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A modified graphical based tuning and performance analysis of second order LADRC . . .
from the increased number of tuning parameters • Establish a generalized tuning approach
and the choice of the ESO order. To overcome applicable to a wide range of system dy-
2
this issue, the ADRC was remodelled with a lim- namics, including stable, unstable, inte-
ited number of tuning parameters that can be eas- grating, and time-delayed systems, and
ily implemented in real-time. This development those with RHPZs. This contrasts with
has significantly expanded the scope of LADRC traditional methods, which often require
in many fields, such as Robotics, MEMS, Power custom tuning rules for specific system
converters, flight control, power plant control sys- types.
tems, gasoline engine control, and induction ma- The major contributions of the paper are sum-
chine control. marised as follows:
The theoretical foundation of ADRC, the (i) A simplified 2-DOF structure of SLADRC
role of tuning methods in LADRC, and various is employed, resulting in a controller with
dimensions of analyzing ADRC were reviewed only two tuning parameters.
in. 3–6 Improved LADRC performance with sim- (ii) Unique tuning formulas for the controller
plified tuning can be achieved by incorporating parameters are derived using frequency-
the known plant dynamics, either entirely or par- domain specifications. Designing con-
tially, into the LADRC structure, 7–11 which re- troller using frequency domain specifica-
sults in a faster control response but reduces its tions provides intuitive insights into sys-
ability to reject output disturbances quickly. In tem stability, performance, and robust-
a few other methods, the performance was en- ness. Trade-offs like speed versus noise
hanced by adding additional structures, such as sensitivity are visually apparent. It en-
the Smith predictor, 12,13 or by combining addi- ables independent tuning for disturbance
tional controllers, such as IMC, for various com- rejection, noise attenuation, and stabil-
plex systems. 14 ity across frequency ranges for SISO and
Existing tuning methods for LADRC MIMO Systems.
are model- dependent, complex, and lack (iii) The admissible region for parameter selec-
standardization. 15–18 Iterative tuning of the tion is determined from the tuning formu-
LADRC was performed 19,20 based on perfor- lae, providing search bounds that satisfy
mance and robustness specifications using the the design specifications.
Nyquist plot for uncertain systems 21 that are not (iv) Two approaches are presented for opti-
suitable for nonlinear and unstable systems and mal selection of design specifications: an
require iterative processes without clear guide- iterative method and a heuristic-based
lines for constraints. method.
Different tuning approaches, such as tun- (v) The effectiveness of the proposed ap-
ing using complex optimization techniques proach is demonstrated through both
with constraints, 22,23 data-driven iterative benchmark simulation problems and real-
approaches, 24 half-gain-based tuning, 25 and op- time DC motor speed control experi-
timal parameter tuning, 26 have been attempted ments.
in the literature. Although improvements have The rest of the paper is organized as follows:
been made, a robust, model-independent tun- Section 2 formulates the problem. Section 3 de-
ing approach is still needed. Although First scribes the proposed tuning. Section 4 presents
order LADRC simplifies tuning, Second-order the optimum controller selection. Section 5 il-
LADRC (SLADRC) offers superior performance lustrates the simulation and experimental study.
in complex systems. However, higher-order Finally, Section 6 draws conclusions.
LADRC increases the tuning complexity and
noise sensitivity. 27 To overcome these limita- 2. Preliminaries and problem
tions, this study proposes a generalized frequency- formulation
domain approach for tuning SLADRC parame- Consider a general nth-order system dynamics as,
ters, aiming to,
• Develop a systematic analytical method n n−1 n−2
d y d y d y
for precise SLADRC parameter optimiza- = f , , . . . , y(t), d(t), t +b 0 u(t)
tion to attain the desired performance ob- dt n dt n−1 dt n−2
(1)
jectives.
• Ensure that the tuning process is intu-
n−1 n−2
itive, accessible to practitioners, and con- d y d y
andf , , . . . , y(t), d(t), t = f(t)
sistently yields robust results. dt n−1 dt n−2
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