Linear Quadratic Optimal Control of Nonlinear Dynamic Systems
Bibliographic record
Abstract
Despite the progress made in the field of control engineering, there are still significant challenges involved in the control of nonlinear dynamic systems.This thesis presents a novel approach to addressing these challenges by leveraging the simplicity of linear optimal quadratic controllers to achieve efficient control of nonlinear dynamic systems that are otherwise considered too difficult to control.In this thesis, three nonlinear dynamic applications are presented: the 3-DOF helicopter, the 6-DOF aircraft landing gear, and the loudspeaker system.These systems face various challenges, including unstable dynamics, landing vibrations, intermodulation distortions, and under-actuation.As such, the Linear Quadratic Regulator (LQR) controller is proposed to control the 3-DOF Helicopter, the Linear Quadratic Gaussian (LQG) controller is proposed for the control of the 6-DOF aircraft landing gear, and both the LQR and the LQG controllers are proposed to control the loudspeaker system.The LQR controller computes the control signals of the systems while the LQG controller acts as a state estimator.The state-space model of each nonlinear dynamic system is derived, and then, the mathematical models of the optimal control strategies are calculated.The control strategies are also tested under various conditions and compared with an equally simple control strategy, the PID controller.To better evaluate the execution and the performance of the LQR and LQG control strategies, two quantitative tracking performance metrics are presented; i) the integral of the tracking errors, and ii) the integral of the control signals of the system.The results obtained affirm the robustness and competence of the proposed control strategies.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".