Modeling and Tracking Control of Nondifferentiable Sandwiched Dynamic Systems: Case Study on Gear Transmission Servo Systems
Bibliographic record
Abstract
Many practical engineering systems, classified as nondifferentiable sandwiched dynamic systems (NSDSs), pose significant challenges to controller design due to their inherent unknown nondifferentiable nonlinearities. Among these, gear transmission servo (GTS) systems constitute a prominent research focus, exemplifying the complexities associated with modeling and control in NSDSs. Specifically, gear backlash introduces internal dead-zone nonlinearities, causing detrimental effects such as vibrations, diminished control accuracy, and potential instability. Such systems, characterized by unknown parameters including dead-zone characteristics, form fourth-order nonlower triangular dynamic structures, further complicated by uncertainties and external disturbances that impede convergence and controller performance. To address these critical challenges, this article proposes a novel block-structured control framework (BSCF) integrating feedforward compensation, nonlinear extended state observers, and dynamic surface control techniques, all built upon system identification results. A rigorous Lyapunov-based analysis is provided to establish that the tracking error converges to a bounded neighborhood of the origin, with the ultimate bound being adjustable through suitable parameter tuning. Experimental results confirm the effectiveness of the proposed strategy in eliminating the adverse effects of dead-zone nonlinearities and achieving satisfactory tracking accuracy. Furthermore, this control framework demonstrates broad applicability and can be extended to other sandwiched systems featuring nondifferentiable nonlinearities and/or nonlower triangular structures.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".