Global Fixed-Time Fault-Tolerant Control for Tracked Vehicles with Hierarchical Unknown Input Observers

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper addresses the issues of sensor failures and actuator faults in mining tracked mobile vehicles that operates in harsh environments. A global fixed-time fault-tolerant control strategy is developed based on a hierarchical unknown input observer. Some suggestions and questions are given to improve the paper.

1. The novelty is not clear enough. Some remarks should be given to further explain. 2
2. How to deal with the nonlinearity in the modelling process? It can influence the UIO design.
3. More comparative results need to be provided to impart the contribution.
4. How to implement the controller in practice?
5. Can the proposed method be applied to other practical models?

Author Response

Comments 1: The novelty is not clear enough. Some remarks should be given to further explain.

Response 1: We appreciate your valuable feedback. The introduction has been revised to better highlight the key contributions and innovative aspects of our research.

Comments 2: How to deal with the nonlinearity in the modelling process? It can influence the UIO design.

Response 2: Due to the inherent nonlinear characteristics of TMV systems, our approach to addressing the nonlinearity issues in the modeling process employs a parameter-dependent linearization technique to transform the nonlinear TMV system into a LPV model. A measurable scheduling parameter vector is defined to reconstruct the complex nonlinear dynamic equations containing sideslip and track slippage into state-space form. The parameter-dependent matrices preserve the nonlinear characteristics of the original system, while the LPV model framework enables observer and controller design based on linear system theory. Although the aforementioned design approach exhibits reduced accuracy compared to nonlinear models under extreme operating conditions, such as complete sensor failure and severe sideslip scenarios, it significantly reduces the computational complexity of the system.

Comments 3: More comparative results need to be provided to impart the contribution.

Response 3: Thank you for your valuable feedback. We have supplemented the study with additional experimental tests, incorporating more complex reference trajectories and sensor fault scenarios to conduct a comprehensive performance comparison analysis of three different sensors.

Comments 4: How to implement the controller in practice?

Response 4: The practical implementation of this controller requires establishing a corresponding hardware platform. Initially, a PLC is configured as the main control unit, with integrated data acquisition cards to enable real-time monitoring. GNSS modules and encoders are deployed to obtain position, attitude, and wheel speed information. Subsequently, parameter tuning is performed through a systematic procedure. First, the fixed-time differentiator parameters are adjusted to satisfy the theoretical convergence conditions. The sliding mode gains and integral gains of the four distributed observers are then configured sequentially. Next, the actuator efficiency observer parameters are set, followed by the determination of sliding mode surface parameters and control gains for the adaptive fault-tolerant controller. Finally, the system's control accuracy and fault-tolerant capability are evaluated through comprehensive testing.

Comments 5: Can the proposed method be applied to other practical models?

Response 5: The proposed approach demonstrates potential applicability to other model systems. The parameter-dependent LPV modeling framework developed herein can potentially be generalized to other nonlinear systems characterized by time-varying parameters. The hierarchical unknown input observer structure provides a systematic approach for handling high-dimensional system complexities. Furthermore, the fixed-time control methodology utilizing dual-power sliding mode surfaces offers theoretical guarantees suitable for applications requiring fixed-time convergence properties. Therefore, with appropriate parameter adjustments, the proposed framework may be transferable to alternative system models.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents a robust tracking control problem for underactuated underwater vehicles in horizontal motion. The article complies with the journal's format; the introduction, methods, results, and conclusions are clearly supported.

Author Response

The reviewer raised no revision suggestions.

Reviewer 3 Report

Comments and Suggestions for Authors

In the article under consideration, the authors propose a method of global fixed-time fault-tolerant control for tracked mobile vehicles (TMVs) that operate in harsh conditions such as mining. The main scientific contribution is the development of a hierarchical architecture of four observers – for state, for interference, for errors in position sensors and for errors in wheel speed sensors – which significantly reduces computational complexity and increases the accuracy of observation. The article presents an innovative solution with a clear contribution in the field of robust control of tracked vehicles in harsh conditions.

I believe that the following recommendations would improve the quality of the article:

1. Although the authors do not directly use the term "Kalman filter," the proposed hierarchical observer architecture and the combined use of models and measurements essentially follow the philosophy of the Kalman filter. This could be clarified or expanded upon by the authors to emphasize the analogy and its benefits, especially for an audience seeking a familiar context for the proposed method.
2. The authors presented only one block diagram, which makes it difficult to follow the information connections between individual observers and control blocks. It is recommended to add at least one or two more block diagrams that clearly illustrate the interaction between the observers and the controller.
3. In some places in the article, many symbols and indices are used (especially in dynamic equations and the LPV model). It would be helpful if the authors included a table with basic notation – this would improve the presentation of the presented results.
4. Although the article focuses on TMV in mining, the method itself could be applied in other areas (e.g. construction machinery, agricultural robots). I would suggest that the authors briefly discuss the potential application to other areas to further expand the impact of the study.

Author Response

Comments 1: Although the authors do not directly use the term "Kalman filter," the proposed hierarchical observer architecture and the combined use of models and measurements essentially follow the philosophy of the Kalman filter. This could be clarified or expanded upon by the authors to emphasize the analogy and its benefits, especially for an audience seeking a familiar context for the proposed method.

Response 1: Your observation is valid. The hierarchical unknown input observer architecture presented in this paper bears conceptual similarities to the Kalman filter methodology. In response to this observation, we have added a supplementary remark in the revised version to emphasize the unique contributions and advantages of the proposed approach, which can be found at the conclusion of the 'Actuator Fault-Tolerant Design' section.

Comments 2: The authors presented only one block diagram, which makes it difficult to follow the information connections between individual observers and control blocks. It is recommended to add at least one or two more block diagrams that clearly illustrate the interaction between the observers and the controller.

Response 2: We acknowledge your feedback and have accordingly redesigned Figure 3 to address the concerns raised.

Comments 3: In some places in the article, many symbols and indices are used (especially in dynamic equations and the LPV model). It would be helpful if the authors included a table with basic notation – this would improve the presentation of the presented results.

Response 3: Thank you for the suggestion. We would like to note that a main symbol table is already included in the appendix, which covers the most important notation used throughout the control system design process.

Comments 4: Although the article focuses on TMV in mining, the method itself could be applied in other areas (e.g. construction machinery, agricultural robots). I would suggest that the authors briefly discuss the potential application to other areas to further expand the impact of the study.

Response 4: We acknowledge your suggestion and have incorporated the pertinent discussion into the concluding section.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I have no questions.