURAL_PID subsystem; the second relates to the

num-ber of neurons of hidden layer used; the third declares the step size

used in real-time operation of PAM system; the fourth declares the

learning rate value used in real-time operation of PAM

manipula-tor; the ﬁfth parameter contains logic value as to choose the

sig-moid function (1) or the hyperbolic tangent function (0); the

sixth parameter contains logic value as to choose the linear

func-tion (0) or the sigmoid/hyperbolic tangent funcfunc-tion (1) of output

layer; and the seventh vector parameter contains the

ofﬂine-train-ing K, Kp, Ki, Kdweighting values and two initial bias weighting

val-ues Biand Bh

The ﬁnal purpose of the PAM manipulator is to be used as an

el-bow and wrist rehabilitation robot Thus, the experiments were

carried out with respect to three different waveforms as reference

input (triangular, trapezoidal and sinusoidal reference) with two

different end-point payloads (Load 0.5 kg and Load 2 kg) as to

demonstrate the performance of novel proposed controller

Fur-thermore, the comparisons of control performance between the

conventional PID controller and the proposed online tuning gain

scheduling MIMO DNN-PID controller were performed

The gain scheduling value K and PID controller parameters Kp, Ki

and Kdwere set to be K = 0.6, Kp= 0.089, Ki= 0.09, Kd= 0.07 for Joint

1 and K = 0.6, Kp= 0.089, Ki= 0.09, Kd= 0.05 for Joint 2 These

parameters of both PID controllers were obtained by

trial-and-er-ror through experiments

The proposed neural DNN-PID control of the 2-axes PAM

manipulator is investigated with initial parameter conﬁguration

as follows: both of DYNAMIC_NEURAL_PID1 and

DYNAMIC_NEU-RAL_PID2 subsystems possessed a three-layer MLFNN structure composes one neurons in hidden layer, three inputs, one output with its structure is shown inFig 2; the sampling time 0.01 s; the learning rate value k is chosen equal 0.0005; the hyperbolic tangent function is chosen as activated function of hidden layer; the linear function is chosen as activated function of output layer; the initial weighting values are chosen with the same value as K,

Kp, Kiand Kd of corresponding PID controller and forwardly, the two initial bias weighting values Biand Bhare chosen equal 0;

ﬁnal-ly error back propagation (BP) method is chosen as fast learning algorithm

First, the experiments were carried out to verify the effective-ness of the proposed online tuning MIMO DNN-PID controller using neural network with triangular reference input.Fig 8a and

b shows the experimental results between the conventional PID controller and the proposed nonlinear DNN-PID controller with re-spect to Joints 1 and 2 in two cases of Load 0.5 kg and Load 2 kg, respectively The online updating of each control parameter ( K,

error2

error1

Y1

XY Graph1

XY Graph

1/z Unit Delay8

z 1

Unit Delay5

1/z

Unit Delay3

z 1

Unit Delay2

Ucontrol2

Ucontrol1

UcontrolPID2

To Workspace6

errorPID2

To Workspace5

errorPID1

To Workspace4

Ypid2

To Workspace2

REF2

To Workspace19

Upid1

To Workspace16

Upid2

To Workspace15

UcontrolPID1

To Workspace13

Ypid1

To Workspace1

REF1

To Workspace

TRIANGLE

Reference2

TRIANGLE

Reference1

TRAPEZOID

Reference2

TRAPEZOID

Reference1

Sine Wave2

Sine Wave1

Saturation1 Saturation

Results

RECTANGLE

Reference2

RECTANGLE

Reference1

PID PID 2

PID PID 1

[error2]

Goto8

[error1]

Goto7

[Y2]

Goto6

[REF2]

Goto5

[Y1]

Goto4

[REF1]

Goto3

[Ucontrol1]

Goto2

[Ucontrol2]

Goto1

0.6 Gain4

0.025 Gain3

1 Gain2

-0.025 Gain1

[Y2]

From9

[REF2]

From8

[Ucontrol2]

From7

[Ucontrol1]

From6

[Y1]

From4

[error2]

From3

[error1]

From2

[REF1]

From

Encoder Input Encoder Input2

Measurement Computing PCI-QUAD04 [auto]

Encoder Input Encoder Input1

Measurement Computing PCI-QUAD04 [auto]

5 Constant2

5 Constant1

Analog

Analog Output2

Advantech PCI-1720 [auto]

Analog

Analog Output1

Advantech PCI-1720 [auto]

Fig 6b Experiment SIMULINK model of 2-axes PAM robot-arm position control using conventional PID control.

Fig 7 Parameter conﬁguration of DYNAMIC_NEURAL_PID subsystem used in proposed online tuning DNN-PID control.

Trang 7

Kp, Kiand Kd) with respect to Joints 1 and 2 in two cases of Load

0.5 kg and Load 2 kg was shown inFig 8c In the experiment of

the proposed online tuning MIMO DNN-PID controller, the initial

values of K, Kp, Kiand Kdare set to be the same as that of conven-tional PID controller Due to the sophisticated online tuning of K,

K, K and K, the error between desired reference y and actual

-10

-8

-6

-4

-2

0

2

JOINT 1 - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg]

0 5 10 15 20

25

JOINT 2 - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg

-1.5

-1

-0.5

0

0.5

1

1.5

2

t [sec]

-2 -1 0 1 2

t [sec]

PID control proposed DNN-PID control PID control

proposed DNN-PID control

Reference PID control proposed DNN-PID control

Fig 8a Triangular response of both joints of the 2-axes PAM robot arm – Load 0.5 kg.

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-8

-6

-4

-2

0

2

JOINT 1 - 2-AXES PAM MANIPULATOR - LOAD 2 [kg

0 5 10 15 20

25 JOINT 2 - 2-AXES PAM MANIPULATOR - LOAD 2 [kg]

-1

0

1

2

t [sec]

-2 -1 0 1 2

t [sec]

PID control proposed DNN-PID control

Fig 8b Triangular response of both joints of the 2-axes PAM robot arm – Load 2 kg

Trang 8

joint angle response y continually decreased Consequently, the

er-ror decreases only in the range ±0.7° with Joint 1 and ±0.6° with

Joint 2 in case of Load 0.5 kg The same good result is obtained with

the error only in the range ±0.8° with Joint 1 and ±0.6° with Joint 2

in case of Load 2 kg These results are really optimistic in

compar-ison with the bad and unchanged error of conventional PID

con-troller (±1.7° with Joint 1 and ±1.8° with Joint 2 in both case of

Load)

Fig 8d shows the reﬁned shape of voltage control U1and U2 ap-plied to Joint 1 and Joint 2, which are generated by the proposed online tuning MIMO DNN-PID controller as to improve the perfor-mance and the accuracy of both joints of the 2-axes PAM robot-arm response

Forwardly, the experiments were carried out to verify the superiority of the proposed online tuning DNN-PID controller with trapezoidal reference input.Fig 9a and b shows the

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6

0.8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

t [sec]

JOINT 1 - 2-AXES PAM MANIPULATOR - LOAD 2 [kg]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

t [sec]

Kp Ki Kd Kgain

Fig 8c The online tuning convergence of proposed MIMO DNN-PID controller parameters with triangular reference

-0.4

-0.2

0

0.2

-0.1 0 0.1 0.2 0.3 0.4

-0.4

-0.2

0

0.2

t [sec]

-0.1 0 0.1 0.2 0.3 0.4 0.5

t [sec]

Fig 8d The voltage control applied to both joints of the 2-axes PAM robot arm with triangular reference.

Trang 9

mental results of the conventional PID controller and the

proposed neural MIMO DNN-PID controller with respect to Joints

1 and 2 in 2 cases of Load 0.5 kg and Load 2 kg, respectively The

online tuning of four DNN-PID controller parameters (K, Kp, Kiand

Kd) with respect to Joints 1 and 2 in two cases of Load 0.5 kg and Load 2 kg was shown inFig 9c In the experiment of the proposed

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-8

-6

-4

-2

0

2

0 5 10 15 20 25 JOINT 2 - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg]

-1

-0.5

0

0.5

1

1.5

t [sec]

-2 -1 0 1 2

t [sec]

Fig 9a Trapezoidal response of both joints of the 2-axes PAM robot arm – Load 0.5 kg.

-10

-8

-6

-4

-2

0

2

0 5 10 15 20

25

-1

-0.5

0

0.5

1

1.5

t [sec]

-2 -1 0 1 2

t [sec]

PID control proposed DNN-PID control PID control

proposed DNN-PID control

Fig 9b Trapezoidal response of both joints of the 2-axes PAM robot arm – Load 2 kg.

Trang 10

online tuning DNN-PID controller, the initial values of K, Kp, Ki

and Kdare set to be the same as that of conventional PID

control-ler These ﬁgures show that due to the reﬁned online tuning of K,

Kp, Kiand Kd, the error between desired reference yREFand actual

joint angle response y continually minimized Consequently, the

optimized error decreases only in the range ±0.7° with Joint 1

and ±0.5° with Joint 2 in case of Load 0.5 kg The same good result

is obtained with the minimized error in the range ±0.7° with Joint

1 and ±0.6° with Joint 2 in case of Load 2 kg These results are really outperforming in comparison with the bad and unchanged error of conventional PID controller (±1° with Joint 1 and ±1.8° with Joint 2 in both case of Load) Furthermore, in case of Load

2 kg, Fig 9b shows that PID controller caused 2-axes PAM robot-arm response begun to be oscillatory and unstable

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

t [sec]

0 0.1 0.2 0.3 0.4 0.5 0.6

t [sec]

Kp Ki Kd Kgain

Fig 9c The online tuning convergence of proposed MIMO DNN-PID controller parameters with trapezoidal reference.

-0.4

-0.2

0

0.2

-0.1 0 0.1 0.2 0.3 0.4

-0.4

-0.2

0

0.2

t [sec]

-0.1 0 0.1 0.2 0.3 0.4 0.5

t [sec]

Fig 9d The voltage control applied to both joints of the 2-axes PAM robot arm with trapezoidal reference.

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