Page 146 - IJOCTA-15-3

E.M. Shaban / IJOCTA, Vol.15, No.3, pp.517-534 (2025)
Previous research on PID+ controllers has bitumen membrane sheet production line
demonstrated their applicability across many using FPGA technology. 15
practical systems. Notable applications include The first demonstrator introduces a slow ther-
robot arm control, 11,12 industrial temperature mal dynamic system, focusing on temperature
regulation of bitumen tank systems, 13 liquid stor- control of bitumen within a tank before it is mixed
age tank loading/unloading control, 14 and speed 13
with additives such as polymers and fillers. In
control in reeling/packing machines equipped
contrast, the second demonstrator represents a
with field programmable gate array (FPGA) fast response dynamic of an electric motor, specif-
modules. 15 These applications cover systems with
ically the speed control of the pulling motor in the
varying response times, from slow thermal pro-
reeling/packing machine used in the production
cesses to fast electric motors, and have shown con- 15
line of bitumen membrane sheets. FPGAs are
sistent on-site success.
leveraged to optimize performance in this appli-
The theoretical foundation of PID+ control cation, taking advantage of their inherent parallel
is built upon state-dependent parameter (SDP) processing capabilities. 15
models, which represent nonlinear systems using Sections 2 and 3 outline the identification
quasi-linear structures. These models describe methodology and the extension of the SDP-PID+
system parameters as functions of state variables, approach, which facilitates the intuitive handling
allowing nonlinear dynamics to be approximated of processes characterized by discrete-time TFs of
as linear systems at each sampling instant. 16 any order and sampling time delays. Sections 4
Such SDP-TF models facilitate the design of non- and 5 describe the seamless implementation of the
linear control laws using well-established linear approach for each demonstrator. Finally, conclu-
techniques. 17–21 Additionally, incorporating non- sions are presented in Section 6.
minimal state space (NMSS) representations en-
ables direct SVF control without observers or re-
constructors, simplifying implementation. 22,23 2. System identification
Conventional PID designs often fail to pro- 2.1. Model structure
vide robust performance for high-order pro-
cesses with significant delays. For example, The deterministic form of the SDP-TF for single-
Chien–Hrones–Reswick and Ziegler–Nichols tun- input, single-output (SISO) models may be de-
16,23
ing have produced noisy control actions in sys- fined as in Equation (1),
tems such as bitumen temperature regulation. 10 T
To address these limitations, the novel SDP- y k = Π Φ k (1)
PID+ control strategy was introduced and ap-
plied in previous studies, 11,13–15 incorporating
additional input/output compensators to ad- where Π is a vector of lagged input and output
dress sampling delays and higher-order dynamics. variables and Φ k is a vector of SDP parameters,
Building upon this foundation, the present work defined in Equation (2).
further enhances the approach by formulating its
T
control algorithms to regulate processes charac- Π = −y k−1 . . . −y k−n u k−1 . . . u k−m
T
terized by discrete-time TFs of any order effec- Φ k = a 1 {χ k } . . . a n {χ k } b 1 {χ k } . . . b m {χ k }
tively and with arbitrary sampling time delays. (2)
This refinement facilitates the seamless imple-
mentation of the SDP-PID+ algorithm across two Here, y k and u k represent the system’s output
distinct industrial applications, 13,15 in regards to and control input, respectively, while a i {χ k } for
their varying response times. Additionally, the i = 1, . . . , n and b j {χ k } for j = 1, . . . , m are
approach streamlines the design process, reducing SDPs for which they are assumed to be functions
computational effort while enhancing robustness of a non-minimal state vector, χ k , not necessar-
and closed-loop control performance. The two ily y k−i . or u k−j . However, for the SDP-PID+
practical applications are as follows: control system design in the current paper, it is
sufficient to limit the model in Equation (1) to
χ k = Π. It is worth noting that any time de-
(i) Industrial bitumen tank system. Temper- lay, i.e. δ ≥ 1, is accounted for by setting the
ature regulation to ensure product quality leading terms b 1 {χ k } . . . b δ−1 {χ k } to zero. Fi-
and safety during mixing. 13 nally, n and m are integers representing the max-
(ii) Industrial reeling/packing machine. imum lag associated with the output and input
Speed control of a pulling motor on the variables, respectively. Therefore, the SDP-TF in
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