Page 156 - IJOCTA-15-3

E.M. Shaban / IJOCTA, Vol.15, No.3, pp.517-534 (2025)
Here, the state vector, x k , for the 5.1. State-dependent parameter model for
bitumen system is defined as x k = reeling/packing machine
T
z k e k ∆e k u k−1 u k−2 . In this indus-
A SIEMENS’s AC three-phase servo motor drives
trial example, SDP-PID+/LQ control was applied the reeling drum (7 kW/2000 rpm) through an
′
by freezing the parameters of {F , g} at ambi-
k analog input signal of 0-10 VDC. The encoder
o
ent temperature, i.e. y k−3 = 30 . Simulation
AUTONICS (2048 PPR/5-24 VDC) is installed
trials showed that the weights R = 1 and Q =
on the floating drum to monitor its speed from 0
diag{5 1 20000 1 1} were appropriate for obtaining
to 1500 rpm, as shown in Figure 9.
the time-invariant P matrix. Equation (30) was Open-loop experiments identified an optimal
then used to calculate the SDP-PID+ gain vec- sampling rate, ∆t = 0.5 sec, balancing accu-
+
tor, k . Finally, the control law in Equation (24)
k rate response measurement without redundant
was implemented for real-time bitumen tempera- encoder reads. The experiments yielded an SDP-
ture control, as depicted in Figure 7. This figure TF model with a triad {1, 1, 3} as follows in
illustrates the practical implementation and sim- Equation (40),
ulation results of the SDP-TF model in Equation
(38). It is worth noting that satisfactory rejection
of the disturbances is shown when controlling the y k = −a 1 (χ k ) y k−1 + b 3 (χ k ) u k−3 (i)
temperature of the bitumen. 13 a 1 (χ k ) = −0.0564 u k−2 + 0.2836 (ii) (40)
The nonlinear SDP-PID+/LQ control b 3 (χ k ) = −0.0675 y k−1 + 192.0957
achieved suitable closed-loop performance, main-
where y k represents the floating drum’s speed
taining the response within the ±5% permissible
(rpm) and u k is the voltage input to the AC three-
range without overshooting. Negligible differ-
phase servo motor of 0 to 10 VDC. The SDPs
ences were observed between the practical and the
a 1 (χ k ) and b 3 (χ k ), denoted as a 1,k and b 3,k respec-
SDP-TF model responses in Equation (38). This tively, are time-variant and depicted in Figure 10.
demonstration marks the first successful onsite The model fit of the estimated SDP-TF in Equa-
application of SDP-PID+ control in an industrial tion (40) to experimental data achieved a satis-
bitumen system, providing robust temperature factory coefficient of determination, R 2 = 0.95,
tracking and control performance. T
as illustrated in Figure 11.

5.2. Controller design and implementation
5. Industrial reeling/packing machine for reeling/packing machine

The industrial reeling/packing machine used in By merging and rearranging Equation (40), the
the bitumen membrane sheet production line at updated SDP-TF model is expressed as follows in
INSUMAT company, Sadat City, Egypt, incor- Equation (41).
porates nonlinear SDP-PID+ control methodol-
ogy integrated into FPGAs. This control sys-
y k = − (0.0675 u k−3 − 0.0564 u k−2 + 0.2836) y k−1
tem manages the pulling motor that regulates
+ 192.0957u k−3
the velocity of the floating drum. Its primary
(41)
function is to maintain the bitumen sheet within
The SDPs may be further refined as Equation
the accumulator at an acceptable range (15–85%)
(42).
by adjusting the motor’s reference speed (Figure
8). The SDP/PID+ control system dynamically
a 1 (χ k ) = 0.0675 u k−3 − 0.0564 u k−2 + 0.2836
counteracts disturbances detected through a feed-
back encoder mounted on the floating drum. The b 3 = 192.0957
FPGA-based control strategy uses the LabVIEW- (42)
FPGA module to enable simultaneous control op- The SDP-TF model in Equation (41) may be
erations. Detailed hardware and software inter- reformulated using the operator, z −1 , as Equation
facing is provided in Shaban et al. 15 (43).
The system’s primary objective is to prevent −3
productivity losses caused by excessive infoldings b 3 z
y k = u k (43)
of bitumen sheets around the reeling drum or in- 1 + a 1 (χ k+1 ) z −1
terruptions due to emergency shutdowns. This Here, the output parameter a 1 (χ k ), defined in
would reduce reliance on operator skills and de- Equation (42), is state-dependent on the lagged
crease workload, enhancing productivity and min- input χ k = f (u k−3 , u k−2 ), while the input pa-
imizing production costs. rameter b 3 , is time-invariant.
528