Multiple robust controllers design for linear uncertain systems
Bibliographic record
Abstract
This thesis presents two design methods for multiple robust controllers (MRC) and a design method for switched robust controllers that can be used for linear systems with parametric uncertainty. These methods are helpful in enhancing the performance of feedback control systems beyond the performance limitations associated with conventional design methods for uncertain linear systems. MRC have been introduced to overcome the performance limitations imposed by the requirements for robustness. The design of MRC involves dividing the uncertainty set of a linear system into a number of subsets, as well as synthesizing of a robust controller for each subset. We propose two methods for the design of the uncertainty set divisions and controllers. The first method determines each controller and each subset in subsequent steps, and can deal with only time-invariant parametric uncertainties. In the second method, we find both each controller and each subset simultaneously. This method can handle both time-invariant and time-varying uncertainties. Switched robust controllers, on the other hand, have the potential to advance the existing performance limitations of a single linear time-invariant robust controller by switching among a set of linear time-invariant controllers. We introduce a new concept, robust finite-time tracking, that is a property of closed-loop uncertain systems. Robust finite-time tracking focuses on the transient response, as opposed to the steady-state response (as in Lyapunov-based techniques). We formulate an optimization problem for the design of switched robust finite-time tracking controllers. The controller design methods that discussed above include nonsmooth non-convex optimization problems. In order to find a local optimum to the problems, nonsmooth optimization techniques are utilized. We compare the performance of developed methods to existing methods in the literature through several numerical examples, such as inverted pendulum and mass-spring-damper systems. Moreover, to demonstrate the advantages of our method for MRC over traditional robust controllers in a practical example, we design multiple robust track-following controllers for hard disk drive servo-systems.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".