Instrumentation & Measurement Magazine 24-2 - 115

Table 4 - Controller tuned parameters
Case

Table 5 - Experimentally tuned parameters

Value
Kp

Ki

Kd

μ

λ

1

7.0544

106.8000

0.1000

0.9844

0.9801

2

8.9941

113.4588

0.1631

0.9184

0.9580

3

4.8279

102.4354

0.1038

0.9187

0.9835

As shown in Fig. 6, the FOPID controller is able to control the system very well, with a very small root mean
square (RMS) error of 0.0132 and maximum overshoot of
0.00418 m/s. Fig. 6 also shows that during the operations,
while there are fluctuations in the pressure signal, the controller maintains output velocity signal smooth and accurate.
Thus, the position signal is smooth while maintaining a maximum control input of 4 V to the motor. In fact, the RMS of

Fig. 6. Controller's performance in the presence of pink noise.
April 2021	

Case

Value
Kp

Ki

Kd

μ

λ

3

4.8279

102.4354

0.1038

0.9187

0.9835

Tuned

4.5

0.10

0.9187

0.9835

81.5

jerk is 0.0836, and the jerk does not exceed 0.6 m/s3 during
the whole simulation.

Experimental Results for the FOPID Controller
Based on the Case 3 parameters of Table 4 (obtained based on
the MNM algorithm), a FOPID controller was designed and
further tuned to compensate for the many different nonlinearity and uncertainties in the actual system which are not present
in the mathematical model upon which the Simulink model
was based. Thus, the FOPID parameters are further adjusted
and chosen as follows, listed in Table 5.
Using the experimental test rig illustrated in Fig. 1, the
FOPID controller with the MNM tuned parameters was
tested for various loads and velocity profiles. Fig. 7 and Fig.
8 describe the results of experiments for a 0.05 (m/s) and 0.07
(m/s) maximum reference velocity, respectively, each for
weights of 0 kg, 163 kg and 367 kg.
As shown in Fig. 7 and Fig. 8, the controller is able to
track the reference with limited oscillation in the velocity
trajectory, which inherently exists in the system because of
the switching nature of the quadrants, and no observable

Fig. 7. Experimental results for reference velocity of 0.05, weights of 0 kg, 163
kg and 367 kg.

IEEE Instrumentation & Measurement Magazine	115



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