A Comparative Study of Nonlinear Control Techniques: Inverted Pendulum on a Cart
Bibliographic record
Abstract
An in depth comparative study is conducted between nonlinear dynamic inversion based controller and immersion and invariance based controller. Immersion and Invariance (I&I) is a constructive nonlinear control design methodology for robust and adaptive controller designs. I&I method, as the name implies, mainly relies upon the notions of system immersion and manifold invariance. The basic idea is to design a control law that asymptotically immerses the system dynamics into the reducedorder desired dynamics. In this work, Immersion and Invariance based controller is systematically compared against nonlinear dynamic inversion based controller using a benchmark control problem of an inverted pendulum on cart (IPCS). Simple yet rich dynamics of an inverted pendulum on cart poses an interesting problem to control. Stabilization and control of IPCS has posed as a benchmark problem for many researchers to test out different control techniques. This motorized contraption consists of a vertical pendulum with a pivot point mounted on a cart. The cart is able to move horizontally through the application of a parallel force, which in turn is the input to the system. The IPCS is a case of an under actuated mechanical system, where the angular acceleration of the pendulum cannot be directly controlled. In this work, I&I based controller designed for IPCS, and its robustness properties are compared with nonlinear dynamic inversion control techniques.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".