Novel reaching law based predictive sliding mode control for lateral motion control of in‐wheel motor drive electric vehicle with delay estimation
Open accessAbstract
The lateral motion control of an in‐wheel motor drive electric vehicle (IWMD‐EV) necessitates an accurate measurement of the vehicle states. However, these measured states are always affected by delays due to sensor measurements, communication latencies, and computation time, which results in the degradation of the controller performance. Motivated by this issue, a novel reaching law based predictive sliding mode control (NRL‐PSMC) is proposed to maintain the lateral motion control of the IWMD‐EV subjected to unknown time delay. Initially, a PSMC framework is built, in which a predictor integrating with the sliding mode control is designed to eliminate the effect of time delay and generate the virtual control signals. Further, to alleviate the chattering phenomenon, a novel‐reaching law is developed, enabling the vehicle to track the desired states effectively. Subsequently, a dynamic control allocation technique is presented to optimally allocate the virtual control input to the actual control input. The accurate estimation of the aforementioned unknown delay is realized through a delay estimator. Finally, simulation and hardware‐in‐the‐loop experiments are performed for three specific driving manoeuvres, and the results demonstrate the effectiveness of the proposed controller design.
AI snapshot
Written from the paper’s full text.
TL;DR
The paper proposes a novel reaching law based predictive sliding mode control (NRL-PSMC) for lateral motion control of in-wheel motor drive electric vehicles under unknown input time delay, combining an FSA predictor, delay estimator, and dynamic control allocation. Simulations and hardware-in-the-loop tests for circular, lane-change, and J-turn manoeuvres show improved tracking and reduced chattering/oscillations versus CSMC, STSMC, and ASMC.
Key findings
- NRL-PSMC suppresses chattering and time-delay-induced oscillations; in the circular manoeuvre with a 0.1 s delay initiated at t = 2 s, CSMC, STSMC, and ASMC show fluctuations while NRL-PSMC remains smooth and tracks desired sideslip angle and yaw rate.
- In the lane-change manoeuvre, ASMC deviated by almost 3 m from the desired path; in the J-turn manoeuvre, ASMC deviated by approximately 4 m, whereas NRL-PSMC followed the desired trajectory accurately.
- The delay estimator tracks the unknown delay, though in the J-turn it fails to track until t = 2 s due to absence of control signal variation, then adjusts quickly. Tire cornering stiffness estimates converge rapidly.
- IAE and ITAE for yaw rate and sideslip angle are notably higher for CSMC, STSMC, and ASMC than for NRL-PSMC. DCA eigenvalues of Q are 0.0028; 0.0028; 0.0028; 0.0028; 0; 0, all inside the unit circle, so DCA is asymptotically stable.
Methods
- A 2DOF vehicle lateral dynamic model with yaw moment is used; tire cornering stiffness is estimated via recursive least squares. An FSA-based predictor and gradient-descent delay estimator handle unknown input delay; PI sliding surfaces, a novel adaptive reaching law, and dynamic control allocation generate and distribute control signals.
- Simulation is performed in MATLAB/Simulink 2022a; HIL experiments use OP4510 RT-LAB and dSPACE1104. The vehicle is assumed at 55 mph with tire-road friction coefficient 0.8; a 0.1 s delay at t = 2 s is used for circular and lane-change cases, and a time-varying delay for the J-turn. Comparisons are made against CSMC, STSMC, and ASMC.
- Lyapunov functions prove asymptotic stability of the sideslip-angle and yaw-rate controllers; DCA stability is assessed via eigenvalues of Q.
Limitations
- Stated in the paper: OP4510 RT-LAB has an amplitude limitation, so HIL results in Figures 9, 13, and 17 are scaled down; detailed four-wheel torque calculation is omitted; the delay estimator cannot track the unknown delay before t = 2 s in the J-turn when the control signal lacks variation.
- Evident from the text: validation is limited to simulation and HIL, with no real-vehicle tests; the 2DOF model and assumptions such as equal front/rear steering angles, low weight transfer, and equal front-left/front-right cornering stiffness may limit generality; the data availability statement says no datasets were generated or analysed.
Model-written summary. Check it against the paper before relying on it.
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Cites
Statistics
Claims the paper makes
2 of 12 cited sources checked · 1 supported · 0 flagged · accuracy not yet measured
- Findingown data
In the lane change manoeuvre with delay, the vehicle states follow the desired states accurately with the proposed NRL-PSMC.
“the vehicle states follow the desired states accurately with the proposed NRL-PSMC.”
Quote in the paperSubstantial claim - Findingown data
In the circular manoeuvre without delay, CSMC exhibits significant chattering.
“the CSMC exhibits significant chattering”
Quote in the paperSubstantial claim - Findingown data
In the circular manoeuvre, the delay estimator tracks the unknown delay more precisely.
“the delay estimator tracks the unknown delay more precisely.”
Quote in the paperNot a substantial claim - Findingreasoning
For sideslip angle control, the control error e_beta(t) tends to 0 as t tends to infinity under control signal (35), sliding surface (29), and NRL (34).
“Theorem 1.To prove that the control error e 𝛽 (t ) → 0 as t → ∞, then the control signal (35), sliding surface (29), and a NRL (34) are adopted to control the sideslip angle in the dynamic model (28)”
Quote in the paperSubstantial claim- The authors state this as an assumption: The unknown input delay is bounded and there exist τ_min, τ_max such that τ_min ≤ τ ≤ τ_max.
- The authors state this as an assumption: For all t ≥ 0, θ(t) ≠ 0.
- Findingown data
In the J-turn manoeuvre with time-varying delay, fluctuations can be observed in the side-slip angle and yaw rate.
“fluctuations can be observed in the side-slip angle and yaw rate”
Quote in the paperSubstantial claim
- Findingreasoning
In the circular manoeuvre with delay, NRL-PSMC is not influenced by the time delay.
“But, the NRL-PSMC is not influenced by the time delay.”
Quote in the paperSubstantial claim - Findingown data
In the J-turn manoeuvre with time-varying delay, for the CSMC method, the vehicle states deviate significantly from their desired values compared to the STSMC and ASMC methods.
“for the CSMC method, the vehicle states deviate significantly from their desired values compared to the STSMC and ASMC methods.”
Quote in the paperSubstantial claim - Findingown data
In the circular manoeuvre without delay, all control methods track the desired sideslip angle and yaw rate.
“all the control methods track the desired sideslip angle and yaw rate.”
Quote in the paperNot a substantial claim - Findingown data
In the circular manoeuvre without delay, STSMC and ASMC decrease chattering significantly.
“the STSMC and ASMC decrease chattering significantly”
Quote in the paperNot a substantial claim - Findingown data
In the lane change manoeuvre, the delay estimator quickly tracks the unknown delay.
“the delay estimator quickly tracks the unknown delay.”
Quote in the paperSubstantial claim - Findingreasoning
As the absolute value of the sliding surface increases, the control gain function converges to g = κ(1+ξ)/ξ > κ.
“as |𝓈 j | increases, that is, the system states are far from the sliding surface, the control gain function converges to g (e j , 𝓈 j ) = 𝜅(1+𝜉) 𝜉 > 𝜅”
Quote in the paperSubstantial claim - Findingown data
In the J-turn manoeuvre with time-varying delay, the proposed NRL-PSMC method demonstrates smooth control signals.
“the proposed NRL-PSMC method demonstrates smooth control signals”
Quote in the paperSubstantial claim - Findingown data
In the lane change manoeuvre with delay, the NRL-PSMC method provides smooth control signals.
“the NRL-PSMC method provides smooth control signals.”
Quote in the paperSubstantial claim - Findingown data
In the J-turn manoeuvre with time-varying delay, the CSMC, STSMC, and ASMC methods are unable to provide precise responses.
“the CSMC, STSMC, and ASMC methods are unable to provide precise responses when subjected to time varying delay.”
Quote in the paperSubstantial claim - Findingown data
In the J-turn manoeuvre with time-varying delay, the virtual control signals of CSMC, STSMC, and ASMC exhibit oscillations caused by the time delay.
“the virtual control signals of CSMC, STSMC, and ASMC exhibit oscillations caused by the time delay.”
Quote in the paperSubstantial claim - Findingreasoning
In the lane change manoeuvre with delay, fluctuations are observed in the sideslip angle and the yaw rate.
“fluctuations are observed in the sideslip angle and the yaw rate”
Quote in the paperSubstantial claim - Findingown data
In the circular manoeuvre with delay, NRL-PSMC has a smooth response in tracking the desired states.
“NRL-PSMC has a smooth response in tracking the desired states.”
Quote in the paperSubstantial claim - Findingreasoning
In the circular manoeuvre with delay, the time delay affects the control performance of CSMC, STSMC, and ASMC with a large number of fluctuations.
“At t = 2 s, the time delay affects the control performance of the CSMC, STSMC, and ASMC with a large number of fluctuations.”
Quote in the paperNot a substantial claim - Findingown data
In the HIL circular manoeuvre, at t=2 s, the sideslip angle and yaw rate follow their desired references more accurately.
“at t = 2 s, the sideslip angle and yaw rate follow its desired references more accurately.”
Quote in the paperNot a substantial claim - Findingreasoning
In the circular manoeuvre without delay, CSMC is subjected to a maximum error.
“the CSMC is subjected to a maximum error.”
Quote in the paperSubstantial claim - Findingown data
In the lane change manoeuvre with delay, the virtual control signals of CSMC, STSMC, and ASMC are affected by oscillations due to time delay.
“The virtual control signals of CSMC, STSMC, and ASMC are affected by oscillations due to time delay”
Quote in the paperSubstantial claim - Findingown data
In the lane change manoeuvre with delay, NRL-PSMC follows the desired trajectory accurately.
“the NRL-PSMC follows the desired trajectory accurately.”
Quote in the paperSubstantial claim - Findingown data
In the lane change manoeuvre, the IAE and ITAE control measures are notably higher for CSMC, STSMC, and ASMC when compared to the proposed method NRL-PSMC.
“tracking performance of the IWMD-EV is evaluated by using IAE and ITAE control measures, is notably higher for CSMC, STSMC and ASMC when compared to the proposed method NRL-PSMC”
Quote in the paperSubstantial claim - Findingown data
In the circular manoeuvre without delay, NRL-PSMC substantially minimizes chattering further compared to previous control methods.
“the proposed NRL-PSMC substantially minimizes the chattering further compared to previous control methods.”
Quote in the paperSubstantial claim - Findingown data
In the HIL lane change manoeuvre, at t=2 s, the proposed NRL-SMC suppresses the oscillations caused by the time delay effect.
“At t = 2 s, it is evident that the proposed NRL-SMC suppresses the oscillations caused due to time delay effect.”
Quote in the paperSubstantial claim - Findingreasoning
In the circular manoeuvre without delay, STSMC and ASMC have a slightly reduced error compared to CSMC.
“STSMC and ASMC have a slightly reduced error compared to CSMC.”
Quote in the paperNot a substantial claim - Findingown data
In the lane change manoeuvre with delay, ASMC is deviated by almost 3 m from the desired path.
“the ASMC is also deviated by almost 3 m far from the desired path”
Quote in the paperSubstantial claim - Findingown data
The direct control allocation (DCA) technique is asymptotically stable.
“Therefore, DCA is considered asymptotically stable.”
Quote in the paperSubstantial claim - Findingown data
In the circular manoeuvre, the tire cornering stiffness estimates are rapidly converging to the final value.
“the estimates are rapidly converging to the final value.”
Quote in the paperNot a substantial claim - Findingown data
In the lane change manoeuvre with delay, CSMC and STSMC diverge off through their desired path with fluctuations.
“the CSMC and STSMC diverge off through their desired path with fluctuations.”
Quote in the paperSubstantial claim - Findingown data
In the HIL circular manoeuvre, the oscillations caused by the time delay are effectively suppressed by the NRL-PSMC approach.
“The oscillations caused by the time delay are effectively suppressed by the NRL-PSMC approach.”
Quote in the paperSubstantial claim - Findingown data
In the lane change manoeuvre with delay, the CSMC, STSMC, and ASMC methods are not able to provide exact responses.
“the CSMC, STSMC, and ASMC methods are not able to provide exact responses when subjected to time delay.”
Quote in the paperSubstantial claim - Findingown data
In the circular manoeuvre with delay, NRL-PSMC completed the desired path more accurately than the STSMC.
“the NRL-PSMC completed the desired path more accurately than the STSMC subjected to fluctuations.”
Quote in the paperSubstantial claim - Findingown data
In the circular manoeuvre with delay, CSMC and ASMC almost deviated from the desired path.
“the CSMC and ASMC almost deviated from the desired path.”
Quote in the paperSubstantial claim - Findingown data
In the lane change manoeuvre with delay, the vehicle states for CSMC deviate significantly from their desired states compared to STSMC and ASMC.
“The vehicle states for CSMC deviate significantly from their desired states compared to STSMC and ASMC.”
Quote in the paperSubstantial claim - Findingreasoning
For yaw rate control, the control error e_gamma(t) tends to 0 as t tends to infinity under control signal (44), sliding surface (38), and NRL (43).
“Theorem 2. To prove that the control error e 𝛾 (t ) → 0 as t → ∞, then the control signal (44), sliding surface (38), and a novel exponential reaching law (43) are adopted to control the yaw rate in the dynamic model (28).”
Quote in the paperSubstantial claim- The authors state this as an assumption: The unknown input delay is bounded and there exist τ_min, τ_max such that τ_min ≤ τ ≤ τ_max.
- The authors state this as an assumption: For all t ≥ 0, θ(t) ≠ 0.
- Findingown data
In the HIL circular manoeuvre, the NRL-PSMC method provides a smooth response despite time delay.
“The NRL-PSMC method executed in HIL perfectly provides the smooth response despite of time delay.”
Quote in the paperSubstantial claim - Findingown data
In the J-turn manoeuvre with time-varying delay, the proposed NRL-PSMC method ensures that the vehicle states closely follow the desired states with high accuracy.
“the proposed NRL-PSMC method ensures that the vehicle states closely follow the desired states with high accuracy.”
Quote in the paperSubstantial claim - Findingown data
In the J-turn manoeuvre with time-varying delay, both CSMC and STSMC deviate from their intended paths with fluctuations.
“both CSMC and STSMC deviate from their intended paths with fluctuations.”
Quote in the paperSubstantial claim - Findingown data
In the J-turn manoeuvre with time-varying delay, ASMC deviates by approximately 4 m from the desired path.
“ASMC also deviate by approximately 4 m from the desired path.”
Quote in the paperSubstantial claim - Findingown data
The HIL experimental results exemplify that the NRL-PSMC makes the vehicle track the desired states accurately.
“The HIL experimental results exemplify that the NRL-PSMC makes the vehicle track the desired states accurately.”
Quote in the paperSubstantial claim - Findingown data
In the J-turn manoeuvre, the IAE and ITAE control measures are notably higher for CSMC, STSMC, and ASMC when compared to the proposed control NRL-PSMC.
“tracking performance of the IWMD-EV is evaluated by using IAE and ITAE control measures, is notably higher for CSMC, STSMC and ASMC when compared to the proposed control NRL-PSMC”
Quote in the paperSubstantial claim - Findingown data
In the J-turn manoeuvre with time-varying delay, the NRL-PSMC method accurately follows the desired trajectory.
“the NRL-PSMC method accurately follows the desired trajectory.”
Quote in the paperSubstantial claim - Findingown data
In the J-turn manoeuvre, until t=2 s, the delay estimator fails to track the unknown delay due to the absence of control signal variation.
“until t = 2 s, the delay estimator fails to track the unknown delay due to the absence of control signal variation.”
Quote in the paperNot a substantial claim - Findingown data
In the HIL J-turn manoeuvre, the NRL-PSMC design allows vehicle states to follow the desired states more accurately despite the time-varying delay.
“The NRL-PSMC design allows vehicle states to follow the desired states more accurately despite the time varying delay.”
Quote in the paperSubstantial claim - Interpretationown data
In the lane change manoeuvre with delay, the proposed NRL-PSMC is robust to time delay.
“the proposed NRL-PSMC is robust to time delay.”
Quote in the paperSubstantial claim - Interpretationown data
NRL-PSMC outperforms CSMC, STSMC, and ASMC in consideration of the chattering phenomenon.
“the developed NRL-PSMC outperforms the CSMC, STSMC, and ASMC in consideration of the chattering phenomenon.”
Quote in the paperSubstantial claim - Interpretationreasoning
The DCA is asymptotically stable if Q = (I - G^{-1}(BG^{-1})†B)G^{-2}G_2^2 has eigenvalues inside the unit circle.
“which has eigenvalues that are inside the unit circle, the DCA is said to be asymptotically stable.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The value of the delayed control signal ϑ(t-τ) is available.
- Interpretationnone given
A delay estimator maximizes the predictor's performance, which mainly depends on the time delay.
“Further, a delay estimator is presented to maximize the predictor's performance, which mainly depends on the time delay.”
Quote in the paperNot a substantial claim- The authors state this as an assumption: The unknown input delay is bounded and there exist τ_min, τ_max such that τ_min ≤ τ ≤ τ_max.
- The authors state this as an assumption: The value of the delayed control signal ϑ(t-τ) is available.
- Premisereasoning
In IWMD-EV lateral motion control, time delays always exist due to sensor measurement, communication latencies, and computation time.
“Thus, a time delay always exists due to sensor measurement, communication latencies, and computation time.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [8] source
- Interpretationown data
In the J-turn manoeuvre with time-varying delay, the proposed control method demonstrates robustness in the face of time-varying delays.
“the proposed control method demonstrates robustness in the face of time-varying delays.”
Quote in the paperSubstantial claim - Premisecitation
There always exists a trade-off between the exact delay and system performance.
“Hence, there always exists a trade-off between the exact delay and system performance [19].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [19] source
- Interpretationreasoning
To ensure EV lateral motion stability, the unknown time delay should be predictable.
“Thus, to ensure EV lateral motion stability, the unknown time delay should be predictable.”
Quote in the paperSubstantial claim - Interpretationown data
In the circular manoeuvre with 0.1 s delay at t=2 s, the virtual control signals suffer a significant mutation at t=2 s primarily due to the sudden change in the vehicle's trajectory from straight-line travel to circular motion.
“at t = 2 s, the virtual control signals suffer from a significant mutation primarily due to the sudden change in the vehicle's trajectory during the transition from straight-line travel to circular motion.”
Quote in the paperNot a substantial claim - Interpretationnone given
The predictor using the finite spectrum assignment (FSA) technique eliminates the effect of unknown time delay by predicting the delayed vehicle states.
“The predictor using the finite spectrum assignment (FSA) technique is employed to eliminate the effect of unknown time delay by predicting the delayed vehicle states.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The unknown input delay is bounded and there exist τ_min, τ_max such that τ_min ≤ τ ≤ τ_max.
- The authors state this as an assumption: The value of the delayed control signal ϑ(t-τ) is available.
- Interpretationreasoning
The proposed NRL controller gain function is adaptive according to variations in system states and sliding surface.
“Hence, it can be stated that the proposed NRL controller gain function is adaptive according to the variations in system states and sliding surface.”
Quote in the paperSubstantial claim - Interpretationnone given
The NRL-PSMC generates virtual control signals for IWMD-EV.
“An NRL-PSMC is proposed to generate the virtual control signals for IWMD-EV.”
Quote in the paperSubstantial claim - Interpretationreasoning
This iterative behaviour gives rise to oscillations in the system's response.
“This iterative behaviour gives rise to oscillations in the system's response.”
Quote in the paperSubstantial claim - Interpretationown data
The tracking performance using the IAE and ITAE control measures shows the superiority of the proposed controller.
“the tracking performance using the IAE and ITAE control measures shows the superiority of the proposed controller.”
Quote in the paperSubstantial claim - Interpretationreasoning
Delayed feedback can create a positive feedback loop, where the system attempts to compensate for the delay by amplifying the control signal.
“This delayed feedback can create a positive feedback loop, where the system attempts to compensate for the delay by amplifying the control signal.”
Quote in the paperNot a substantial claim - Interpretationreasoning
The proposed method is suitable for achieving its objective in a real-time environment.
“the proposed method is suitable for achieving its objective in a real-time environment.”
Quote in the paperSubstantial claim - Study design and conductown data
Simulation results of three different manoeuvres validate the effectiveness of the NRL-PSMC.
“Simulation results of three different manoeuvres validate the effectiveness of the NRL-PSMC.”
Quote in the paperSubstantial claim - Interpretationown data
In comparison with CSMC, STSMC, and ASMC, the proposed NRL-PSMC outperforms in minimizing the fluctuations caused due to time delay.
“in comparison with CSMC, STSMC, and ASMC, the proposed NRL-PSMC outperforms in minimizing the fluctuations caused due to time delay.”
Quote in the paperSubstantial claim - Interpretationreasoning
The fluctuations (oscillations) are due to delayed feedback in the closed-loop control system.
“These fluctuations (also termed as oscillations) are due to delayed feedback in the closed-loop control system.”
Quote in the paperSubstantial claim - Interpretationown data
The NRL-PSMC is benefited in alleviating the chattering phenomenon.
“the NRL-PSMC is also benefited in alleviating the chattering phenomenon.”
Quote in the paperSubstantial claim - Study design and conductnone given
An asymptotical stability of the system is proved by adapting an appropriate Lyapunov function.
“An asymptotical stability of the system is proved by adapting an appropriate Lyapunov function.”
Quote in the paperSubstantial claim - Interpretationreasoning
Due to time delay, the fluctuations indicate that the IWMD-EV is on the verge of instability.
“Due to time delay, these fluctuations indicate that the IWMD-EV is on the verge of instability.”
Quote in the paperSubstantial claim
- May combine two claims. 14
- Classified as probably not a substantial claim. 6
- The quote only partly states this claim. 1
May combine two claims.
PremisecitationIf time delays are left unattended, they degrade control performance or even drive the system to instability.
“Furthermore, if these delays are left unattended, it degrades the control performance or even drives the system to instability [9,10].”
Quote in the paperSubstantial claim1 of 2 sources checked- cites [9] source
The Introduction (p. 2) says that performance was clearly degraded as delay increased in a system without predictive control. That supports the performance part of the claim, but the passages do not say that unattended delays drive the system to instability. (LLM, conf=0.84)
Experimental — accuracy not yet measured - cites [10] source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe convergence proof of the delay estimator is presented in [9].
“The convergence proof of the delay estimator is presented in [9].”
Quote in the paperNot a substantial claim1 of 1 sources checked- cites [9] source
May combine two claims.
FindingreasoningIn the circular manoeuvre with delay, the time delay causes large fluctuations in the vehicle states and deteriorates the performances of CSMC, STSMC, and ASMC.
“the time delay causes large fluctuations in the vehicle states and deteriorates the performances of CSMC, STSMC, and ASMC.”
Quote in the paperSubstantial claimThe quote only partly states this claim.
Findingown dataIn the circular manoeuvre without delay, NRL-PSMC is subjected to a minimum error.
“the proposed NRL-PSMC is subjected to a minimum error.”
Quote in the paperSubstantial claimMay combine two claims.
FindingreasoningThe closed-loop system is asymptotically stable, proved theoretically using the Lyapunov function.
“An asymptotic stability criterion of the closed-loop system is proved theoretically using the Lyapunov function.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The unknown input delay is bounded and there exist τ_min, τ_max such that τ_min ≤ τ ≤ τ_max.
- The authors state this as an assumption: For all t ≥ 0, θ(t) ≠ 0.
Classified as probably not a substantial claim.
FindingreasoningThe optimal actual control input ū(t) is obtained as (49).
“The optimal actual control input ū(t ) is obtained as ū (t ) = {G -1 ( BG -1 ) † θ (t ) + [ I - ( G -1 ( BG -1 ) † B )] [ G -2 G 2 2 ū (t -T ) ] } (49 )”
Quote in the paperSubstantial claim- The authors state this as an assumption: The value of the delayed control signal ϑ(t-τ) is available.
May combine two claims.
Findingown dataIn the J-turn manoeuvre, after t=2 s, the delay estimator quickly adjusts and successfully tracks the unknown delay.
“Thereafter, it quickly adjusts and successfully tracks the unknown delay.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningIn the lane change manoeuvre with delay, the vehicle states deviate from the desired states, which indicates the criticality of vehicle instability.
“the vehicle states deviate from the desired states, which indicates the criticality of vehicle instability.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
PremisecitationVarious techniques such as higher-order SMC, adaptive SMC, and reaching law method are implemented to overcome the chattering phenomenon.
“Various techniques, such as higher-order SMC, adaptive SMC (ASMC), and reaching law method, are implemented to overcome the chattering phenomenon [23,24].”
Quote in the paperSubstantial claim0 of 2 sources checkedMay combine two claims.
Interpretationnone givenA new control gain function adjusts itself based on the absolute value of a sliding surface to alleviate chattering and improve tracking performance.
“A new control gain function is introduced, which adjusts itself based on the absolute value of a sliding surface to alleviate the chattering and improve the tracking performance.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Study design and conductreasoningThe OP4510 RT-LAB has a limitation on the amplitude, so the HIL experimental results shown in Figures 9, 13, and 17 are scaled down with an appropriate ratio.
“The OP4510 RT-LAB has the limitation on the amplitude.Therefore, to perform HIL, the experimental results shown in Figures 9, 13, and 17 are scaled down with appropriate ratio.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationThe dynamic control allocation (DCA) approach uses the objective function for control input constraints and has gained wide acceptance for translating virtual control signals into actual control signals.
“However, the dynamic control allocation (DCA) approach uses the objective function for control input constraints, has gained wide acceptance for translating virtual control signals into actual control signals [20,21].”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [20] source
- cites [21]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
May combine two claims.
Interpretationown dataIn the J-turn manoeuvre with time-varying delay, the vehicle's states deviate from the desired states, highlighting the criticality of vehicle instability.
“the vehicle's states deviate from the desired states, highlighting the criticality of vehicle instability.”
Quote in the paperSubstantial claimMay combine two claims.
PremisecitationFor all the aforementioned methods, time delays are assumed to be known and time-invariant.
“For all the aforementioned methods, time delays are assumed to be known and time-invariant.”
Quote in the paperSubstantial claim0 of 3 sources checkedProbably not a substantial claim: may not pass S4 (based).
PremisereasoningThe IWMD-EV is subjected to very less weight transfer because the battery pack is beneath the floor and the motors are attached in wheels.
“However, the IWMD-EV is subjected to very less weight transfer because the battery pack is beneath the floor and the motors are attached in wheels.”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationreasoningThe amplified control signal overshoots the desired setpoint, resulting in output overshoot.
“this amplified control signal overshoots the desired setpoint, resulting in output overshoot.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationown dataThe unknown time delays are eliminated, and the effectiveness and robustness of the NRL-PSMC method are validated using three cases.
“it is evident that the unknown time delays are eliminated, and the effectiveness and robustness of the NRL-PSMC method are validated using three cases.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationown dataThe proposed method is superior to counteract the input time delay and is most suitable for real-time applications.
“the proposed method is superior to counteract the input time delay and is most suitable for real-time applications.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningThe system corrects for the overshoot by reducing the control signal, leading to undershoot and the cycle continues.
“the system corrects for the overshoot by reducing the control signal, leading to undershoot and the cycle continues.”
Quote in the paperNot a substantial claim
The authors state this as an assumption.
The unknown input delay is bounded and there exist τ_min, τ_max such that τ_min ≤ τ ≤ τ_max.
“Assumption 1. The unknown input delay is bounded and there exist 𝜏 min , 𝜏 max such that 𝜏 min ≤ 𝜏 ≤ 𝜏 max (17 )”
The authors state this as an assumption.
For all t ≥ 0, θ(t) ≠ 0.
“Assumption 2. For all t ≥ 0, θ (t ) ≠ 0. (22 )”
The authors state this as an assumption.
The value of the delayed control signal ϑ(t-τ) is available.
“Remark 1.It is assumed that the value of delayed control signal 𝜗(t -𝜏) is available.”
The authors state this as an assumption.
The input time delay τ is constant.
“where 𝜏 is an input time delay considered as constant (𝜏 ∈ ).”
The authors state this as an assumption.
The front and rear steering angles are the same.
“For this reason, the steering angles for the front and rear wheels are assumed to be the same [28].”
The authors state this as an assumption.
The front left and front right tire cornering stiffness values are the same.
“Considering this feature, it is assumed that the front left and front right tire cornering stiffness values are the same.”
The paper relies on this without support.
Very few literature investigated time delays for lateral motion control of IWMD-EV.
“As far as the author's knowledge, very few literature investigated time delays for lateral motion control of IWMD-EV.”
The paper relies on this without support.
SMC outperforms other control strategies in robustness to disturbances, modelling errors, and insensitivity to parameter perturbations.
“Among all the control strategies, SMC outperforms in robustness to disturbances, modelling errors, and insensitivity to parameter perturbations.”
The paper relies on this without support.
The reaching law method has effectively proven to minimize chattering.
“Of the above methods, the reaching law method has effectively proven to minimize the chattering.”
The paper relies on this without support.
SMC has a limitation of high-frequency oscillations called chattering.
“Though, it has a limitation of high-frequency oscillations called as chattering phenomenon.”
The paper relies on this without support.
In real-time scenarios, the input time delay is often time varying.
“However, in real-time scenarios, the delay is often time varying.”
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.
Rear tire-force equation uses the front axle distance
MinorEquation (5) defines rear tire sideslip using a 2, but the rear tire-force equation (11) uses a 1 in its yaw-rate term. Substituting the stated rear sideslip into the tire-force model gives a term containing a 2 instead.
“Ḟ yr = - 1 𝛼 r F yr - k r 𝛼 r 𝛽 + k r a 1 𝛼 r V 𝛾 + k r 𝛼 r 𝛿 r (11”
“𝛽 f = 𝛽 + a 1 𝛾 V -𝛿 f , 𝛽 r = 𝛽 - a 2 𝛾 V -𝛿 r (5”
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Self-citation
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- Authors
- Chiliveri, V. R., Kalpana, R., Subramaniam, U., Muhibbullah, M., & Padmavathi, L.
- Affiliations
- National Institute of Technology Karnataka (IN)
- Prince Sultan University (SA)
- Bangladesh University (BD)
- Central Electronics Engineering Research Institute (IN)
- Corresponding author
- Muhibbullah, Md
- Venue
- IET Intelligent Transport Systems
- Published
- 2023-12-22
- Volume
- 18
- Issue
- 5
- Pages
- 872-888
- ISSN
- 1751-956X (ISSN-L)
- 1751-9578
- OpenAlex
- W4390144154
- Cited by
- 15
- References
- 31
- Citations by year
- 2026: 4 · 2025: 7 · 2024: 4
- FWCI
- 1.10
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- IET Intelligent Transport Systems (publishedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- National Institute of Technology Karnataka, Surathkal
- Prince Sultan University
- Topics
- Physical Sciences › Engineering › Automotive Engineering › Vehicle Dynamics and Control Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Control and Dynamics of Mobile Robots
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Keywords
- lateral control, reaching law, time delay estimation, unknown time delay, chattering reduction, dynamic control allocation, virtual control signals
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