Instrumentation & Measurement Magazine 24-2 - 114

Fig. 3. Block diagram for optimization simululation.

Fig. 5. Optimization results for three controllers: (a) Case 1, (b) Case 2 and (c)
Case 3, (zoomed).

Control of the EHA

Fig. 4. Optimization results for three controllers: (a) Case 1, (b) Case 2 and (c)
Case 3.

The simulations produced the optimal controller parameters [Kp, Ki, Kd, μ, λ], as listed in Table 4.
Out of the three controllers studied above, the third case is
chosen as the final controller because it is less sensitive to noise
and disturbance which exists in the actual system compared to
the other two.

The structure of the control strategy is the same as in Fig.
3, with the only difference being that the parameters of the
FOPID controller are chosen based on Case 3 tuned parameters obtained from the MNM algorithm.
The simulation has been done with the sampling frequency
of fS = 1 kHz frequency and the parameters shown in Table 2.
The results of the experiment are shown in Fig. 6. Furthermore,
a correlated fractional pink noise with the power of 0.001 and
frequency of 1 kHz has been added to the simulation to study
the controller's performance.
The reference signal for the simulation is based on four
pulses with the magnitude of 0.05 m/s. This reference, from
the home position, essentially brings up the arm, performs a
dig and goes back to the home position.

Table 3 - Parameters for the Tuning Simulations
Parameter

Symbol

Value

Number of poles and zeros in the approximation method

M

2

FOPID parameter upper bounds

Λmax

[200, 200, 200, 1, 1]

FOPID parameter lower bounds

Λmin

[0.1, 0.1, 0.1, 0.01, 0.01]
2500

Maximum number of iterations for each run

Nmax

Maximum number of restarts (runs)

R

20

Weight of error term

wE

1, 1.5

Weight of jerk term

wJ

0.2111, 0.1111

114	

IEEE Instrumentation & Measurement Magazine	

April 2021



Instrumentation & Measurement Magazine 24-2

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