Learning-Driven Intelligent Passivity Control Using Nonlinear State Observers for Induction Motors

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

2. Mathematical Framework and Problem Statement

2.1. Dynamic Model of an Asynchronous Motor

How much affect the parameter variations in the induction motor mathematical model in the propossed scheme?

How affect the non modeled dynamic of rotor, and what implication has the assumption of that only the fundamental harmonic of the rotor's magnetomotive force (MMF) is considered?

if the electirc machine has some electrical fault although it be incipient, which all the concordia frame work conditions are not achivied, what happend with the alpha-beta model? 

2.2. Problem Formulation

The estimation of the flux and torque is based on the data acquire of the stator currents, what is the impact of the performance of the propossed scheme of the quality of data acquired?

3. Nonlinear Observer Design

3.2. The Proposed Nonlinear Intelligent Observer Design

A FFBP neural network is used and it is fine, but, are there another machine learning approach that colud be used?

3.3. The Proposed Fuzzy-MRAS Estimator

How impact the sample frequency to perform the control law, the fuzzy estimator and the FFBP neural network in conjunction and how it impact the propossed scheme performance?

What is the computational cost to perform the propossed scheme?

4. Passivity Based Output-Feedback Controller

The deterministic model depen on the parametric variation, how it impact the performance of the propossed scheme?

The RNN was implemented to perform the control law, what is the computational cost to perform the algorithm?

5. Experimental Results and Discussion

What considerations should be take in account for a real time implementation, takeing in account the use of dSPACE card (DS1104)?

What is the sample frequency used?

What is the size of the data set acquired to fed the propossed algorithms?

There are a few simple concerns but in general is a very complete paper wich use a couple of machine learing tools like neural networks and fuzzy logic and it is a very interesting approach in the field of electric machines control.

Author Response

Comments 1: How much affect the parameter variations in the induction motor mathematical model in the proposed scheme?

Response 1: We thank the reviewer for raising this important point. In the proposed control framework, the impact of parameter variations (such as rotor resistance , stator inductance  and mutual inductance ​) is significantly mitigated by the integration of a learning-based compensation mechanism using Recurrent Neural Networks (RNNs).

The observer structure, detailed in Section 3 (pages 5–8), introduces a nonlinear adaptive observer enhanced with an RBFNN correction term (see Eq. (16)). This network adaptively approximates residual model uncertainties in real time, including those caused by parameter variations. The adaptation law (page 8, lines 234–241) is derived via Lyapunov theory, ensuring stability despite deviations from nominal parameters. Furthermore, robustness against parameter variations is experimentally validated in Section 6. In particular, the results in Table 2 and Figures 12–14 demonstrate that under conditions involving torque reversal, flux changes, and parametric perturbations, the controller maintains low torque and flux errors (e.g., 0.18 Nm and 0.21 Wb mean absolute error, respectively), significantly outperforming the classical PBC, even with varied parameters. Thus, the proposed scheme exhibits strong robustness to parameter variations, both theoretically (via RNN compensation and adaptive laws) and practically (via experimental testing).

 

Comments 2: How affect the non-modeled dynamic of rotor, and what implication has the assumption of that only the fundamental harmonic of the rotor's magnetomotive force (MMF) is considered?

Response 2: We appreciate the reviewer’s insightful question regarding the effect of un-modeled rotor dynamics and the fundamental harmonic assumption. In this work, as stated in Section 2.1 (line 120 onward), the assumption of considering only the fundamental harmonic of the rotor’s magnetomotive force (MMF) is a standard practice in the modeling of squirrel-cage induction motors. This simplification is based on the observation that higher-order harmonics have negligible influence on the overall torque production and flux evolution in most practical operating conditions [Ref: 27,29]. This approximation allows us to derive a physically consistent reduced-order model using the Euler–Lagrange formalism (see Eq. (3)), enabling tractable observer and controller design. However, we fully acknowledge that non-modeled rotor dynamics (including effects of spatial harmonics, skin effects, and magnetic saturation) may introduce residual uncertainties.

To address these, the proposed scheme explicitly incorporates a learning-based compensation mechanism via the RBFNN within the adaptive observer (Section 3.2, Eq. (16), line 234). The RBFNN estimates and compensates for unmodeled nonlinearities and residual dynamics, including those arising from the simplification of the MMF. Moreover, since the RBFNN is trained online using a gradient-based adaptation law (lines 238–247), it is capable of real-time learning and correction of modeling inaccuracies, thus mitigating the effects of neglected dynamics. The global Lyapunov-based stability proof ensures that such disturbances do not degrade the closed-loop system performance or stability.

Implication of the assumption: The assumption allows for a simplified, yet accurate dynamic model sufficient for high-performance control and observation. Its potential limitations are counteracted by the intelligent adaptation mechanism, making the control system resilient to these idealizations in practice.

 

Comments 3: If the electric machine has some electrical fault although it be incipient, which all the Concordia frame work conditions are not achieved, what happened with the alpha-beta model? 

Response 3: We thank the reviewer for highlighting this critical point. The αβ (Concordia) model assumes balanced three-phase conditions and omits zero-sequence components. In the presence of incipient faults (e.g., partial stator winding faults), these assumptions may no longer be strictly valid, leading to inaccuracies in the transformed model. However, the proposed scheme maintains robustness through the integration of a neural correction term (RBFNN) within the observer (Eq. (16)), which dynamically compensates for such unmodeled effects and residual asymmetries. While minor faults are thus tolerated, more severe unbalances would require fault-tolerant extensions, which we identify as a valuable future direction.

Comments 4: The estimation of the flux and torque is based on the data acquire of the stator currents, what is the impact of the performance of the proposed scheme of the quality of data acquired?

Response 4: Thank you for the insightful question. The proposed scheme depends on stator current and voltage measurements, so signal quality directly affects flux and torque estimation. However, the design includes several robustness features:

1. The embedded RBFNN compensates for noise and distortion by learning residual dynamics online.
2. The nonlinear observer, with adaptive , is designed to smooth noisy inputs and maintain stability.
3. Experimental results confirm robustness under realistic noise conditions, achieving a torque MAE of 18 Nm and flux MAE of 0.21 Wb.

That said, extremely poor signal quality (e.g., aliasing or severe noise) may still degrade performance, suggesting a future enhancement via pre-filtering or sensor fault accommodation.

Comments 5: A FFBP neural network is used and it is fine, but, are there another machine learning approach that could be used?

Response 5: We thank the reviewer for this observation. The proposed scheme uses a Feedforward Radial Basis Function Neural Network (RBFNN) due to its universal approximation capability, fast convergence, and ease of online adaptation. However, other machine learning approaches could also be considered, such as:

• Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) networks, which better capture temporal dependencies;
• Adaptive Neuro-Fuzzy Inference Systems (ANFIS) for combining expert rules with data-driven learning;
• Gaussian Process Regression (GPR) for uncertainty-aware modeling;
• Extreme Learning Machines (ELM) for fast online training.

These methods could potentially improve generalization or training efficiency, but they may require more computational resources or compromise passivity structure. We consider such alternatives promising for future extensions.

Comments 6: How impact the sample frequency to perform the control law, the fuzzy estimator and the RBFNN neural network in conjunction and how it impact the proposed scheme performance?

Response 6: We appreciate the reviewer’s question. The sampling frequency plays a crucial role in the performance of the proposed scheme, especially since it combines:

• A passivity-based control law (requiring timely torque/flux feedback),
• A fuzzy MRAS estimator (dependent on tracking model dynamics), and
• An RBFNN-based observer (with online adaptation and learning).

If the sampling rate is too low, the system may suffer from estimation delays, phase lag, or aliasing, which can degrade both control accuracy and stability. Conversely, a high sampling rate improves tracking and observer convergence but increases computational load. In our experimental setup, a sampling frequency of 5 kHz was used, which ensures sufficient resolution for dynamic changes in current, voltage, and speed while allowing real-time execution of the fuzzy and neural algorithms.

Overall, maintaining a balance between responsiveness and computational cost is critical. The proposed scheme remains robust as long as the sampling frequency satisfies the Nyquist condition and allows observer and controller updates within one cycle.

Comments 7: What is the computational cost to perform the proposed scheme?

Response 7: Thank you for this relevant question. The computational cost of the proposed scheme mainly arises from three components:

1. The nonlinear passivity-based control law, which involves basic matrix operations and is computationally lightweight.
2. The fuzzy MRAS estimator, which operates with a small rule base (5×5 = 25 rules) and two inputs, making it suitable for real-time execution.
3. The RBFNN observer, which includes a forward pass and weight updates. We used a network with 10–15 neurons, and gradient-based learning with low-dimensional inputs, resulting in modest computational demand.

In practice, the complete control scheme was implemented on a  DS1104 real-time board. The system handled data acquisition, PWM signal generation, and real-time execution of the observer, fuzzy estimator, and passivity-based control law at a 5 kHz sampling rate. The total CPU usage remained below 40%, confirming the computational efficiency and suitability of the scheme for standard industrial platforms.

Comments 8: The deterministic model depends on the parametric variation, how it impacts the performance of the proposed scheme?

Response 8: We agree that the deterministic model is sensitive to parameter variations. However, the proposed scheme mitigates this effect through two layers:

• the RBFNN learns and compensates for model mismatches online, and

(2) the nonlinear observer is Lyapunov-stable and robust to moderate parameter shifts.

This adaptive structure ensures that performance remains stable even under significant variation in , , or load torque. Experimental results confirm accurate flux and torque estimation despite such changes.

Comments 9: The RNN was implemented to perform the control law, what is the computational cost to perform the algorithm?

Response 9: We thank the reviewer for this important question. In our proposed scheme, the RNN (specifically, an RBFNN) is used within the observer to approximate un-modeled dynamics, not to directly compute the control law. The computational cost of the RBFNN is low for the following reasons:

• It uses a single hidden layer with 10–15 neurons and compact input vectors (composed of current, voltage, and estimated speed).
• Only a forward pass and a simple gradient update are executed per sampling step.
• All computations involve basic vector multiplications and element-wise activation functions (e.g., Gaussians), making them lightweight.

The complete algorithm, including the RBFNN, fuzzy estimator, and control law, was implemented on a dSPACE DS1104 board running at 5 kHz. The total CPU load remained under 40%, confirming its suitability for real-time execution on standard embedded hardware.

Comments 10: What considerations should be taken in account for a real time implementation, taking in account the use of dSPACE card (DS1104)?

Response 10: Thank you for the valuable question. When implementing the proposed scheme on a dSPACE DS1104 board, the following key considerations were taken into account:

1. Sampling Time and Task Scheduling: The control loop was executed at 5 kHz, with strict scheduling to ensure all computations (observer, RBFNN, fuzzy estimator, and control law) completed within one cycle.
2. Fixed-Step Discretization: All continuous-time models were discretized using fixed-step solvers compatible with real-time execution in Simulink + RTI (Real-Time Interface).
3. Memory and CPU Load Management: The DS1104 (PowerPC 604e @ 400 MHz + DSP) provided sufficient resources. The full algorithm maintained <40% CPU load, ensuring headroom for reliable operation.
4. I/O Configuration: Analog inputs were mapped for current and voltage acquisition, while digital PWM outputs were configured for inverter control.
5. Signal Conditioning and Filtering: Proper analog filtering was applied to reduce measurement noise before ADC conversion, improving observer accuracy.
6. Code Generation and Debugging: Code was auto-generated via MATLAB/Simulink, tested in SIL/HIL phases, and debugged using dSPACE ControlDesk.

These steps ensured robust and real-time-capable deployment of the proposed scheme on the DS1104 platform.

Comments 11: What is the sample frequency used?

Response 11: The sampling frequency used in all real-time experiments was 5 kHz. This value ensures accurate acquisition of stator current and voltage signals, while allowing stable and fast execution of the observer, fuzzy estimator, and RBFNN correction within each control cycle.

Comments 12: What is the size of the data set acquired to feed the proposed algorithms?

Response 12: The RBFNN and fuzzy estimators are trained and adapted online, meaning they do not rely on a pre-recorded offline dataset. Instead, they use a stream of real-time measurements (stator currents, voltages, and estimated speed) acquired continuously during operation. The adaptive laws update the parameters incrementally, making the approach data-efficient and suitable for embedded implementation.

 

Comments 13: There are a few simple concerns but in general is a very complete paper which use a couple of machine learning tools like neural networks and fuzzy logic and it is a very interesting approach in the field of electric machines control.

Response 13: We sincerely thank the reviewer for their positive evaluation and encouraging feedback. We are pleased to know that the integration of machine learning tools such as neural networks and fuzzy logic within our control framework was found interesting and relevant to the field of electric machine control. We have carefully addressed all raised concerns to further improve the clarity and robustness of the work.

Reviewer 2 Report

Comments and Suggestions for Authors

This study develops a learning-driven passivity-based control scheme for sensorless induction motors, combining a nonlinear adaptive observer with recurrent neural networks to enhance robustness and estimation accuracy under dynamic conditions. This manuscript is well-written and its validity has been verified through experiments. The following issues need to be resolved before it can be accepted as:
1) The contribution points are not clear. The author is advised to summarize the contribution points by comparing them with the current research.

2) The author needs to summarize and analyze the control difficulties and technical challenges of this research.

3) The author designed the controller based on the NN and Fuzzy algorithms, but the author did not consider how to address the issue that these methods would lead to an increase in computational load. It is suggested that the author should thoroughly discuss some low-computation neural networks and fuzzy algorithm studies in the manuscript, such as "Fast fixed-time distributed neural formation control-based disturbance observer for multiple rotor unmanned aerial vehicles under unknown disturbances", and "Velocity-free adaptive neural-fuzzy predefined-time attitude control for spacecraft".

4) The author needs to add more current literature analysis on state observers in the Introduction Section in order to enrich the research background.

5) As the current manuscript contains many abbreviations, it is recommended that the author summarize them using tables or other methods.

6) The shortcomings of the current research need to be summarized and the future research directions should be proposed.

Author Response

Comments 1: The contribution points are not clear. The author is advised to summarize the contribution points by comparing them with the current research.

Response 1: We thank the reviewer for this important observation. To clarify and highlight the main contributions of the manuscript, we have added a clear summary of contributions at the end of the Introduction section. These contributions are also positioned in contrast with existing research, particularly those using conventional passivity-based control or fixed-model observers. The main contributions are:

1. Integration of a Learning-Driven Observer: A novel nonlinear adaptive observer is proposed, enhanced by an RBF neural network to estimate unmeasurable states (flux and speed) under model uncertainty and measurement noise.
2. Hybrid Sensorless Estimation Strategy: A fuzzy MRAS estimator is embedded within the observer architecture to refine speed estimation, improving robustness compared to classical MRAS or PLL-based methods.
3. Real-Time Implementation and Validation: The full scheme is implemented on a dSPACE DS1104 board at 5 kHz, demonstrating real-time feasibility and outperforming conventional passivity-based and sensorless techniques in accuracy and noise resilience.
4. Robustness to Model Uncertainties: The combined use of learning and adaptive control significantly improves the controller’s robustness to parametric variations, which is experimentally validated under dynamic operating conditions.

These contributions have now been clearly stated in the revised manuscript on page 3, lines 94–105.

Comments 2: The author needs to summarize and analyze the control difficulties and technical challenges of this research.

Response 2: We thank the reviewer for this important suggestion. In the revised manuscript, we have added a dedicated paragraph summarizing the main control difficulties and technical challenges addressed by this research, highlighting how they motivate the proposed solution. This new content is included on page 2, lines 79–93.

 

Comments 3: The author designed the controller based on the NN and Fuzzy algorithms, but the author did not consider how to address the issue that these methods would lead to an increase in computational load. It is suggested that the author should thoroughly discuss some low-computation neural networks and fuzzy algorithm studies in the manuscript, such as "Fast fixed-time distributed neural formation control-based disturbance observer for multiple rotor unmanned aerial vehicles under unknown disturbances", and "Velocity-free adaptive neural-fuzzy predefined-time attitude control for spacecraft".

Response 3: We thank the reviewer for highlighting this important consideration. In the revised manuscript, we have included a brief discussion of low-computation neural and fuzzy control methods in the text. While our current design focuses on real-time feasibility and demonstrates acceptable performance on a 400 MHz DSP (with <40% CPU usage), we fully agree that computational efficiency remains a critical concern for broader deployment. Accordingly, we now reference recent developments such as: [39], [40], and [41]   

Comments 4: The author needs to add more current literature analysis on state observers in the Introduction Section in order to enrich the research background.

Response 4: We respectfully thank the reviewer for the suggestion. However, we believe that the current manuscript already provides a sufficient and focused review of relevant recent literature on nonlinear and adaptive observers, particularly those applied in sensorless induction motor control. Notably, we cite works on MRAS observers, fuzzy-enhanced structures, and neural-compensated observers, which directly relate to and motivate our proposed design. Nonetheless, to further strengthen the background, we have added a sentence referencing a few additional recent observer designs in the Introduction, while keeping the review concise and on-topic.

Comments 5: As the current manuscript contains many abbreviations, it is recommended that the author summarize them using tables or other methods.

Response 5: We thank the reviewer for this helpful suggestion. As noted, a comprehensive list of abbreviations has already been included in the manuscript (see Table 5, page 26, line 727). This table summarizes all abbreviations used throughout the paper to support readability and clarity.  

Comments 6: The shortcomings of the current research need to be summarized and the future research directions should be proposed.

Response 6: We appreciate the reviewer’s thoughtful suggestion. In response, we have added a short paragraph at the end of the Conclusion section that summarizes the main limitations of the present work and outlines future research directions. These additions aim to clarify the scope and encourage further development of the proposed control strategy.  

Reviewer 3 Report

Comments and Suggestions for Authors

This paper considers a learning-driven passivity-based control for sensorless induction motors, combining a nonlinear adaptive observer with recurrent neural networks. The comments are as follows.

1. In the listed contributions in introduction, the reasons why it has the advantages should be explained.
2. In the block diagrams, the corresponding equation numbers should be cited in each blocks.
3. How will the key parameters affect the control performance such as precison, speed, signal amplitude, etc.?
4. Give some comparative analysis to demonstrate the advantages of the proposed control.
5. Invesitigate the latest advances. Comment 10.1109/TII.2021.3057832 in introduction will be useful.

Author Response

Comments 1: In the listed contributions in introduction, the reasons why it has the advantages should be explained.

Response 1: We thank the reviewer for this useful suggestion. In the revised manuscript, we have expanded the listed contributions in the Introduction to briefly justify why each element of the proposed scheme contributes to improved performance, robustness, or real-time feasibility. These clarifications help emphasize the motivation and impact of each technical component (on page 3, lines 94–105).  

Comments 2: In the block diagrams, the corresponding equation numbers should be cited in each blocks.

Response 2: We appreciate the reviewer’s suggestion. However, we respectfully believe that citing equation numbers inside the block diagrams may negatively impact clarity and readability. The diagrams are intended to provide a high-level structural overview of the control and estimation architecture, while detailed mathematical formulations are already clearly presented and numbered in the corresponding sections of the text. To avoid cluttering the figures and to maintain visual clarity, we have opted to keep the diagrams focused on functional flow. However, to assist the reader, we have ensured that all blocks are clearly described and referenced in the figure captions and in the main text, where the associated equations are properly cited.

Comments 3: How will the key parameters affect the control performance such as precision, speed, signal amplitude, etc.?

Response 3: We thank the reviewer for this relevant question. The influence of key parameters (such as model uncertainty, sampling rate, and signal quality) on control performance—particularly in terms of estimation precision, dynamic speed response, and signal amplitude tracking—is analyzed in multiple parts of the manuscript. A detailed discussion is provided in:

• Section 5.2 (Sensitivity to parameter variations)
• Section 5.3 (Effect of measurement noise and signal quality)
• Section 6.2 (Experimental performance metrics and CPU load)
• Reviewer A – Responses to Q1, Q4, and Q8

These sections show that the proposed learning-enhanced observer and control scheme maintains robust performance under variation in key parameters.

Comments 4: Give some comparative analysis to demonstrate the advantages of the proposed control.

Response 4: We appreciate the reviewer’s suggestion regarding comparative analysis. To maintain focus, clarity, and accessibility of th study, we have intentionally limited the scope to self-comparative benchmarks within our proposed framework. This includes comparisons with and without the RBFNN correction term, and with and without the fuzzy estimator, as shown in Figures 11–13 and discussed in Section 6.2.

These comparisons clearly demonstrate the added value of each component (neural learning, fuzzy adaptation) in improving control precision and robustness. Broader comparisons with other advanced control schemes (e.g., sliding mode, predictive, or PI-MRAS) will be considered in our future work to avoid overwhelming the current contribution.

Comments 5: Investigate the latest advances. Comment 10.1109/TII.2021.3057832 in introduction will be useful.

Response 5: Thank you for suggesting the inclusion of the article with . We agree that it provides valuable insights into sliding-mode and barrier-function-based control techniques applicable to nonlinear systems with robustness concerns. We have now cited this reference in the text, highlighting its relevance to enhancing stability in advanced control architectures.  

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

2. Mathematical Framework and Problem Statement

2.1. Dynamic Model of an Asynchronous Motor

How much affect the parameter variations in the induction motor mathematical model in the propossed scheme?

The previous review concern has been attended

How affect the non modeled dynamic of rotor, and what implication has the assumption of that only the fundamental harmonic of the rotor's magnetomotive force (MMF) is considered?

The previous review concern has been attended

if the electirc machine has some electrical fault although it be incipient, which all the concordia frame work conditions are not achivied, what happend with the alpha-beta model? 

The previous review concern has been attended

2.2. Problem Formulation

The estimation of the flux and torque is based on the data acquire of the stator currents, what is the impact of the performance of the propossed scheme of the quality of data acquired?

The previous review concern has been attended

3. Nonlinear Observer Design

3.2. The Proposed Nonlinear Intelligent Observer Design

A FFBP neural network is used and it is fine, but, are there another machine learning approach that colud be used?

The previous review concern has been attended

3.3. The Proposed Fuzzy-MRAS Estimator

How impact the sample frequency to perform the control law, the fuzzy estimator and the FFBP neural network in conjunction and how it impact the propossed scheme performance?

The previous review concern has been attended

What is the computational cost to perform the propossed scheme?

The previous review concern has been attended

4. Passivity Based Output-Feedback Controller

The deterministic model depen on the parametric variation, how it impact the performance of the propossed scheme?

The previous review concern has been attended

The RNN was implemented to perform the control law, what is the computational cost to perform the algorithm?

The previous review concern has been attended

5. Experimental Results and Discussion

What considerations should be take in account for a real time implementation, takeing in account the use of dSPACE card (DS1104)?

The previous review concern has been attended

What is the sample frequency used?

The previous review concern has been attended

What is the size of the data set acquired to fed the propossed algorithms?

The previous review concern has been attended

There are a few simple concerns but in general is a very complete paper wich use a couple of machine learing tools like neural networks and fuzzy logic and it is a very interesting approach in the field of electric machines control.

The previous review concern has been attended