Experiments on IMC-Based PID Controller Designfor a Two-link SCARA Robot
Sipaseuth SUVILATH 1, Taworn BENJANARSUTH 2, Noriyuki KOMINE3 and Khamphong KHONGSOMBOUN 4121International College, King Mongkut’s Institute of Technology Ladkrabang, Thailand
Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Thailand
3
School of Information and Telecommunication Engineering, Tokai University, Japan
4
Faculty of Engineering, National University of Laos, Laos

Introduction

A SCARA robot (Selective Compliance Assembly RobotArm) is a type of robots widely used in factory automation asassembly products robot, soldering robot and so on. In order toperform accurately and robustly, the robot controller should bedesigned suitably. Various schemes such as fuzzy logic [1],Neural network [2], IMC [3] and so on, have been proposed andapplied to SCARA robot controller design. Among variouscontrollers, PID controller is the most popular in industrial scene
due to its simplicity and availability in the market. Mostly, PID
parameters are determined by trial and error process by a skilledexpert. So, in this paper, an easy IMC-Based PID method isapplied to the Two-Link SCARA robot controller design.
In IMC controller design, it consists of 2 steps and its lowpass filter should be selected suitably because it affects theperformance of the system. Many of filters have been selected
for difference kind of models in [4] and [5] but those filters
cannot be used as a filter for the SCARA robot model. So asuitable filter is selected in this paper. Then the IMC controller
is approximated by Maclaurin series expansion to obtain PID
parameters. Then, the parameters are simulated byMatlab/Simulink. Besides, they are also applied to controllercoding in experiment.
2

Mathematical Model

The schematic diagram of the two-link robot manipulator
considered in this paper is shown in Fig.1

while {a, b, a11, a12 , a21, a22 , b11, b12} ∈ R+ .
3

IMC-Based PID Controller Design
The structure of IMC control system is shown in Fig. 2, in

which G is a controlled object, Ĝ is the model of thecontrolled object, C is an IMC controller.
D(s )
U (s)

R (s)
CY (s )GĜFig.2. IMC control system.

In IMC controller design, it composes of two steps.
Step1: Divide the model of the controlled object Gˆ ( s ) into twoparts as Gˆ ( s ) = Gˆ + ( s )Gˆ − ( s ) , where Gˆ + ( s ) contains all thetime delays and right-half-plane zeros. While Gˆ − ( s ) is thetransfer function with minimum phase characteristic andcontains no predictive item.
Step2: To design the internal model controller, a low-pass filterf ( s ) must be added to Gˆ − ( s )−1 to ensure the stability androbustness of the control system.
After rearrange the structure of IMC in Fig.2, the generalclosed loop control can be obtained as Fig.3.
D(s )
R(s)
K

U (s)

Y (s)

GFig. 3. General closed loop control.
Fig. 1. SCARA Robot Diagram.

Then a controller K ( s ) can be expressed as in equation (3).
In order to design a controller by IMC technique, the nonlinear
model [6], [7], is linearized. Then the linear transfer matrix canbe derived as equation (1),K (s) =

Gˆ −−1 ( s )f −1 ( s ) − Gˆ ( s )(3)+G (s) =

θ (s)
E (s)

=− a12 s  a11s + b11−asas + as + bs 2122 s + b22 
132(1)

With a suitable choice of f ( s ) , the controller K ( s ) can possess
the integral action and appear in the following form,

1
K ( s) = Q( s) .
s(4)By performing the Maclaurin series expansion
for Q( s) , the controller K ( s ) can be expressed as&&(0)s 2
1
QK (s ) ≅ Q(0) + Q& (0)s ++ ... .
s 2!
(5)By ignoring the higher order terms, the PID controller
can be obtained as

Ki+ Kd s ,swhere its parameters areK (s) ≅ K p +Fig. 5. Simulation and Experimental results for the firstlink.

(6)&&(0) / 2 .
K p = Q& (0), K i = Q(0) and K d = Q
In this paper, the suitable filter is selected as equation (7).

f (s) =4

zs + 1(7)xs + ys 2 + zs + 1
3Fig. 6. Simulation and Experimental results for thesecond link.

Simulation and Experimental Results

Two closed loop PID controllers are designed independentlyto control each link as depicted in Fig. 4.

r1

e1

u1

θ1

r2

e2

u2

θ2Fig. 4. Proposed control system structure.

5References[1]

The filter’s parameters x, y and z are tuned and thecorresponding PID parameters can be computed as in Table 1.

[2]

Table 1. The parameters both controllers

yxzKpKi

Kd

PID1

15.10−5

5.10−3

5.10−1

4165

4PID2−5−3−1

4673

420.10

4.10

5.10Conclusion

In this paper, previous works, mathematical model, IMCBased PID controller design method and simulation results arebriefly reviewed. The PID parameters obtained in IMC-BasedPID controller design are applied to the actual Two-Link
SCARA robot. From the experiments, the results are nearly
identical to the simulations. Both simulations and experiments
demonstrate that the outputs of the proposed control system cantrack the reference inputs without steady-state error. Moreover,the effects of input disturbances can be rejected.

The parameters in Table 1. are applied in both simulations
and experiments as follows.
The step reference inputs at 45o are applied to both links
separately until the outputs reach the desired positions and thenthe input disturbances at 4 volts are applied to both links at 4.5
seconds as shown in Fig. 5 and Fig. 6.
We can observe that the step output responses from both
simulation and experimental results can attain to the set point
rapidly and identically with overshoot about 14% but withoutsteady-state error. Meanwhile, the system can reject the input
disturbance and return to the set point within 2 seconds.

[3]

[4]

[5]

[6]
[7]

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