A comparative study on time-delay estimation for time-delay nonlinear system control
Open accessAbstract
Time delay and disturbances are commonly encountered in real-world application systems, and their existence significantly hampers the operation of various controllers available in the discipline of control systems theory. Time-delay estimation and disturbance compensation are closely related to obtaining the desired system stability and efficient controller operation. This paper discusses state-of-the-art methods for time-delay estimation (TDE)-based methods related to active disturbance rejection control (ADRC) methods and proportional-integral-derivative (PID) controllers found in the latest literature on control systems theory. The methodology includes simulation designs incorporating the integration of predictive extended state observer-based ADRC (PESO-ADRC) and conventional PID controllers with the TDE mechanism, followed by their respective control on systems with time delay and disturbances. A comparative analysis performed on the TDE compensation methods highlights that TDE enhances the robustness to time delay, various uncertainties, and nonlinear dynamics existing in the controlled system. The time-varying delay, nonlinear backlash-like hysteresis, and an added system external disturbance were considered in the simulation. The performance was measured based on specific transient response characteristics such as the rise time, settling time, overshoot criteria, and performance index measures such as the integral of time-weighted absolute error (ITAE) and the percentage of improvement by the decrease in overshoot given by $ {P}_{i} $ (%). Further, a sensitivity analysis of TDE parameters to the controllers' operation was also performed. Experimental results indicate stability and a strong capacity to regulate the transient and steady-state responses under the impact of various uncertainties. Therefore, the comparative analysis conducted between TDE-ADRC and TDE-PID control methods signifies the importance of TDE with disturbance compensation in time-delayed systems, commonly found in real-world industrial applications.
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Written from the paper’s full text.
TL;DR
This paper compares time-delay estimation (TDE)-based predictive ESO-ADRC and TDE-based PID controllers for a second-order time-delay system under hysteresis, parameter perturbation, external disturbances, and varying delay. It finds TDE improves robustness, with TDE-PESO-ADRC better for nonlinear/periodic disturbances and TDE-PID better for larger time delays.
Key findings
- With no uncertainties, TDE-PESO-ADRC improved rise time by 23.81%, settling time by 62.07%, overshoot by 55.25%, and ITAE by 52.26%; TDE-PID improved rise time by 19.49%, settling time by 25.18%, and ITAE by 28.54%, but overshoot increased from 0.0000% to 1.2581%.
- Under nonlinear backlash-like hysteresis, TDE-PESO-ADRC improved ITAE by 81.23% and overshoot by 52.29%; TDE-PID improved settling time by 61.09% and ITAE by 64.74%, but rise time worsened by 20.04% and overshoot improved only 0.68%.
- Under hysteresis plus 25% parameter perturbation, TDE-PESO-ADRC improved settling time by 34.79%, ITAE by 80.44%, and overshoot by 42.64%; TDE-PID showed ITAE improvement of approximately 0%, settling time improvement of 8.61%, overshoot improvement of 12.13%, and rise time improvement of 11.66%.
- With added external disturbances, TDE-PESO-ADRC handled step and periodic disturbances where non-TDE PESO-ADRC was unstable; TDE-PID was unstable under the periodic disturbance. For varying delays, TDE-PID withstood delays up to 0.6 s, while TDE-PESO-ADRC compensated up to 0.16 s.
Methods
- Simulation-based comparative study of TDE-PESO-ADRC and TDE-PID on a second-order time-delay system \(G(s)=2/(s^2+3s+2)e^{-\tau s}=1/((s+1)(0.5s+1))e^{-\tau s}\), with system delay \(\tau=0.1\) s and state-space matrices \(A=[-3\ 1;2\ 0]\), \(B=[0;2]\), \(C=[1\ 0]\).
- Seven experiments: no uncertainty; Duhem backlash-like hysteresis; 25% parameter perturbation at 20 s; added step and periodic external disturbances; varying system time delay; control signal saturation; and sensitivity analysis of TDE parameters.
- Performance measured by rise time, response time, settling time, overshoot, ITAE, and percentage improvement \(P_i(\%)\); ADRC parameters were optimized using MATLAB genetic algorithm, while PID gains were manually tuned to \(K_p=1\), \(K_i=0.8\), \(K_d=0.1\), with gain factor \(b=0.2\).
Limitations
- The paper states future work is needed for adaptive TDE gains under periodic disturbances, improved TDE for unknown and higher delay values, and consideration of noise and friction on higher-order systems; hardware-based human-machine interface and digital twin work is underway.
- Evident from the text: the study is simulation-only on a second-order benchmark, not a hardware validation; TDE-PESO-ADRC was tested only up to 0.16 s delay, and TDE-PID responses oscillated for delay values of 0.5 s and above.
- Evident from the tables: several comparisons are limited by unstable or unplotted responses, such as non-TDE PESO-ADRC under added disturbance and TDE-PID under periodic disturbance, so some \(P_i(\%)\) values could not be tabulated.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
3 of 29 cited sources checked · 2 supported · 0 flagged · accuracy not yet measured
- Findingown data
For the PID control scheme, rise time was 1.0316 s with TDE versus 1.1677 s without TDE.
“The RT was 1.0316 s with TDE vs 1.1677 s without TDE for the PID control scheme, and 0.4007 s with TDE compared to 0.7052 s without TDE for the PESO-ADRC approach.”
Quote in the paperSubstantial claim - Findingown data
For PESO-ADRC with TDE control, ITAE value is decreased by 52.26%.
“Further, the settling time, ITAE value, and overshoot are decreased by 62.07%, 52.26%, and 55.25%, thus showing a greater performance improvement for PESO-ADRC with TDE control.”
Quote in the paperSubstantial claim - Findingown data
For the TDE-PID controller with added disturbance f1, the overshoot decreased by 14% between 20 and 25 seconds.
“However, for the TDE-PID controller with added disturbance in Equation ( 21), the overshoot decreased by 14% between 20 and 25 seconds.”
Quote in the paperNot a substantial claim - Findingown data
For the TDE-PESO-ADRC method, the initial system response's overshoot was greatly reduced by 45%.
“For the TDE-PESO-ADRC method, the initial system response's overshoot was greatly reduced by 45%; however, for the case of PID with TDE, the decrease in initial overshoot was not observed.”
Quote in the paperSubstantial claim - Findingown data
For PESO-ADRC with TDE control, settling time is decreased by 62.07%.
“Further, the settling time, ITAE value, and overshoot are decreased by 62.07%, 52.26%, and 55.25%, thus showing a greater performance improvement for PESO-ADRC with TDE control.”
Quote in the paperSubstantial claim
- Findingown data
The ITAE index measure with TDE present is 2.1260 for the PID controller.
“Further, the ITAE index measure with the TDE present is 2.1260 and 1.0130 for both PID and PESO-ADRC controllers, respectively, which shows an improvement of 64.74% and 81.23% as compared to without the TDE approach present.”
Quote in the paperSubstantial claim - Findingown data
The ITAE improvement with TDE present is 81.23% for the PESO-ADRC controller compared to without the TDE approach.
“Further, the ITAE index measure with the TDE present is 2.1260 and 1.0130 for both PID and PESO-ADRC controllers, respectively, which shows an improvement of 64.74% and 81.23% as compared to without the TDE approach present.”
Quote in the paperSubstantial claim - Findingown data
Under the effect of parameter perturbation at 20 s, the TDE system reached a faster settling time for both TDE with PID and PESO-ADRC control approaches.
“However, from Table 3, under the effect of parameter perturbation at 20 s, the TDE system reached a faster settling time for the cases of both TDE with PID and PESO-ADRC control approaches.”
Quote in the paperSubstantial claim - Findingown data
The TDE mechanism is effective in counteracting the nonlinear nature of the hysteresis effect on the PESO-ADRC method.
“Figure 7 and Table 2 demonstrate the effectiveness of the TDE mechanism in counteracting the nonlinear nature of the hysteresis effect on the PESO-ADRC method.”
Quote in the paperSubstantial claim - Findingown data
The TDE-PID controller showed a slight increase in response between 0 and 5 s for the case of added disturbance f1.
“contrary to the slight increase in response obtained in the TDE-PID controller between 0 and 5 s for the case of added disturbance 𝑓 1 𝑥 𝑡 , 𝑡 given by Equation (21).”
Quote in the paperNot a substantial claim - Findingown data
For the PESO-ADRC controller, the system response was unstable at the onset of the external disturbance in the absence of TDE.
“For the PESO-ADRC controller, the system response was unstable at the onset of the external disturbance in the absence of TDE.”
Quote in the paperSubstantial claim - Findingown data
A similar improvement in rise time of 23.81% is obtained for the TDE-PESO-ADRC method.
“A similar improvement in rise time of 23.81% is also obtained for the TDE-PESO-ADRC method.”
Quote in the paperNot a substantial claim - Findingown data
The ITAE index measure with TDE present is 1.0130 for the PESO-ADRC controller.
“Further, the ITAE index measure with the TDE present is 2.1260 and 1.0130 for both PID and PESO-ADRC controllers, respectively, which shows an improvement of 64.74% and 81.23% as compared to without the TDE approach present.”
Quote in the paperSubstantial claim - Findingown data
The ITAE improvement with TDE present is 64.74% for the PID controller compared to without the TDE approach.
“Further, the ITAE index measure with the TDE present is 2.1260 and 1.0130 for both PID and PESO-ADRC controllers, respectively, which shows an improvement of 64.74% and 81.23% as compared to without the TDE approach present.”
Quote in the paperSubstantial claim - Findingown data
With TDE present, the controlled system rose faster for both TDE-PID and TDE-PESO-ADRC control scenarios.
“It was observed that with the TDE present, the controlled system rose faster for both control scenarios (TDE-PID and TDE-PESO-ADRC), i.e., for the PID controller RT = 1.5263 s with TDE, and RT = 1.8958 s without the TDE mechanism.”
Quote in the paperSubstantial claim - Findingown data
For the PESO-ADRC approach, rise time was 0.4007 s with TDE compared to 0.7052 s without TDE.
“The RT was 1.0316 s with TDE vs 1.1677 s without TDE for the PID control scheme, and 0.4007 s with TDE compared to 0.7052 s without TDE for the PESO-ADRC approach.”
Quote in the paperSubstantial claim - Findingown data
For both cases, with the TDE mechanism, the predictive-based ADRC's response shows system instability after adding an external disturbance to the perturbed time-delay system under nonlinear hysteresis.
“For both cases, with the TDE mechanism, the predictive-based ADRC's response shows system instability after adding an external disturbance to the perturbed time-delay system under nonlinear hysteresis.”
Quote in the paperSubstantial claim - Findingown data
For PESO-ADRC with TDE control, overshoot is decreased by 55.25%.
“Further, the settling time, ITAE value, and overshoot are decreased by 62.07%, 52.26%, and 55.25%, thus showing a greater performance improvement for PESO-ADRC with TDE control.”
Quote in the paperSubstantial claim - Findingown data
A significant improvement in performance measures was not obtained for the TDE-PID control method in comparison to its non-TDE structure.
“However, a significant improvement in performance measures was not obtained in the case of the TDE-PID control method in comparison to its non-TDE structure, as seen in Table 1.”
Quote in the paperSubstantial claim - Findingown data
For the case of PID with TDE, the decrease in initial overshoot was not observed.
“For the TDE-PESO-ADRC method, the initial system response's overshoot was greatly reduced by 45%; however, for the case of PID with TDE, the decrease in initial overshoot was not observed.”
Quote in the paperSubstantial claim - Findingown data
Under the no-uncertainty scenario, integration of TDE with the ADRC strategy provided a better response than its respective non-TDE version and TDE-PID control approach.
“Hence, under this scenario, the integration of TDE with the ADRC strategy provided a better response than its respective non-TDE version and TDE-PID control approach.”
Quote in the paperSubstantial claim- Rests on an assumption: The second-order system with time delay is a benchmark system representative for various industrial plants.
- Findingnone given
The TDE-PESO-ADRC method showed endurance to a small range of carrying system time delay.
“On the other hand, the TDE-PID control approach could sustain a satisfactory and stable response to an increasing system time delay, unlike the TDE-PESO-ADRC method, which showed endurance to a small range of carrying system time delay.”
Quote in the paperSubstantial claim - Findingnone given
The TDE-PID control approach could sustain a satisfactory and stable response to an increasing system time delay.
“On the other hand, the TDE-PID control approach could sustain a satisfactory and stable response to an increasing system time delay, unlike the TDE-PESO-ADRC method, which showed endurance to a small range of carrying system time delay.”
Quote in the paperSubstantial claim - Findingown data
For the TDE-PESO-ADRC control method, for eta values tuned to 0.001, 0.01, 0.1, and 0.2, the performance appears to increase slightly for all transient response characteristics (RT, ST, OV, ITAE).
“It can be inferred from Figure 17 that for 𝜂 values tuned to 0.001, 0.01, 0.1, and 0.2, the performance appears to increase slightly for all transient response characteristics (RT, ST, OV, ITAE).”
Quote in the paperSubstantial claim - Findingown data
For both the TDE-PESO-ADRC and TDE-PID control methods, the output response curves obtained with saturation present are in accordance with those obtained from the non-saturation case.
“For both the TDE-PESO-ADRC and TDE-PID control methods, it is noted that the output response curves obtained with saturation present are in accordance with those obtained from the non-saturation case.”
Quote in the paperNot a substantial claim - Findingown data
The TDE-PID control method took longer to achieve a steady state.
“However, the TDE-PID control method took longer to achieve a steady state, as seen in Figure 13 (b).”
Quote in the paperNot a substantial claim - Findingown data
For the TDE-PID-based controller, the peak values of the oscillating response were decreased for different time-delay situations, such as tau_s = 0.2 s, 0.4 s, and 0.6 s, following the onset of the external disturbance f1 and 25% parameter perturbation at 30 s.
“Further, for the TDE-PID-based controller, the peak values of the oscillating response were decreased for different time-delay situations, such as 𝜏 𝑠 = 0.2 s, 0.4 s, and 0.6 s, following the onset of the external disturbance given by Equation (21) and 25% parameter perturbation at 30 s (as seen in Figure 12).”
Quote in the paperSubstantial claim - Findingown data
Under all scenarios tested, the TDE-PESO-ADRC approach improved the estimation and mitigation of the uncertain prevailing nonlinearities compared to its non-TDE counterpart.
“Under all these scenarios, the TDE-PESO-ADRC approach improved the estimation and mitigation of the uncertain prevailing nonlinearities compared to its non-TDE counterpart.”
Quote in the paperSubstantial claim - Findingown data
The TDE-PESO-ADRC method could estimate and counteract the different forms of periodic and step forms of external disturbances added to the perturbed system to be controlled.
“However, it was demonstrated that the TDE-PESO-ADRC method could estimate and counteract the different forms of periodic and step forms of external disturbances added to the perturbed system to be controlled, unlike the TDE-PID controller, which showed an unstable response under the impact of a periodic kind of disturbance, hence directing the use of adaptive TDE gains under future scope.”
Quote in the paperSubstantial claim - Findingown data
For the TDE-PID controller, performance criteria measures experience certain changes when b is varied from 0.001, 0.01, 0.1, to 0.2 with eta=0.001.
“Hence, it is seen that the performance criteria measures experience certain changes when 𝑏 of the TDE-PID controller is varied, but these variations observed are within acceptable limits, hence showcasing less sensitivity to varying 𝑏 parameter in a relatively small range.”
Quote in the paperSubstantial claim - Findingown data
The TDE-PID controller showed an unstable response under the impact of a periodic kind of disturbance.
“However, it was demonstrated that the TDE-PESO-ADRC method could estimate and counteract the different forms of periodic and step forms of external disturbances added to the perturbed system to be controlled, unlike the TDE-PID controller, which showed an unstable response under the impact of a periodic kind of disturbance, hence directing the use of adaptive TDE gains under future scope.”
Quote in the paperSubstantial claim - Findingown data
For TDE-PESO-ADRC control, the controlled object could withstand smaller delay values.
“For TDE-PESO-ADRC control, the controlled object could withstand smaller delay values (seen in Figure 11 and Table 5).”
Quote in the paperSubstantial claim - Findingnone given
The response curve oscillates for delay values of 0.5 s and above.
“However, the response curve oscillates for delay values of 0.5 s and above, paving the way for further research.”
Quote in the paperSubstantial claim - Findingown data
The TDE-PESO-ADRC method reached a steady state much earlier for a range of smaller, varying time-delay values.
“Figure 13 (a) shows that the TDE-PESO-ADRC method reached a steady state much earlier for a range of smaller, varying time-delay values.”
Quote in the paperNot a substantial claim - Findingown data
The TDE-PID control signal reaches 11 at the beginning of the control.
“It is to be noted that the TDE-PID is more aggressive at the beginning of the control (the control signal reaches 11), which might trigger hard constraints for some applications.”
Quote in the paperSubstantial claim - Findingown data
For TDE-PID control, the controlled object showed resilience to higher system delay values.
“Meanwhile, for TDE-PID control, the controlled object showed resilience to higher system delay values (shown in Figure 12 and Table 6).”
Quote in the paperSubstantial claim - Findingown data
For the TDE-PID controller, the transient response characteristics (RT, ST, OV, ITAE) remain consistent for eta values 0.001, 0.01, 0.1, and 0.2 with b constant at 0.2.
“It is noted that the transient response characteristics measured, such as the RT, ST, OV, and ITAE, remain consistent for all the abovementioned 𝜂 values.”
Quote in the paperSubstantial claim - Interpretationown data
The comparative analysis between TDE-ADRC and TDE-PID control methods signifies the importance of TDE with disturbance compensation in time-delayed systems commonly found in real-world industrial applications.
“Therefore, the comparative analysis conducted between TDE-ADRC and TDE-PID control methods signifies the importance of TDE with disturbance compensation in time-delayed systems, commonly found in real-world industrial applications.”
Quote in the paperSubstantial claim- Rests on an assumption: In most TDE-based methods, the stability and performance of the controller design are greatly impaired under the influence of external disturbances and varying system time-delay circumstances.
- Premisecitation
By setting r0 to r and applying the nonlinear function fhan, the fastest convergence from v1 to v with the least amount of overshoot is achieved.
“By setting 𝑟 0 to 𝑟 and applying the nonlinear function fhan(𝑣 1 -𝑟, 𝑣 2 , 𝑟 0 , ), which is defined by a series of relations in Equation ( 8), the fastest convergence from 𝑣 1 to 𝑣 with the least amount of overshoot is achieved [7].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [7] Han J (2009) From PID to Active Disturbance Rejection Control. <i>IEEE T Ind Electron</i> 56: 900‒906. https://doi.org/10.1109/TIE.2008.2011621 source
- Premisecitation
Model-based control approaches are affected by the system's parameter uncertainty and unmodelled dynamics.
“The former is affected by the system's parameter uncertainty and unmodelled dynamics.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [4][5][6]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning
When the sample period ts decreases, the TDE estimate gets stronger as the TDE can operate effectively.
“Furthermore, when the sample period 𝑡 𝑠 decreases, the estimate 𝜁 𝑡 gets stronger as the TDE can operate effectively, according to Equation (3).”
Quote in the paperNot a substantial claim - Interpretationreasoning
The TDE-PESO-ADRC control method is less susceptible to different forms of input disturbances like periodic, nonlinear, and step forms applied to the concerned controlled object, in contrast to the TDE-PID control mechanism.
“Hence, it is inferred that the TDE-PESO-ADRC control method is less susceptible to different forms of input disturbances like periodic, nonlinear, and step forms applied to the concerned controlled object, in contrast to the TDE-PID control mechanism.”
Quote in the paperSubstantial claim - Premisecitation
Time delays and uncertainties are significantly associated with inefficient operation of the overall control system.
“In the domain of automation and teleoperation systems, time delays and uncertainties are significantly associated with inefficient operation of the overall control system [1][2][3].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [1][2][3]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationown data
The TDE-PID controlled system is less sensitive to changes in eta.
“Therefore, this indicates that the TDE-PID controlled system is less sensitive to changes in 𝜂.”
Quote in the paperSubstantial claim - Interpretationown data
An acceptable minimal difference is observed in the output responses by limiting the value of the control signal to the overall system.
“Hence, an acceptable minimal difference is observed in the output responses by limiting the value of the control signal to the overall system.”
Quote in the paperNot a substantial claim - Interpretationreasoning
The TDE-PID control method showed more robust and endurance behavior when affected by variations in system time delay.
“Thus, this showcases the more robust and endurance behavior of the TDE-PID control method when affected by variations in system time delay.”
Quote in the paperSubstantial claim - Interpretationown data
The TDE-PESO-ADRC control method is less sensitive to eta values.
“Hence, the TDE-PESO-ADRC control method is less sensitive to 𝜂 values.”
Quote in the paperSubstantial claim
- Classified as probably not a substantial claim. 20
- May combine two claims. 15
- The quote only partly states this claim. 4
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationOther controller methods commonly used in integration with the TDE mechanism for attenuation of system nonlinearities include PID, adaptive sliding mode controller (SMC), and fuzzy logic approach-based control methods.
“Other controller methods commonly used in integration with the TDE mechanism for attenuation of system nonlinearities include, for example, the PID controller [18], adaptive sliding mode controller (SMC) [19], and fuzzy logic approach-based [20] control methods.”
Quote in the paperNot a substantial claim1 of 3 sources checked- cites [18] Wang Y, Peng J, Zhu K, Chen B, Wu H (2020) Adaptive PID-fractional-order nonsingular terminal sliding mode control for cable-driven manipulators using time-delay estimation. <i>Int J Syst Sci</i> 51: 3118‒3133. https://doi.org/10.1080/00207721.2020.1808732. source
- cites [19] Taefi M, Khosravi MA (2024) A model free adaptive‐robust design for control of robot manipulators: time delay estimation approach. <i>Int J Robust Nonlinear Control</i> 34: 8227‒8247. https://doi.org/10.1002/rnc.7379 source
- cites [20] Glida HE, Chelihi A, Abdou L, Sentouh C, Perozzi G (2023) Trajectory tracking control of a coaxial rotor drone: Time-delay estimation-based optimal model-free fuzzy logic approach. <i>ISA T</i> 137: 236‒247. https://doi.org/10.1016/j.isatra.2022.12.015 source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe PID controller depicts decent accomplishment in overcoming various nonlinearities, such as the chattering effect, delay, and external disturbances present in robotic industries.
“The PID controller depicts decent accomplishment in overcoming various nonlinearities, such as the chattering effect, delay, and external disturbances present in robotic industries [14].”
Quote in the paperNot a substantial claim1 of 1 sources checked- cites [14] Pham TT, Nguyen CN (2023) Adaptive PID sliding mode control based on new Quasi-sliding mode and radial basis function neural network for Omni-directional mobile robot. <i>AIMS Electronics & Electrical Engineering</i> 7: 121‒134. https://doi.org/10.3934/electreng.2023007 source
The Abstract and Conclusions report reduced chattering for a PID sliding-mode controller combined with a quasi-sliding-mode function and an RBF neural network. Section 4 reports robust trajectory tracking under simulated sensor noise and parameter changes. The paper does not show that a PID controller alone overcomes these effects or demonstrate that the proposed controller overcomes communication delay; delay appears only as a problem mentioned in the Introduction. Page numbers are unavailable in our copy. (LLM, conf=0.87)
Experimental — accuracy not yet measured
Probably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductcitationThe selection of the ESPO observer bandwidth ωe is regulated by the Hurwitz stability criterion.
“The Hurwitz stability criterion regulates the selection of 𝜔 𝑒 ; thus, the complete details of the ESPO used in this study are outlined in [30,31].”
Quote in the paperNot a substantial claim1 of 2 sources checked- cites [30] Nahri SNF, Du S, van Wyk BJ (2023) Predictive Extended State Observer-Based Active Disturbance Rejection Control for Systems with Time Delay. <i>Machines</i> 11: 144. https://doi.org/10.3390/machines11020144 source
- cites [31] Xue W, Liu P, Chen S, Huang Y (2016) On extended state predictor observer based active disturbance rejection control for uncertain systems with sensor delay. <i>2016 16th International Conference on Control, Automation and Systems (ICCAS), </i> 1267‒1271. IEEE. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1109/ICCAS.2016.7832475">https://doi.org/10.1109/ICCAS.2016.7832475</ext-link> source
May combine two claims.
Findingown dataThe TDE mechanism improved performance for the PID controller regarding quicker settling time, smaller steady-state error, and smaller ITAE.
“Meanwhile, the TDE mechanism improved performance for the PID controller regarding quicker settling time, smaller steady-state error, and smaller ITAE.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataFor the PID controller, rise time was 1.5263 s with TDE and 1.8958 s without the TDE mechanism.
“It was observed that with the TDE present, the controlled system rose faster for both control scenarios (TDE-PID and TDE-PESO-ADRC), i.e., for the PID controller RT = 1.5263 s with TDE, and RT = 1.8958 s without the TDE mechanism.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe TDE-PESO-ADRC could conquer the unsteady behavior and provide an acceptable response curve that demonstrated considerable resistance to system uncertainties.
“However, by incorporating the TDE mechanism in this circumstance, the TDE-PESO-ADRC could conquer this unsteady behavior and provide an acceptable response curve that demonstrated considerable resistance to system uncertainties (Figure 10 and Table 4).”
Quote in the paperSubstantial claimThe quote only partly states this claim.
Findingown dataBoth TDE-PID and TDE-PESO-ADRC controlled systems displayed a shorter rise time (RT) when TDE was introduced under hysteresis, parameter perturbation, and added external disturbance.
“As indicated in Table 4, Figures 9 and 10 demonstrate that both the controlled system with the TDE mechanism displayed a shorter rise (RT) when the TDE was introduced.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThere is a minimal decrease in system overshoot in the TDE-PID control strategy and a longer rising time.
“However, as shown in Table 2, there is a minimal decrease in system overshoot in the TDE-PID control strategy and a longer rising time.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataExperimental results indicate stability and a strong capacity to regulate the transient and steady-state responses under the impact of various uncertainties.
“Experimental results indicate stability and a strong capacity to regulate the transient and steady-state responses under the impact of various uncertainties.”
Quote in the paperSubstantial claim- Rests on an assumption: Time delay is the most crucial aspect that greatly impairs the performance of the controlled system.
- Rests on an assumption: Time delay impairments include response overshooting with oscillations, reduced damping ratio, and moving the closed-loop system response to instability.
May combine two claims.
Findingown dataIntegrating TDE with the predictive ADRC method gives a system response with robustness, less oscillatory behavior, reduced overshoot, and quick system recovery to uncertainties, contrary to the TDE-PID system response and performance.
“Furthermore, by integrating the TDE with the predictive ADRC method, the system response in Figure 7 shows robustness and thus less oscillatory behavior, reduced overshoot, and quick system recovery to uncertainties, contrary to the TDE-PID system response and performance.”
Quote in the paperSubstantial claim- Rests on an assumption: Time delay is the most crucial aspect that greatly impairs the performance of the controlled system.
- Rests on an assumption: Time delay impairments include response overshooting with oscillations, reduced damping ratio, and moving the closed-loop system response to instability.
The quote only partly states this claim.
Findingown dataThe TDE mechanism in TDE-PESO-ADRC showed a decrease in overshoot at the beginning of the transient response under hysteresis, parameter perturbation, and added disturbance f1.
“In addition, the TDE mechanism in the TDE-PESO-ADRC showed a decrease in overshoot at the beginning of the transient response”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
FindingreasoningBoth Figure 10 and Table 4 do not include the system response's performance measures for the TDE-PID method because of the oscillatory character of the periodic external disturbance f2 added to the system under test.
“Similarly, both Figure 10 and Table 4 do not include the system response's performance measures for the TDE-PID method because of the oscillatory character of the periodic external disturbance given in Equation ( 22) added to the system under test, seen in Equation (18).”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe systems responded more quickly and had a shorter rise when TDE was present.
“Table 3 and Figure 8 demonstrate that the systems responded more quickly and had a shorter rise when TDE was present.”
Quote in the paperSubstantial claimThe quote only partly states this claim.
Findingown dataFor the TDE-PESO-ADRC method, the initial amplitude of the control signal is reduced from almost 10 to 5 when a saturation block with upper limit 5 and lower limit -5 is added.
“As observed in Figure 14(a), for the TDE-PESO-ADRC method, the initial amplitude of the control signal is reduced from almost 10 to 5.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataFor the TDE-based PESO-ADRC controller, system responses were oscillatory for greater system latencies, but they could compensate for nonlinear uncertainties, demonstrating decent strength and steady performance for distinct delay scenarios.
“It is seen that the system responses were therefore oscillatory for greater system latencies, but they could compensate for nonlinear uncertainties, demonstrating decent strength and steady performance for distinct delay scenarios.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe performance criteria displayed in Table 6 for changes in the TDE-PID controlled system delay responses showed robustness and significant compensation for all forms of disturbances present.
“Furthermore, the performance criteria displayed in Table 6 for changes in the TDE-PID controlled system delay responses showed robustness and significant compensation for all forms of disturbances present.”
Quote in the paperSubstantial claimThe quote only partly states this claim.
Findingown dataFor the TDE-PID control method, the initial peak is reduced from 11 to 5 when a saturation block with upper limit 5 and lower limit -5 is added.
“Moreover, for the TDE-PID control method, the initial peak is reduced from 11 to 5.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe TDE-PID controller showed good robustness to various uncertainties, with shorter rise time and settling time, stable system response, and decreased oscillations.
“Also, the TDE-PID controller showed good robustness to various uncertainties, with shorter rise time and settling time, stable system response, and decreased oscillations.”
Quote in the paperSubstantial claimMay combine two claims.
PremisecitationIn control systems, hysteresis can result in oscillation, instability, and incorrect positioning.
“Therefore, in control systems, hysteresis can result in oscillation, instability, and incorrect positioning.”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [27] Ikhouane F (2018) A survey of the hysteretic Duhem model. <i>Arch Comput Method Eng</i> 25: 965‒1002. https://doi.org/10.1007/s11831-017-9218-3 source
- cites [28] Jing N, Qiang C, Xuemei R (2018) Chapter 16 - Hysteresis Dynamics and Modeling. In: Jing N, Qiang C, Xuemei R, editors. <i>Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics</i>, 249‒256. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1016/B978-0-12-813683-6.00021-0">https://doi.org/10.1016/B978-0-12-813683-6.00021-0</ext-link>
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationThe ESO is an integral feature of the ADRC controller and accomplishes the active disturbance measurement and compensation.
“This is accomplished with an extended state observer (ESO), an integral feature of the ADRC controller [7].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [7] Han J (2009) From PID to Active Disturbance Rejection Control. <i>IEEE T Ind Electron</i> 56: 900‒906. https://doi.org/10.1109/TIE.2008.2011621 source
May combine two claims.
Interpretationown dataTDE enhances the robustness to time delay, various uncertainties, and nonlinear dynamics existing in the controlled system.
“A comparative analysis performed on the TDE compensation methods highlights that TDE enhances the robustness to time delay, various uncertainties, and nonlinear dynamics existing in the controlled system.”
Quote in the paperSubstantial claim- Rests on an assumption: Time delay is the most crucial aspect that greatly impairs the performance of the controlled system.
- Rests on an assumption: In most TDE-based methods, the stability and performance of the controller design are greatly impaired under the influence of external disturbances and varying system time-delay circumstances.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationModel-free control approaches consider a variety of system uncertainties, including internal and external disturbances, nonlinear hysteresis, sensor noise, and varying time delay.
“In contrast, the latter considers a variety of system uncertainties, including internal and external disturbances, nonlinear hysteresis, sensor noise, and varying time delay [4][5][6].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [4][5][6]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Premisenone givenFor α < 1, the error e will decrease to zero more quickly.
“For 𝛼 < 1, the error (𝑒) will decrease to zero more quickly.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S2 (checkable).
PremisecitationDespite consistent efforts to conquer the time-delay problem, the adverse effects of delay are still difficult to overcome.
“However, despite consistent efforts to conquer the time-delay problem, the adverse effects of delay are still difficult to overcome.”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [15] Ran M, Wang Q, Dong C, Xie L (2020) Active disturbance rejection control for uncertain time-delay nonlinear systems. <i>Automatica</i> 112: 108692. https://doi.org/10.1016/j.automatica.2019.108692 source
- cites [16] Chen S, Xue W, Zhong S, Huang Y (2018) On comparison of modified ADRCs for nonlinear uncertain systems with time delay. <i>Sci China Inform Sci</i> 61: 1‒15. https://doi.org/10.1007/s11432-017-9403-x source
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationThe hysteresis effect affects the precision of both closed-loop and open-loop control systems and leads to persistent oscillations.
“The hysteresis effect is widely acknowledged to affect the precision of both closed-loop and open-loop control systems and lead to persistent oscillations.”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [27] Ikhouane F (2018) A survey of the hysteretic Duhem model. <i>Arch Comput Method Eng</i> 25: 965‒1002. https://doi.org/10.1007/s11831-017-9218-3 source
- cites [28] Jing N, Qiang C, Xuemei R (2018) Chapter 16 - Hysteresis Dynamics and Modeling. In: Jing N, Qiang C, Xuemei R, editors. <i>Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics</i>, 249‒256. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1016/B978-0-12-813683-6.00021-0">https://doi.org/10.1016/B978-0-12-813683-6.00021-0</ext-link>
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S2 (checkable).
InterpretationreasoningThe TDE control mechanism is crucial for analyzing and mitigating all kinds of nonlinear phenomena subjected to a time-delayed system under control.
“Therefore, this emphasizes how crucial the TDE control mechanism is for analyzing and mitigating all kinds of nonlinear phenomena subjected to a time-delayed system under control.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe ESO is a fundamental element of the ADRC that actively estimates and compensates for the overall disturbance f(t) imposed on the controlled object.
“The ESO is a fundamental element of the ADRC that actively estimates and compensates for the overall disturbance 𝑓 𝑡 imposed on the controlled object given by Equation ( 1).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [7] Han J (2009) From PID to Active Disturbance Rejection Control. <i>IEEE T Ind Electron</i> 56: 900‒906. https://doi.org/10.1109/TIE.2008.2011621 source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationADRC is one of the most widely employed model-free controllers, whose model is updated continually to perform disturbance compensation in time-delay control.
“In the literature, one of the most widely employed model-free controllers is an active disturbance rejection control (ADRC), whose model is updated continually to perform disturbance compensation in time-delay control [7,8].”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [7] Han J (2009) From PID to Active Disturbance Rejection Control. <i>IEEE T Ind Electron</i> 56: 900‒906. https://doi.org/10.1109/TIE.2008.2011621 source
- cites [8] Nahri SNF, Du S, van Wyk BJ, Nyasulu TD (2024) Time-Delay Estimation Improves Active Disturbance Rejection Control for Time-Delay Nonlinear Systems. <i>Machines</i> 12: 552. https://doi.org/10.3390/machines12080552 source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe PID controller is one of the most widely used control processes in the field of industrial applications.
“The PID controller is one of the most widely used control processes in the field of industrial applications [32].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [32] Borase RP, Maghade D, Sondkar S, Pawar S (2021) A review of PID control, tuning methods and applications. <i>International Journal of Dynamics and Control</i> 9: 818‒827. https://doi.org/10.1007/s40435-020-00665-4 source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe performance of an ADRC controller concerning estimation and attenuation of nonlinear backlash-like hysteresis under time delay and uncertainties is greatly improved in conjunction with TDE mechanisms.
“Moreover, recent research has shown that the performance of an ADRC controller concerning estimation and attenuation of nonlinear backlash-like hysteresis under time delay and uncertainties is greatly improved in conjunction with TDE mechanisms [8,17].”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [8] Nahri SNF, Du S, van Wyk BJ, Nyasulu TD (2024) Time-Delay Estimation Improves Active Disturbance Rejection Control for Time-Delay Nonlinear Systems. <i>Machines</i> 12: 552. https://doi.org/10.3390/machines12080552 source
- cites [17] Nahri SNF, Du S, Van Wyk B, Ajayi OK, Nyasulu TD, Yu H (2025) Improvement of Proportional-Integral-Derivative Control for Time-Delay Nonlinear Systems by a Time-Delay Estimation Method. <i>2025</i> <i>33rd Southern African Universities Power Engineering Conference (SAUPEC 2025), </i> 1‒6. IEEE. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1109/SAUPEC65723.2025.10944363">https://doi.org/10.1109/SAUPEC65723.2025.10944363</ext-link> source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe ESO component has been amended over time to accommodate ADRC operation in industrial applications, including robotic systems, power plants, teleoperation systems, and piezoelectric-related medical fields.
“Therefore, to mitigate the effects of different types of uncertainties acting on a concerned system, the ESO component has been amended over time to accommodate the ADRC operation in industrial applications; for example, in robotic systems [10], power plants [11], teleoperation systems [12], and piezoelectric-related medical fields [13].”
Quote in the paperNot a substantial claim0 of 3 sources checked- cites [10] Fareh R, Khadraoui S, Abdallah MY, Baziyad M, Bettayeb M (2021) Active disturbance rejection control for robotic systems: A review. <i>Mechatronics</i> 80: 102671. https://doi.org/10.1016/j.mechatronics.2021.102671 source
- cites [11] Sun L, Xue W, Li D, Zhu H, Su ZG (2021) Quantitative tuning of active disturbance rejection controller for FOPTD model with application to power plant control. <i>IEEE T Ind Electron</i> 69: 805‒815. https://doi.org/10.1109/TIE.2021.3050372 source
- cites [12] Gu S, Zhang J, Liu X (2024) Event-Triggered Finite-Time Variable Gain ADRC for Master–Slave Teleoperated Parallel Manipulators. <i>IEEE Transactions on Circuits and Systems II: Express Briefs</i> 71: 3383‒3387. https://doi.org/10.1109/TCSII.2024.3359318 source
Classified as probably not a substantial claim.
PremisecitationTime-delay estimation followed by compensation is still a work in progress for various disturbance rejection control methods.
“Thus, time-delay estimation followed by compensation is still a work in progress for various disturbance rejection control methods [15,16].”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [15] Ran M, Wang Q, Dong C, Xie L (2020) Active disturbance rejection control for uncertain time-delay nonlinear systems. <i>Automatica</i> 112: 108692. https://doi.org/10.1016/j.automatica.2019.108692 source
- cites [16] Chen S, Xue W, Zhong S, Huang Y (2018) On comparison of modified ADRCs for nonlinear uncertain systems with time delay. <i>Sci China Inform Sci</i> 61: 1‒15. https://doi.org/10.1007/s11432-017-9403-x source
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisenone givenTDE reduces the total effect of cumulative disturbances.
“Consequently, the TDE reduces the total effect of cumulative disturbances.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe characteristic feature of ADRC is its ability to measure internal and external disturbances actively, generally coined as total disturbance, and then compensate for these total disturbance effects in real-time via the feedback loop.
“The characteristic feature of the ADRC controller is its ability to measure internal and external disturbances actively, generally coined as -total disturbance‖, and then compensate for these total disturbance effects in real-time via the feedback loop.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [7] Han J (2009) From PID to Active Disturbance Rejection Control. <i>IEEE T Ind Electron</i> 56: 900‒906. https://doi.org/10.1109/TIE.2008.2011621 source
Classified as probably not a substantial claim.
Study design and conductown dataThe results obtained were validated using measures such as performance index metrics and transient response characteristics.
“The results obtained were validated using measures such as performance index metrics and transient response characteristics.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationown dataThe variations in performance criteria measures when b is varied are within acceptable limits, showing less sensitivity to varying b parameter in a relatively small range.
“Hence, it is seen that the performance criteria measures experience certain changes when 𝑏 of the TDE-PID controller is varied, but these variations observed are within acceptable limits, hence showcasing less sensitivity to varying 𝑏 parameter in a relatively small range.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductnone givenA sensitivity analysis was conducted on the choice of specific TDE parameters for TDE-based controllers to validate their respective selected values.
“Furthermore, a sensitivity analysis was conducted on the choice of specific TDE parameters for TDE-based controllers to validate their respective selected values.”
Quote in the paperNot a substantial claim
The paper relies on this without support.
Time delay is the most crucial aspect that greatly impairs the performance of the controlled system.
“Further, the time delay aspect is the most crucial aspect that greatly impairs the performance of the controlled system.”
The paper relies on this without support.
Time delay impairments include response overshooting with oscillations, reduced damping ratio, and moving the closed-loop system response to instability.
“Impairments include response overshooting with oscillations, reduced damping ratio, and moving the closed-loop system response to instability.”
The paper relies on this without support.
In most TDE-based methods, the stability and performance of the controller design are greatly impaired under the influence of external disturbances and varying system time-delay circumstances.
“Therefore, in most TDE-based methods, it has been observed that the stability and performance of the controller design are greatly impaired under the influence of external disturbances and varying system time-delay circumstances.”
The paper relies on this without support.
When nonlinearity or disturbance is added to a PID-controlled system, it drives the system to instability or inadequate performance.
“When nonlinearity or disturbance is added to a PID-controlled system, it drives the system to instability or inadequate performance.”
The paper relies on this without support.
The second-order system with time delay is a benchmark system representative for various industrial plants.
“Such a system is chosen as a benchmark system under testing for various industrial plants.”
The paper relies on this without support.
Factors like time delay, hysteresis, parameter perturbation, external disturbances, and noise are inevitable in real-world system applications.
“This is mainly due to factors like time delay, hysteresis, parameter perturbation, external disturbances, and noise, which are inevitable in real-world system applications.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Experiment 4 gives opposite stability claims for TDE-PESO-ADRC
MinorThe text says the TDE-PESO-ADRC response is unstable for both external-disturbance cases and is not plotted, then says adding TDE overcomes that instability and produces an acceptable response curve. Table 4 also lists numerical performance measures for both TDE-included cases.
“For both cases, with the TDE mechanism, the predictive-based ADRC's response shows system instability after adding an external disturbance to the perturbed time-delay system under nonlinear hysteresis.Thus, the system response for the same is not plotted in both Figures 9 and 10.”
“However, by incorporating the TDE mechanism in this circumstance, the TDE-PESO-ADRC could conquer this unsteady behavior and provide an acceptable response curve that demonstrated considerable resistance to system uncertainties (Figure 10 and Table 4).”
State-space matrix does not represent the stated transfer function
MinorThe stated matrix A has a positive 2 in its lower-left position. Together with the stated B and C, it produces a denominator of s2+3s−2, rather than the s2+3s+2 denominator in Equation (18).
“𝐺 𝑠 = 2 𝑠 2 +3𝑠+2 𝑒 -𝜏𝑠 = 1 (𝑠+1) 0.5𝑠+1 𝑒 -𝜏𝑠 (18”
“the state-space matrix values obtained are 𝐴 = -3 1 2 0 , 𝐵 = 0 2 , 𝐶 = 1 0 ; and system delay 𝜏 = 0.1 s.”
Cites
From PID to Active Disturbance Rejection Control
Han, J. (2009) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2008.2011621 · Cited by 6,803 · see citing works
Disturbance-Observer-Based Control and Related Methods—An Overview
Chen, W., Yang, J., Guo, L., & Li, S. (2015) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2015.2478397 · Cited by 3,005 · see citing works
A review of PID control, tuning methods and applications
Borase, R. P., Maghade, D. K., Sondkar, S. Y., & Pawar, S. N. (2021) · International Journal of Dynamics and Control · doi:10.1007/s40435-020-00665-4 · Cited by 1,036 · see citing works
An Overview of Finite/Fixed-Time Control and Its Application in Engineering Systems
Liu, Y., Li, H., Lu, R., Zuo, Z., & Li, X. (2022) · IEEE/CAA Journal of Automatica Sinica · doi:10.1109/jas.2022.105413 · Cited by 514 · see citing works
On the centrality of disturbance rejection in automatic control
Gao, Z. (2013) · ISA Transactions · doi:10.1016/j.isatra.2013.09.012 · Cited by 485 · see citing works
Prescribed-Time Control and Its Latest Developments
Song, Y., Ye, H., & Lewis, F. L. (2023) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2023.3240751 · Cited by 430 · see citing works
Modified active disturbance rejection control for time-delay systems
Zhao, S., & Gao, Z. (2013) · ISA Transactions · doi:10.1016/j.isatra.2013.09.013 · Cited by 244 · see citing works
Active disturbance rejection control for robotic systems: A review
Fareh, R., Khadraoui, S., Abdallah, M. Y., Baziyad, M., & Bettayeb, M. (2021) · Mechatronics · doi:10.1016/j.mechatronics.2021.102671 · Cited by 192 · see citing works
Sun, L., Xue, W., Li, D., Zhu, H., & Su, Z.-G. (2022) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2021.3050372 · Cited by 178 · see citing works
Ahmed, S., Wang, H., & Tian, Y. (2019) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2019.2895588 · Cited by 173 · see citing works
Active disturbance rejection control for uncertain time-delay nonlinear systems
Ran, M., Wang, Q., Dong, C., & Xie, L. (2020) · Automatica · doi:10.1016/j.automatica.2019.108692 · Cited by 136 · see citing works
On comparison of modified ADRCs for nonlinear uncertain systems with time delay
Chen, S., Xue, W., Zhong, S., & Huang, Y. (2018) · Science China Information Sciences · doi:10.1007/s11432-017-9403-x · Cited by 122 · see citing works
A Survey of the Hysteretic Duhem Model
Ikhouane, F. (2018) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-017-9218-3 · Cited by 66 · see citing works
A Review on Haptic Bilateral Teleoperation Systems
Nahri, S. N. F., Du, S., & van Wyk, B. J. (2021) · Journal of Intelligent & Robotic Systems · doi:10.1007/s10846-021-01523-x · Cited by 54 · see citing works
Self-citationActive Disturbance Rejection Control for Piezoelectric Smart Structures: A Review
Li, J., Zhang, L., Li, S., Mao, Q., & Mao, Y. (2023) · Machines · doi:10.3390/machines11020174 · Cited by 54 · see citing works
Li, J., Zhang, L., Li, S., & Su, J. (2023) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2023.3253504 · Cited by 41 · see citing works
Xue, W., Liu, P., Chen, S., & Huang, Y. (2016) · 2016 16th International Conference on Control, Automation and Systems (ICCAS) · doi:10.1109/iccas.2016.7832475 · Cited by 35 · see citing works
Glida, H. E., Chelihi, A., Abdou, L., Sentouh, C., & Perozzi, G. (2023) · ISA Transactions · doi:10.1016/j.isatra.2022.12.015 · Cited by 26 · see citing works
TDE Based Model-free Control for Rigid Robotic Manipulators under Nonlinear Friction
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Self-citationWang, Y., Peng, J., Zhu, K., Chen, B., & Wu, H. (2020) · International Journal of Systems Science · doi:10.1080/00207721.2020.1808732 · Cited by 21 · see citing works
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Anjum, Z., Zhou, H. D., & Guo, Y. H. (2021) · Transactions of the Institute of Measurement and Control · doi:10.1177/01423312211013330 · Cited by 13 · see citing works
Taefi, M., & Khosravi, M. A. (2024) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.7379 · Cited by 13 · see citing works
Event-Triggered Finite-Time Variable Gain ADRC for Master–Slave Teleoperated Parallel Manipulators
Gu, S., Zhang, J., & Liu, X. (2024) · IEEE Transactions on Circuits and Systems II: Express Briefs · doi:10.1109/tcsii.2024.3359318 · Cited by 7 · see citing works
Time-Delay Estimation Improves Active Disturbance Rejection Control for Time-Delay Nonlinear Systems
Nahri, S. N. F., Du, S., van Wyk, B. J., & Nyasulu, T. D. (2024) · Machines · doi:10.3390/machines12080552 · Cited by 7 · see citing works
Self-citationLi, L., Su, Y., Kong, L., et al. (2022) · IEEE Access · doi:10.1109/access.2022.3232555 · Cited by 6 · see citing works
Hysteresis Dynamics and Modeling
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Nahri, S. N. F., Du, S., van Wyk, B. J., & Nyasulu, T. D. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-72059-8_22 · Cited by 3 · see citing works
Self-citationFatima Nahri, S. N., Du, S., van Wyk, B. J., Kayode Ajayi, O., Nyasulu, T. D., & Yu, H. (2025) · 2025 33rd Southern African Universities Power Engineering Conference (SAUPEC) · doi:10.1109/saupec65723.2025.10944363 · Cited by 3 · see citing works
Self-citationZhang, Y., Fang, L., Song, T., et al. (2023) · Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science · doi:10.1177/09544062231160350 · Cited by 2 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- Wen-bin Y, Dong Y (2015) Modeling and Simulation of an Active Disturbance Rejection Controller Based on Matlab/Simulink. <i>International Journal of Research in Engineering and Science (IJRES)</i> 3: 62‒69.
Cited by
Sorted by citations
Nahri, S. N. F., Du, S., van Wyk, B. J., Ajayi, O. K., Nyasulu, T. D., & Yu, H. (2025) · IEEE Access · doi:10.1109/access.2025.3645727
“…disturbances are categorized into two main groups, first, the internal disturbances, which include parameter perturbations and unmodeled system dynamics; and second, external disturbances, encompassing system input and output disturbances, measurement noise, and hysteresis effects [15], [16].”
Self-citationGeometric Attitude Control of Spacecraft with Time Delays on the Left-error Function of SO(3)
Fu, C., Guo, J., Zheng, Z., et al. (2026) · doi:10.1109/icaisisas68969.2026.11567798
“To solve the problem caused by unknown external disturbances on SO (3) model, researchers investigate and adopt TDE scheme [7].”
PID and ADRC Controller: A Comparative Analysis for Induction Motor Speed Regulation
Abdulredha, S. H., Hassan, S. K. A., & Latif, I. H. (2026) · Al-Nahrain Journal for Engineering Sciences · doi:10.29194/njes.29030426
“Several works [16],[17] have demonstrated that ADRC outperforms traditional controllers in terms of robustness, fast response, and reduced overshoot.”
- Authors
- Nahri, S. N. F., Department of Electrical Engineering, F. O. E. A. T. B. E., Du, S., van Wyk, B. J., & Ajayi, O. K.
- Affiliations
- Tshwane University of Technology (ZA)
- Venue
- AIMS Electronics and Electrical Engineering
- Published
- 2025
- Volume
- 9
- Issue
- 3
- Pages
- 314-338
- ISSN
- 2578-1588 (ISSN-L)
- OpenAlex
- W4411110641
- Cited by
- 3
- References
- 31
- Citations by year
- 2026: 2 · 2025: 1
- FWCI
- 1.18
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- cc-by-nc-sa
- Locations
- AIMS Electronics and Electrical Engineering (publishedVersion, cc-by-nc-sa)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Funders
- National Research Foundation
- Tshwane University of Technology
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Design
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Keywords
- time delay estimation, active disturbance rejection control, extended state observer, PID control, time-delay systems, disturbance compensation, backlash-like hysteresis, time-varying delays, nonlinear systems, transient response, robustness to uncertainty
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