controller parameter tuning of delta robot based on servo

CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 28,aNo. 2,a2015

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DOI: 10.3901/CJME.2014.1117.169, available online at www.springerlink.com; www.cjmenet.com; www.cjme.com.cn

Controller Parameter Tuning of Delta Robot Based on Servo Identification

ZHAO Qing, WANG Panfeng*, and MEI Jiangping

Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, China

Received August 18, 2014; revised November 11, 2014; accepted November 17, 2014

Abstract: High-speed pick-and-place parallel robot is a system where the inertia imposed on the motor shafts is real-time changing with

the system configurations. High quality of computer control with proper controller parameters is conducive to overcoming this problem

and has a significant effect on reducing the robot’s tracking error. By taking Delta robot as an example, a method for parameter tuning

of the fixed gain motion controller is presented. Having identifying the parameters of the servo system in the frequency domain by the

sinusoidal excitation, the PD+feedforward control strategy is proposed to adapt to the varying inertia loads, allowing the controller

parameters to be tuned by minimizing the mean square tracking error along a typical trajectory. A set of optimum parameters is obtained

through computer simulations and the effectiveness of the proposed approach is validated by experiments on a real prototype machine.

Let the traveling plate undergoes a specific trajectory and the results show that the tracking error can be reduced by at least 50% in

comparison with the conventional auto-tuning and Z-N methods. The proposed approach is a whole workspace optimization and can be

applied to the parameter tuning of fixed gain motion controllers.

Keywords: parallel robot, servo system identification, parameter tuning, mean square error

1 Introduction

In the past few decades, it has witnessed ever increasing applications of high-speed pick-and-place parallel robots in many sectors such as electronics, pharmaceutical, food, and other light industries thanks to the light-limb design and base-situated actuator arrangements[1–2]. This statement can be exemplified by very successful Delta[3] and Adept Quattro[4] robots amongst others.

It is well accepted that the capability and efficiency of pick-and-place parallel robots rely not only upon the appropriate topological structures, right geometric dimensions, good stiffness and desirable elastic dynamic behaviors[5–9], but also upon sound trajectory planning and high quality of the computer control[10–11]. Due to the effects of heavily coupling and time varying dynamics in nature[12–13], ideally it is better off to adopt more sophisticated control strategies such as fuzzy neural network, rule-adaptive fuzzy control, and position-force switching control, etc.[14–18], for ensuring either the positioning or tracing accuracy. However, it is difficult if impossible to implement these control strategies in practice because they are rarely equipped in the commercialized motion controllers available on market. Thus, it gives rise

* Corresponding author. E-mail: [email protected] Supported by National Natural Science Foundation of China(Grant Nos.

51305293, 51135008) © Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2015

to a practical issue of how to tune the fixed gain PID controller in an off-line manner such that the desirable positioning and tracing accuracy can be achieved throughout the entire workspace. For doing this, ALI, et al[19], proposed a Metamodeling technique that allows the motion controller to be tuned by reducing the time of off-line optimization. A flexible robot manipulator was studied and the Radial Basis Function Neural Network metamodel was used to give a good approximation to the optimum controller parameters. However, time consumption wasn’t a pressing issue for off-line tuning and there was a lack of evaluation targeted on the tuning effectiveness. YANG, et al[20], proposed a parameter tuning method of a 3-HSS parallel kinematic machine by minimizing the mean square error of the trajectory of the end effector. However, it only took into account the dynamics of the velocity loop though the dynamics of the position loop may have significant bearings on the trajectory tracing accuracy of the end effector. Thus, both the dynamics of the velocity loop and the position loop should be considered in the modeling of control system[21–22]. In fact, for the constant outer load, the most classical method for tuning controller parameters is Ziegler-Nichols method. But it should be noted that the real-time change of the inertia imposed on the motor shafts will unavoidably degrade the moving precision of the robot. Thus, how to tune the controller parameters of the parallel robot with varying inertial load to make the dynamic performance of the system optimal in the whole workspace

Y ZHAO Qing, et al: Controller Parameter Tuning of Delta Robot Based on Servo Identification

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still remains to be a difficult problem in the process of industrialization.

This paper presents a method for parameter tuning of the fixed gain motion controller. The kinematic and dynamic analyses of Delta robot are addressed briefly and the servo system identification in the frequency domain is proposed. The optimization procedure for parameter tuning of the PD+feedforward controller is presented with taking into account the varying inertia loads. Simulations and experiments are carried out to validate the effectiveness of this approach.

2 Kinematic and Dynamic Modeling

In order to implement the controller parameters tuning,

the inverse kinematic and dynamic analyses of Delta robot are carried out. Fig. 1 shows a 3D solid model of Delta robot, which is composed of a base, a traveling plate and three identical kinematic chains. Since the traveling plate undergoes pure translational motion and the motions of the two distal links within a parallelogram are identical, the kinematic model of the robot can be simplified as shown in Fig. 2.

Fig. 1. 3D model of Delta robot

Fig. 2. Kinematic model of Delta robot

A base coordinate system O xyz- is fixed on the base

with the y-axis along the vector from O to 2A . In this

coordinate system, the position vector of reference point O¢ on the traveling plate can be written as

1 2 , 1, 2, 3,i i il l i= + + =r e u w (1)

where T(cos sin 0) ( 1, 2, 3)i ie i = =ie is the vector

pointing from O to iA ; ( )π 6 2π 1 3i i =- / + - / ; 1l ,

2l , iu and iw are the lengths and unit vectors of the

proximal and distal links, and

( )Tcos cos sin cos sini i i i i i = -u , (2)

where i is the position angle of the ith proximal link.

The inverse position analysis gives

2 2 2

2arctan , 1, 2, 3,i i i ii

i i

E E G Fi

G F

- - - += =

- (3)

where

( )

( ) ( )

( ) ( )

T1

T1

T 2 21 2

ˆ2 ,

ˆ ˆ2 cos sin ,

.

i i

i i i i

i i i

E l

F l

G l l

= -

=- - +

= - - + -

r e z

r e x y

r e r e

x , y and z are the unit vectors of three orthogonal axes

of the O xyz- . Thus iu can be determined by Eq. (2)

and iw can be determined by

12

1( )i i il

l= - -w r e u . (4)

Differentiating Eq. (1) with respect to time yields

1 2( ) , 1, 2, 3,i i i i il l i= ´ + ´ =r v u ω w (5)

where r is the velocity of O¢ ; i is the magnitude of

angular velocity of proximal link i; iω is the angular

velocity of the ith distal link; Tsin cos 0i i i v is

unit vector of the rotation axis of the ith proximal link, which is normal to the plane spanned by ie and iu .

Taking dot product with iw on both sides of Eq. (5) and rewriting in matrix form gives the inverse velocity model of the robot

, =θ Jr (6)

where ( )T

1 2 3 =θ , 1x

-=J J J is the Jacobian,

and ( )T1diag i i il

é ù= ´ê úë ûJ w v u , ( )T1 2 3x =J w w w are

the direct and indirect Jacobian respectively.

CHINESE JOURNAL OF MECHANICAL ENGINEERING

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Differentiating Eq. (6) with respect to time leads to the inverse acceleration model of the system

( ), = +θ Jr f r (7)

where r is the acceleration of O¢ ; ( )T

1 2 3 =θ

with i being the signed magnitude of the angular

acceleration of the ith proximal link; and

( )

( )

T T1 2 3

T T

2 21

TT T1

3 32

T

, ,

( ) ( )1

( ) ( ),

,

i i

i i i i i ii

i i

i i i i i i

i i

i i i i

f f f f

l

l

l

= =

é ´ ´ê= +êêë

ùæ ö æ ö´ ´ ú÷ ÷ç ç÷ ÷ç ç- - ú÷ ÷ç ç÷ ÷÷ ÷ç ç úè ø è øúû= ´

f r H r

v w v u w wH

v u w v u wE E

w v u

3E is a unit matrix of order 3.

In the formulation of inverse dynamics, the following assumptions are made:

(1) Neglect friction and elasticity in joints; (2) Neglect the moment of inertia of each distal link

because of its lightweight design and divide its mass into two lumped masses concentrated at its two extremities, i.e. 2/3 at the extremity connected with the proximal link and 1/3 at the extremity connected with the traveling plate. This assumption is justifiable as the moment of inertia of a uniform slim rod of length l and mass m about its endpoint is given by ml2/3[23].

Then the virtual work principle gives

( ) ( )T T

A Ag ˆg 0,I m m - - - + =τ θ τ θ r z r (8)

where ( )T1 2 3 =τ is the driving torque vector

imposed upon the proximal links; platform loadm m m= + +

rod2 3m / is the equivalent mass of the traveling plate,

platformm is the mass of the traveling plate, loadm is the

mass of the payload, rodm is the mass of the distal links; 2 2

A arm gear rod 12 3I I j I m l= + + / is the equivalent moment

of inertia of the proximal link about its axis of rotation,

armI is the inertia of the proximal link itself, gearI is the

inertia of the reducer and j is its reduction ratio;

( )TAg A A 1 2 3g cos cos cosm r =τ is the gravitational

torque vector of the proximal link with A Am r being the

equivalent mass-radius product about its axis of rotation. Substituting =θ J r into Eq. (8) yields the

simplified model of rigid body dynamics

g ,a v= + +τ τ τ τ (9)

where ,aτ vτ and gτ are the inertial, centrifugal/Coriolis, and gravitational components, respectively,

( )TA ,a m I -= +τ J J r

A ( ),v I =τ f r

TAg ˆgg m-= +τ τ J z .

3 Servo Drive Dynamics

In order to ensure the positioning accuracy of the traveling plate at high speed and high acceleration, a fixed gain PD controller with acceleration feed-forward capability is used as shown in Fig. 3 to compensate for the following error caused by the inertia load variations. Prior to tuning the fixed gain motion controller, the AC servo should be regulated by means of adaptive or manual adjustment. Thus, it is essential to identify the parameters (gain, resistance, inductance and other coefficients) of the servo drive to achieve a precise control model.

Fig. 3. Control scheme of Delta robot

3.1 Servo drive description Fig. 4 shows the block diagram of the AC servo drive of

the robot.

Fig. 4. Block diagram of the AC servo drive

By employing the equivalent transformation law and

the superposition theorem, the AC servo drive can be modeled by the following transfer function:

2

2 1 0r3 2

3 2 1 0

,( )

b s b s b

R s a s a s a s a

+ +=

+ + + (10)


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ìïïïïíïïïïî

where

0 T pi T iva K K K= ,

1 E T T pi T pva K K K K K= + ,

2 ph pi ii T pi Ta J R J K K K K¢ ¢= + + ,

3 Da J L¢= ,

0 pi T ivb K K K= ,

1 pi T pvb K K K= ,

2 pi Tb K K= .

Among the parameters of the servo drive above, some of them are intrinsic and are set or determined by the manufacturer. Their values cannot be altered by us and their significations are listed below:

piK —Plus of current adjuster,

TK —Plus of torque, iiK —Plus of current feedback loop,

phR —Resistance of stator,

DL —Inductance of motor, EK —Coefficient of induction electromotive force,

J ¢—Rotation inertia of motor, T —Feedback coefficient of speed loop.

However, the exact values of the parameters above are not provided and need to be identified. Besides, the parameters of the speed controller pvK and ivK in the model are proportional gain and integral coefficient of the motor driver respectively, which are adjusted and known.

3.2 Identification principle

We use the frequency-sweeping technique to identify the parameters of the servo drive. Assume that the servo drive is excited by the analog voltage representing the command velocity:

m( ) sin( )u t A t= , (11)

where mA and denote the amplitude and circular frequency of the sinusoidal excitation. Then, its response, i.e. the actual velocity of the servo motor can be formulated as follows since the servo drive is linear in nature as modeled by Eq. (10):

T

f f

sin( ) cos( ) sin( )

cos( ) sin

ty t A t A

t

æ ö æ ö÷ ÷ç ç÷ ÷= + = ç ç÷ ÷ç ç÷ ÷ç çè ø è ø

, (12)

where fA and denote the amplitude and phase angle of

the response. Thus, the following discrete time series can be generated:

( )T(0) ( ) ( )y y h y nh=Y ,

Tsin( 0) sin( ) sin( )

cos( 0) cos( ) cos( )

h nh

h nh

æ ö÷ç ÷= ç ÷ç ÷çè øΨ ,

1 f 2 fcos , sinc A c A = = .

So, Y can be expressed as

1

2

c

c

æ ö÷ç ÷= ç ÷ç ÷çè øY Ψ . (13)

Thus, the estimated values of 1c and 2c can be obtained by the least square method:

1 T 1 T

2

ˆ

ˆ

c

c-æ ö÷ç ÷=ç ÷ç ÷çè ø

Ψ Ψ Ψ Y（） . (14)

As a result, the amplitude and phase angle of the response can be determined by

2 2f 1 2ˆ ˆA c c , 2

1

ˆ= arctan

ˆ

c

c

. (15)

For each value of the varying angular frequency, the amplitude and phase angle of the response can be worked out and the parameters in the transfer function can be identified via the curve fitting technique.

4 Controller Parameter Tuning

Since the dynamics of Delta robot is heavily nonlinear and coupled in nature, and inertias imposed upon the motor shafts vary with system configurations, it is impossible to tune the fixed gain controller simply at a specific configuration for achieving satisfactory control quality throughout the entire workspace. Nevertheless, it would be reasonable to tune the controller by minimizing following errors of the travelling plate along a specified path, for example, the Extended Adept Cycle shown in Fig. 5. By only taking into account the dynamics of servo drives, the actual trajectory of the traveling plate can be obtained via the forward kinematic analysis.

( )2 4 2

,

C

,

,

x x

y y

z B B A A

x a z b

y a z b

= - -

+

- /

=

= + (16)

where

( )

( ) ( )

( ) ( )

( ) ( )( )( )

( )

T1 2

T T1 2 1 2

T T1 2 1 2

T T 2 21 1 2 2 1 2

T1 2

T1

2

3

2 2

2

,

ˆ

ˆ

ˆ,

ˆ ˆ

1,

2

ˆ,

1

2

ˆ

2

x y

x x y y x

y

x y x y

x

y

a a

B a b a b a

a

b b b b

a

A

C

a

l l

=

+ -

+ - +

= + + +

+ +

= + -

+ - -

æ öæ ö ÷ç÷ ÷ç ç÷ ÷=-ç ç÷ ÷ç ç÷ ÷çè ø ç ÷ø

+ +

-

è

-

-

t t x

t t y t t z

t t x t t y

t t t t

tQ

t z

t t z


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( ) ( )( ) ( )

( ) ( )

( ) ( )

T T 2 21 1 2 2 1 2

T T 2 21 1 3 3 1 3

T T1 2 1 2

T T1 3 1

1

3

1

,

ˆ ˆ,

ˆ ˆ

.

1

2

i i i

x

y

l l

l l

l

b

b

-

æ ö÷æ ö ç ÷- + -

- + -

- -

-

÷ çç ÷÷ ç=ç ÷÷ çç ÷÷ç ç ÷è ø ÷çè ø

æ ö÷ç ÷ç ÷= ç ÷ç ÷ç ÷è ø-

= +

t t t t

t t t t

t t x t t y

t t x y

t e

Q

t t

u

Q

iu is represented by the position angle of the active joint

i as expressed in Eq. (2).

Fig. 5. Path of the Extended Adept Cycle

It is easy to see that for a given set of controller

parameters pK , dK and affK , the actual joint angular velocity iθ

can be predicted as long as the transfer

function of the servo drive has been available via parameter identification. Thus, the actual angles of the proximal links can be generated. As a result, the actual position of the reference point O¢ can then be calculated. By comparing the discrepancy of actual and the command values of the joint angles, the square root of the positioning error associated with a given configuration along the trajectory can thus be determined as follows:

2 2 2( ) ( ) ( )j j j j j j je x x y y z z¢ ¢ ¢= - + - + - . (17)

( , , )j j j jA x y z represents the coordinate of the jth discrete

point on the actual trajectory and ( , , )j j j jA x y z¢ ¢ ¢ ¢ represents its corresponding coordinate on the theoretical trajectory.

Accordingly, the following optimization problem can be formulated by minimizing the following errors of the travelling plate along the path:

2

1

1

min max

1 p 2 d 3 aff

min ,

s.t. ,

= , = , = .

n

jmj

ii

e

En

x K x K x K

≤ ≤

=

Î=

=å

åx

x x x (18)

Where n represents the number of the discrete points on one trajectory, m represents the number of the chosen trajectories according to different values of angle in Fig. (5), and for each typical trajectory a weight i is given for the sake of good universality of the trajectories.

5 Simulations and Experiments

Simulations and experiments are carried out on a Delta prototype machine developed by Tianjin University to validate the effectiveness of the proposed approach.

Table 1 and Table 2 show the geometry and inertia parameters of Delta robot. For the Extended Adept Cycle

aR and h are given with 350 mm and 25 mm, respectively. By utilizing the 3-4-5 polynomial as the motion rule along both horizontal and vertical directions, we assume in this study the maximum acceleration of the horizontal direction gives 100 m/s2 and that of the vertical direction 50 m/s2. Thus far the input angular velocity could be decided which will be used later.

Table 1. Geometry parameters of Delta robot mm

Parameter Value

Length of the proximal links 1l 375

Length of the distal links 2l 950

Equivalent radius of the base a 175

Equivalent radius of the traveling plate b 50

The offset e in the kinematic model equals a–b.

Table 2. Inertia parameters of Delta robot

Parameter Value

Mass of the traveling plate platformm /kg 0.718

Mass of the payload loadm /kg 0.1

Mass of the distal links rodm /kg 0.773

Inertia of the proximal link armI / (kg·m2) 4422 10-´

Inertia of the reducer gearI /(kg·m2) 46.25 10-´

Reduction ratio of the reducer j 14

The setup of the experiment is illustrated in Fig. 6, of

which the hardware includes an industrial computer, the NI PCI-7354 motion controller, the UMI 7764 interface board, the NI USB-6251 DAQ card, Panasonic servo amplifiers and servo motors assembled on the prototype. In order to guarantee the real-time characteristic, the Windows operating system is adopted. First, the computer makes the signal discrete, and then the signal is changed into analog output by the motion controller. After that the output is sent to the servo amplifier via UMI-7764 interface board. Thereafter, the velocity closed-loop control of the servo system can be done. At the same time the computer also gathers the pulse signal feedback of the encoder via the servo amplifier such that the position closed-loop control can be done. The USB-6251 DAQ card is employed to gather both the command velocity speed signal and the actual velocity signal from the monitoring ports of the servo amplifier for the sake of the servo identification and the validation.


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Fig. 6. Block diagram of experiment equipment

5.1 Servo identification The motor for Delta robot is chosen as Panasonic

MDME202S1H and the corresponding servo amplifier is MEDHT7364. In the identification process, the frequency of the input ranges from 1 Hz to 50 Hz. For each value of the frequency, the amplitude and phase angle of the response can be worked out and then the transfer function of the servo system is established via the curve fitting technique provided by MATLAB, i.e., the invfreqs(·) function and the freqs(·) function. The identification values of the servo system parameters are listed below in Table 3.

Table 3. Identification values of the servo

system parameters

Parameter Value

Plus of current adjuster piK 60

Plus of torque TK /(N·m·A–1) 1.58

Plus of current feedback loop iiK /(V·A–1) 1

Resistance of statorphR / 16

Inductance of motor DL /mH 41.5

Coefficient of induction electromotive force

EK /(V·s·rad–1) 1.315

Rotation inertia of motor J ¢ /(kg·m2) 410 10-´

Feedback coefficient of speed loop T /(V·s·rad–1) 0.106

Fig. 7 shows the comparison between the frequency

response drawn from the test results and that from the fitted transfer function. One can see that the frequency responses of the identified model inosculate with the measured results very well. In the whole test wave band, the absolute error of the amplitude is less than 0.5 dB and that of the phase is less than 6 degrees, which verifies the correctness of the identification.

5.2 Controller parameter tuning

The controller parameters are tuned in the Simulink circumstance of MATLAB. As the prescribed workspace of Delta robot is a cylinder and considering the symmetry of the robot, two representative trajectories are chosen as listed in Table 4. For the certain mounting and practical application of the robot studied in this paper, these two directions are conventional and of equal importance.

Fig. 7. Comparison between the measured and the fitted results

Table 4. Trajectory setting and weight

Position angle /(°) Weight i

0 0.5 30 0.5

It has been noted before that the moment of inertia of

load imposed on the motor shaft is real-time changing when the traveling plate is running the Extended Adept Cycle. In order to accurately reflect the transfer function of the servo system so that the simulation is more realistic, the mass matrix of the robot is derived as follows

( )T 1 2L A 3m I j- -= + /I J J E , (19)

where T 1m J J is the contribution of the traveling plate and A 3I E is the contribution of the equivalent moment of inertia of the proximal links.

When conducting the simulation, replace J ¢ in Eq. (10) with( L ( , )J i i¢ + I )at all the discrete points of the trajectory,

1, 2, 3i . Fig. 8 shows the variations of moment of inertia of load imposed on the motor shafts when the traveling plate moves in the mid-plane of the workspace. The inertia values along the two representative directions in the simulation are marked.

The ranges of the controller parameters have to be determined before tuning. According to controller tuning principle and application practice, usually the proportional


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gain pK of the motion controller should be adjusted in the first place and then the differential coefficient dK and the acceleration feed-forward gain affK are adjusted in sequence. It is indicated beforehand that the objective function in Eq. (18) is unimodal when a single parameter is being adjusted. In this case, when the range of one controller parameter is determined, Fibonacci search method is applied to fast narrow the parameter’s range by comparing the simulation results at the division points. Fibonacci search method[24] is a technique for finding the extremum of a strictly unimodal function by successively narrowing the range of values inside which the extremum is known to exist. It provides a routine for reducing the size of the bracketing of the solution with the help of Fibonacci numbers. Eventually the optimum solution will be achieved rapidly after finite rounds of iterations with the trajectory error of the traveling plate dramatically reduced.

Fig. 8. Variations of moment of inertia imposed

on the motor shafts when the traveling plate moves in the mid-plane of the workspace

In this research for the NI PCI-7354 motion controller,

the ranges of the parameters are restricted as follows: [ ]p 1 30K Î ， , [ ]d 1 60K Î ， , [ ]aff 1 60K Î ， . Figs. 9–11

show the tuning process of the parameters. It concludes that after 7, 9 and 9 rounds of iterations respectively, the optimum parameters are given, namely

( ) ( )p d aff 5 13 22 ,K K K = which make the mean square error of the trajectory of the traveling plate

325.9 10 mmE -= ´ .

Fig. 9. Tuning process of pK

Fig. 10. Tuning process of dK

Fig. 11. Tuning process of affK

5.3 Experimental verification Experiments are conducted on the Delta prototype

machine for purpose of assessing the robot performance under the optimum parameters.

The unit step response of a uniaxial system is shown in Fig. 12, from which one can make out that under the optimized parameters the setting time of the movement is 11.6 ms and the maximum overshoot is 2.39%, while the auto-tuning results lead to 35.4 ms setting time and 10.4% maximum overshoot, the Z-N method lead to 42.4 ms setting time and 19.2% maximum overshoot. It is evident that optimization results are much better.

Let the traveling plate undergoes the Extended Adept Cycle with position angle 0 = and the maximum acceleration of the horizontal direction ,maxha = 100 m/s2. The angular displacements of the three motors are gathered and the differences between the measured signals and the command signals are calculated. The experimental results of one motor compared with that using the auto-tuning method and the Z-N method are displayed in Fig. 13. Fig. 14 shows the trajectory error converted to Cartesian space under the three different parameters respectively. It is observed that the proposed method in this paper leads to more satisfactory results. Compared with other two methods, it reduces the trajectory error of the traveling plate by at least 50%. It can be concluded the Z-N method generates the worst results due to its less consideration of the varying inertia loads on the motor shaft.


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Fig. 12. Step response of the uniaxial system

Fig. 13. Following error comparison in joint space

Fig. 14. Trajectory error comparison in Cartesian space

6 Conclusions

(1) The inverse position, velocity and acceleration models and forward position model of Delta robot are developed, which provide essential mathematics for the trajectory error estimation and parameter optimization.

(2) The parameters of the servo system is identified in the frequency domain by the sinusoidal excitation with variable frequencies.

(3) By taking the mean square tracking error along a typical trajectory as the optimal objective, the parameters of the motion controller (NI PCI-7354) for Delta robot are determined as ( ) ( )p d aff 5 13 22 .K K K = The proposed method takes full account of the varying inertia

loads and its effectiveness is validated by experiments. The tracking error can be reduced by at least 50% in comparison with the conventional auto-tuning and Z-N methods.

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Biographical notes ZHAO Qing, born in 1987, is currently a PhD candidate at Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, China. His research interests include parallel robots and control technology. E-mail: [email protected] WANG Panfeng, born in 1978, is currently an associate researcher at Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, China. He received his PhD degree from Tianjin University, Tianjin, China, in 2008. His research interests include parallel robots, manufacturing equipments and numerical control technology. E-mail: [email protected] MEI Jiangping, born in 1969, is currently an associate professor and a PhD candidate supervisor at Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, China. He received his PhD degree from Tianjin University, Tianjin, China, in 2002. His research interests include manufacturing equipments and systems, industrial robots and production logistic system. E-mail: [email protected]

controller parameter tuning of delta robot based on servo

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