Microsoft Word - CET--006.docx


 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 59, 2017 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Zhuo Yang, Junjie Ba, Jing Pan 
Copyright © 2017, AIDIC Servizi S.r.l. 
ISBN 978-88-95608- 49-5; ISSN 2283-9216 

Design of Joint Controller for Welding Robot and Parameter 

Optimization 

Chengxiang Li 

Automible Department, W eifang University of Science and Technology, Shouguang 262700, China 

LICHENGXIANG@163.com 

Joint control is the basis for welding robot to complete task space trajectory tracking, and the precision of joint 

control is directly related to the motion performance and precision of the robot. For the coherent and non-

linear dynamic characteristics of welding robot, we use fuzzy logic to dynamically adjust the controller 

parameters, to improve the performance of trajectory tracking control. And then we set up the fuzzy rules to 

adjust the PID parameters according to the trajectory tracking error and the error change rate, and obtain the 

optimal initial PID parameters by optimal algorithm at the beginning of the trajectory tracking. In the trajectory 

tracking process, the PID parameter increment calculated by fuzzy controller is superimposed on the initial 

PID parameter, so that dynamically optimize joint controller parameters. The study shows that, application of 

dynamic fuzzy PID control can bring better single-joint step response performance and multi-joint linkage 

trajectory tracking performance than mere PID control. 

1. Introduction 

Joint control is the basis for welding robot to complete task space trajectory tracking, and the precision of joint 

control is directly related to the motion performance and precision of the robot. The classical robot control 

method is to utilize PID controller of each joint (Wen et al., 2009), and then carry out tuning and optimization of 

the PID controller. In order to make the PID controller parameters adapt to the changes of the robot dynamics, 

we may adopt the intelligent methods such as fuzzy logic, genetic algorithm and neural network to conduct 

dynamic adjustment on PID controller parameters, or directly use the intelligent controller to track the control 

of the welding robot. 

Almost all the international mature robot products are taking PID controller as the basic controller, and 

combined with parameter dynamic optimization strategy and compensation strategy, that is because PID 

controller parameter adjustment is simple, and it can achieve high precision trajectory tracking under certain 

conditions. While intelligent control methods often need to consume a lot of computing resources, and the 

controller parameter adjustment process is complicated. In this paper, for the coherent and non-linear dynamic 

characteristics of welding robot, we use fuzzy logic to dynamically adjust the controller parameters, to improve 

the performance of trajectory tracking control. And then we set up the fuzzy rules to adjust the PID parameters 

according to the trajectory tracking error and the error change rate, and obtain the optimal initial PID 

parameters by optimal algorithm at the beginning of the trajectory tracking (Martin et al., 2008). In the 

trajectory tracking process, the PID parameter increment calculated by fuzzy controller is superimposed on the 

initial PID parameter, so that dynamically optimize joint controller parameters (Xiao et al., 2016). 

2. Design of joint controller for welding robot 

Welding robot has coherent and non-linear dynamic characteristics. In the process of exercise, the equivalent 

inertia moment of each joint is changing. In order to make the PID controller to adapt to a large degree of time 

characteristics of the robot process, we use fuzzy logic to adjust the controller parameters online, and 

construct the fuzzy PID controller. The fuzzy PID controller is based on PID controller, to carry out fuzzy 

inference with certain fuzzy rules, and get the adjustment of PID parameters, so that update PID controller 

parameters.  

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1759017

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Chengxiang Li, 2017, Design of joint controller for welding robot and parameter optimization, Chemical Engineering 
Transactions, 59, 97-102  DOI:10.3303/CET1759017   

97



The core of fuzzy PID controller design is to establish appropriate fuzzy rules according to technical 

knowledge and practical experience of engineering designer, and then with the error e and error change rate ė, 
to get the fuzzy control table adjusting the three controller parameters of kp, ki, kd

 (Khooban et al., 2013).  

The fuzzy rules of adjustment of kp, ki, kd are respectively shown as Table 1~ Table 3. 

Table 1: Fuzzy rules of △kp 

△kp 
ė 

NB NM NS ZO PS PM PB 

e 

NB PB PB PM PM PS ZO ZO 

NM PB PB PM PS PS ZO NS 

NS PM PM PM PS ZO NS NS 

ZO PM PM PS ZO NS NM NM 

PS PS PS ZO NS NS NM NB 

PM PS ZO NS NM NM NM NB 

PB ZO ZO NM NM NM NB NB 

Table 2: Fuzzy rules of △ki 

△ki 
ė 

NB NM NS ZO PS PM PB 

e 

NB NB NB NM NM NS ZO ZO 

NM NB NB NM NS NS ZO ZO 

NS NB NM NS NS ZO PS PS 

ZO NM NM NS ZO PS PM PM 

PS NM NS ZO PS PS PM PB 

PM ZO ZO PS PS PM PB PB 

PB ZO ZO PS PM PM PB PB 

Table 3: Fuzzy rules of △kd 

△kd 
ė 

NB NM NS ZO PS PM PB 

e 

NB PS NS NB NB NB NM PS 

NM PS NS NB NM NM NS ZO 

NS ZO NS NM NM NS NS ZO 

ZO ZO NS NS NS NS NS ZO 

PS ZO ZO ZO ZO ZO ZO ZO 

PM PB NS PS PS PS PS PB 

PB PB PM PM PM PS PS PB 

 

When the velocity closed loop parameters are fixed, the position closed loop PID parameters have a certain 

range of adjustment. The fuzzy sets of △kp, △ki and △kd are defined as {NB, NM, NS, ZO, PB, PS, PM, PB}. 

The domain boundary is set as the corresponding parameter adjustment of each joint in the maximum and 

minimum inertia. Similarly, the fuzzy sets of the error e and error change rate ė are also defined as {NB, NM, 
NS, ZO, PB, PS, PM, PB}, and their domains need to be determined according to actual situation, and the 

specific process is: firstly, take the PID parameters optimized at the start of the trajectory as fixed values, to 

control the trajectory tracking robot, and get the variation range of error and error change rate; then enlarge 

the range appropriately as the domain of enlarge the range appropriately in fuzzy position PID controller. The 

membership function of each fuzzy variable in the neighborhood of the domain boundary is the trapezoidal 

membership function, and the other segments are triangular membership functions. 

This paper uses Matlab to establish the fuzzy PID control simulation model of robot joint controller, as shown 

in Figure 1, and then take use of the position PID parameter optimization method to get the initial PID 

parameters. 

98



 

Figure 1: Fuzzy PID control simulation model of robot joint controller 

In the process of joint movement, dynamically adjust PID parameters by fuzzy logic, to get the error curve of 

the step response of fuzzy PID control, and thus compare it with the Step response error curve of fixed PID 

parameter, as shown Figure 2. 

 

 

Figure 2: Step response comparison between fuzzy PID and fixed PID 

We can see that, when adopting the fuzzy PID controller, both the overshoot and adjustment time of joint step 

response are smaller than that of fixed PID control. The adjustment time of the former is 0.045s, while the 

adjustment time of the latter is 0.091s. PID dynamic parameter adjustment process is shown in Figure 3. 

 

 

Figure 3: PID dynamic parameter adjustment process 

3. Parameter optimization of joint controller for welding robot 

Single joint control of robot is the basis of six joint control and trajectory tracking control (Reham et al., 2016). 

When using PID controller as robot joint controller, the initial control parameters of each joint should be 

adjusted, to make the robot's motion performance and trajectory tracking achieve the desired state and the 

effects of gravity and inertia coupling are neglected (Liu, 2014). First of all, we adjust the parameter of speed 

closed loop PI controller, and then adjust the parameter of position closed loop PID controller (Meza et al., 

2012). 

Using PI controller can make the speed closed loop remains stable. The speed closed loop transfer function is 

as below: 

99



G𝑚𝑣 (S) =
Ω(𝑆)

𝑉(𝑆)
=

𝐾𝑣𝑝 𝐾𝐼 (𝑇𝑣𝑖 𝑆+1)

𝑇𝐽𝑇𝑣𝑖 𝑆
2+(𝐾𝑣𝑝𝐾𝐼 𝑇𝑣𝑖 )𝑆+𝐾𝑣𝑝 𝐾𝐼

  (1) 

The coefficients of the closed loop transfer function are positive real numbers, according to Routh criterion, we 

can know that the speed closed-loop is stable. Slow response of the closed-loop speed will cause the delay of 

the closed loop, in the absence of vibration of the robot joint, the setting value of 𝐾𝑣𝑝 is larger, the faster speed 

closed-loop response will be.  

In order to make the speed closed-loop controller work in an ideal state, the control parameters 𝐾𝑣𝑝 and 𝑇𝑣𝑖  

need to be optimized. The step response can effectively test the transient and steady state performance of the 

controller, therefore, the step response is used to analyze the controller performance under various PI control 

parameters. We adopted the sequential quadratic programming algorithm to establish the PI controller 

parameter optimization model, whose optimization target is as below: 

min(t𝑠) 

𝑠. 𝑡. 𝑀𝑝 ≤ 1%, 𝑒𝑠𝑠 ≤ 0.1%, 𝜏𝑚𝑎𝑥 ≤ 𝜏𝑈𝑃   (2) 

In the formula, t𝑠 is adjustment time; 𝑀𝑝 is maximum overshoot; 𝑒𝑠𝑠 is steady - state error; 𝜏𝑚𝑎𝑥  is maximum 

control torque. 

In order to make the speed closed loop has a faster response performance, the maximum permissible 

overshoot is 1%; maximum permissible steady state error is 0.1%. Under the two circumstances of maximum 

inertia and minimum inertia pose, we optimized the parameters of the speed closed-loop controller, to find out 

the optimal PI parameters for each joint to reach a certain speed in the shortest time.  

Taking the joints of the welding robot as the control object, and establish a single joint speed controller 

parameter optimization model with Matlab, as shown in Figure 4. 

 

Figure 4: Parameter optimization model of single - joint speed controller 

We use the sequential quadratic programming algorithm to optimize the parameters of the speed controller, 

and obtain the optimized PI controller parameters and step response performance of each joint of welding 

robot, as show in Table 4. 

The PID controller can be used to make the single joint position closed loop with good robustness and control 

precision. For the position closed loop, speed closed loop is a second order system, so reasonable 

configuration of position PID parameters will help achieve arbitrary configuration of the position closed-loop 

system pole (Sood, 2011), so as to guarantee the stability of position closed loop. The transfer function of 

closed loop control of robot joint position control is as below: 

G𝑚𝑝(S) =
θ(𝑆)

𝑅(𝑆)
=

𝑏0𝑆
3+𝑏1𝑆

2+𝑏2𝑆+𝑏3

𝑎0𝑆
4+𝑎1𝑆

3+𝑎2𝑆
2+𝑎3𝑆+𝑎4

  (3) 

Still taking each joint of welding robot as the control object, establish the optimization model of single joint 

position controller parameters by Matlab, as shown in Figure 5. 

 

100



 

Figure 5: Optimization model of single joint position controller parameters 

Table 4: Optimized PI controller parameters and step response performance of each joint 

Joint 
Inertia 

(Kg·m2) 

Jump amplitude 

(°/s) 

Overshoot 

(%) 

Proportional 

gain 

Adjustment time 

(s) 

Steady-state 

error (°) 

1 

7.8238 

1.00 0.0087 133.9 0.003 3.9e-6 

60.00 0.1873 2.231 0.129 2.1 e-5 

148.76 0.0429 0.090 0.364 -5.9 e-4 

58.6888 

1.00 0.4906 92.39 0.020 4.3 e-6 

60.00 1.2437 1.54 0.751 3.1 e-8 

148.76 0.0068 0.62 2.712 -2.7 e-7 

2 

26.9309 

1.00 0.4016 105.9 0.004 1.2 e-6 

60.00 2.4318 1.77 0.244 -2.7 e-4 

111.11 0.0064 0.95 0.435 1.8 e-4 

42.5914 

1.00 0.6033 92.06 0.006 9.8 e-6 

60.00 0.0109 1.53 1.002 2.5 e-4 

111.11 0.0113 0.83 1.165 4.1 e-4 

3 

3.6440 

1.00 0.0161 188.80 0.001 5.4 e-6 

60.00 0.0012 3.15 0.088 1.3 e-4 

148.76 0.3347 1.27 0.152 -1.2 e-4 

5.6005 

1.00 0.2585 152.9 0.002 4.3 e-6 

60.00 0.0032 2.55 0.129 1.5 e-4 

148.76 0.0822 1.03 0.288 -8.5 e-5 

4 0.9575 

1.00 0.2909 87.8 0.0029 7.6 e-6 

60.00 0.0012 1.4627 0.1434 3.0 e-5 

150.00 0.0807 0.5851 0.2833 3.2 e-6 

5 0.0180 

1.00 0.0000 60 0.0008 -4.6 e-7 

60.00 0.0345 1.9457 0.0294 4.9 e-4 

225.00 0.9132 0.5185 0.0377 -2.6 e-4 

6 0.0003 

1.00 1.0000 124.8 0.0000 -2.6 e-7 

60.00 0.0000 86.4 0.0003 6.9 e-5 

225.00 0.0033 23.0376 0.0641 6.2 e-4 

 

fffWe still use step response as an evaluation method for the single joint position controller, and the 

optimization objective is as below: 

min(t𝑠) 

𝑠. 𝑡. 𝑎0 ≥ 0.001, 𝑎1 ≥ 0.001, 𝑏1 ≥ 0.001, 𝑐1 ≥ 0.001, 𝑑1 ≥ 0.001  

 𝑀𝑝 ≤ 1%, 𝑒𝑠𝑠 ≤ 0.1%, 𝜏𝑚𝑎𝑥 ≤ 𝜏𝑈𝑃  (4) 

What is different from speed closed loop optimization index is that, the position closed loop requires the speed 

controller parameters and position PID controller parameters to be configured in order to ensure the stability of 

the system, and position closed loop requires small overshoot, to avoid the flutter phenomenon in the process 

of robot motion. Sequential quadratic programming algorithm was adopted for parameter optimization of 

position controller, and obtained the optimal parameters of each joint position controller, as shown in Table 5. 

101



Table 5: Optimized parameters and step response performance of each joint 

Joint 

Jump 

amplitude 

(°/s) 

Inertia 

(Kg·m2) 

Position 

loop Kpp 

Position 

loop Kpi 

Position 

loop Kpd 

Speed 

loop 

KvpKI 

Speed 

loop Tvi 

Adjustment 

time (s) 

1 7.924e-4 
7.824 277.594 0.923 2.108 10.621 0.223 0.032 

58.689 277.110 0.577 5.920 7.339 0.076 0.045 

2 5.917e-4 
26.904 264.549 1.901 1.617 11.817 0.266 0.022 

42.591 224.890 1.910 1.787 11.972 0.297 0.026 

3 7.924e-4 
3.644 288.763 44.684 0.855 14.398 0.093 0.012 

5.601 305.885 64.799 1.325 11.007 0.066 0.017 

4 7.990e-4 0.958 483.340 476.051 3.775 3.963 0.018 0.019 

5 0.0012 0.018 383.741 417.428 0.811 4.428 0.114 0.016 

6 0.0012 0.001 1882.600 1817.500 2.000 40.100 0.216 0.006 

Reference  

Khooban M.H., Alfi A., Abadi D.N.M., 2013, Teaching–learning-based optimal interval type-2 fuzzy PID 

controller design: a nonholonomic wheeled mobile robots, Robotica, 31(7), 1059-1071, DOI: 

10.1017/S0263574713000283. 

Liu Z., 2014, The Hardware Design of Control System of Coal Mine Detection Robot AC Servo Drive, Applied 

Mechanics & Materials, 556-562, 2229-2232, DOI: 10.4028/www.scientific.net/AMM.556-562.2229. 

Martins F.N., Celeste W.C., Carelli R., 2008 An adaptive dynamic controller for autonomous mobile robot 

trajectory tracking, Control Engineering Practice, 16(11): 1354-1363, DOI: 

10.1016/j.conengprac.2008.03.004. 

Meza J.L., Santibanez V., Soto R., 2012, Fuzzy Self-Tuning PID Semiglobal Regulator for Robot Manipulators, 

IEEE Transactions on Industrial Electronics, 59(6), 2709-2717, DOI: 10.1109/TIE.2011.2168789. 

Reham H., Bendary F., Elserafi K., 2016, Trajectory Tracking Control for Robot Manipulator using Fractional 

Order-Fuzzy-PID Controller, International Journal of Computer Applications, 134, DOI: 

10.5120/ijca2016908155. 

Sood V., 2011, Autonomous Robot Motion Control Using Fuzzy PID Controller. High Performance Architecture 

and Grid Computing, Springer Berlin Heidelberg, 385-390, DOI: 10.1007/978-3-642-22577-2_52. 

Wen G., Xu L., He F., 2009, Offline Kinematics Simulation of 6-DOF Welding Robot, IEEE Computer Society, 

DOI: 10.1109/ICMTMA.2009.608. 

Xiao Y.J., Jing R., Song H.P., Zhu N., Yang H., 2016, Design and experiment on zinc-air battery continuous 

power controller based on microcontroller, Chemical Engineering Transactions, 51, 91-96, DOI: 

10.3303/CET1651016. 

 

102