Research Paper Example: PID, LQR, and Integral State-Feedback for a Saturated Inverted Pendulum
A cleaned standalone engineering paper derived from a real Basis Draft Paper run. It preserves the nonlinear benchmark framing, controller synthesis arc, and selection guidance while removing placeholder summary figures and public-facing provenance noise.
This is the clearest engineering-comparison paper we have from paper mode. It shows Basis carrying a common-model benchmark, controller synthesis, nonlinear evaluation, and decision guidance through a real manuscript rather than a short derivation note.
ObjectiveCompare PID, LQR, and integral state-feedback controllers on the same nonlinear cart-pendulum benchmark under actuator saturation and disturbances, then turn that benchmark into scenario-specific selection guidance rather than a fake universal winner.
Original runOriginal Basis run: Draft Paper
OutputsPDF · references · curated viewer
ViewerA cleaned standalone paper derived from a real Draft Paper run. The original run artifact remains unchanged.
Run summary
What this run had to deliver.
Basis had to satisfy a concrete objective, keep the assumptions explicit, and leave behind artifacts
a human could inspect and continue.
Objective
Research Paper Example: PID, LQR, and Integral State-Feedback for a Saturated Inverted Pendulum
Compare PID, LQR, and integral state-feedback controllers on the same nonlinear cart-pendulum benchmark under actuator saturation and disturbances, then turn that benchmark into scenario-specific selection guidance rather than a fake universal winner.
Scope
What had to be covered
Hold the plant, actuator limit, and disturbance family fixed across all three controllers.
Interpret results through recoverability, disturbance tolerance, and saturation burden instead of a hidden score.
Keep the argument publishable by removing placeholder figure exports and run-only provenance language.
Artifacts
What persisted after the run
Cleaned standalone paper PDF
Curated references
Controller benchmark tables and equations
Cleaned public screenshots for the examples page
Editorial readout
What this run found, what surprised us, and what still needs work.
These notes summarize the actual content of the run, not just the artifact shell.
Findings
What Basis found
LQR is the strongest default when local regulation quality is the main goal and clipping is not the dominant transient mechanism.
Integral state-feedback is the better choice when sustained constant-disturbance rejection is central to the application.
PID remains viable as a simpler baseline, but only in the smaller recoverable regime under the shared actuator and disturbance limits.
Interesting results
What was unexpected
The paper’s most useful result is not a flashy time trace but the disciplined refusal to force a single winner across incompatible operating priorities.
Saturation burden emerges as the main bridge between nominal linear design logic and realized nonlinear performance.
The cleaned manuscript is stronger after removing the placeholder summary figures because the remaining argument has to stand on the benchmark tables and explicit selection logic.
Further investigation
What still needs work
A stronger next version would add hardware-facing effects such as observer error, sensor noise, and delay rather than stopping at the shared nonlinear simulation matrix.
Anti-windup, gain scheduling, and constrained-control variants should be compared explicitly against the same baseline envelope.
A future public edition should restore one or two fully materialized comparative figures derived directly from the benchmark records instead of relying mainly on the text-and-table synthesis.
Inside the output
What the document actually says.
Primary resultThe benchmark supports conditional controller selection rather than a single universal winner.
Benchmark disciplineAll three controllers are synthesized from the same upright model and tested under the same nonlinear constraints.
Cleanup outcomeThe public edition removes placeholder summary figures while preserving the actual comparative argument.
What the benchmark concludes
Representative summary
The paper’s core conclusion is conditional rather than universal: LQR is the strongest default near the nominal operating point when clipping is limited, integral state-feedback is most attractive when steady-state disturbance rejection is central, and PID remains a credible low-complexity baseline only in the smaller recoverable regime.
That conclusion matters because the manuscript keeps all three controllers on the same nonlinear plant, the same actuator bound, and the same disturbance semantics. The selection guidance is therefore driven by a shared benchmark rather than by apples-to-oranges controller narratives.
Title page and abstract from the cleaned standalone benchmark paper.Core comparative-results section translating the benchmark into recoverability and disturbance tradeoffs.Closing selection guidance and the retained external reference grounding the paper’s control-literature context.
Actual PDF
Read the output directly.
A cleaned standalone paper derived from a real Draft Paper run. The original run artifact remains unchanged.
