Changeset 806
- Timestamp:
- 02/09/10 11:07:13 (14 years ago)
- Files:
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- 1 modified
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applications/dual/texts/pmsm_system.lyx (modified) (7 diffs)
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applications/dual/texts/pmsm_system.lyx
r753 r806 338 338 \begin_inset Formula \begin{eqnarray} 339 339 \hat{x}_{t} & = & g(\hat{x}_{t-1})-K\left(y_{t}-h(\hat{x}_{t-1})\right).\label{eq:ekf_mean}\\ 340 R_{y} & = & C 'P_{t-1}C+R_{t},\nonumber \\341 K & = & P_{t-1}C R_{y}^{-1}(y_{t}-h(\hat{x}_{t-1})),\nonumber \\340 R_{y} & = & CP_{t-1}C'+R_{t},\nonumber \\ 341 K & = & P_{t-1}C'R_{y}^{-1},\nonumber \\ 342 342 P_{t} & = & A\left(P_{t-1}-P_{t-1}C'R_{y}^{-1}CP_{t-1}\right)A+Q_{t}.\label{eq:ekf_cov}\end{eqnarray} 343 343 … … 379 379 0 & 0 & \Dt & 1\end{array}\right],\quad C=\left[\begin{array}{cccc} 380 380 1\\ 381 & 1\\ 382 & & 0\\ 383 & & & 0\end{array}\right]\] 381 & 1\end{array}\right]\] 384 382 385 383 \end_inset … … 452 450 \end_layout 453 451 452 \begin_layout Standard 453 Limits: 454 \begin_inset Formula \begin{eqnarray*} 455 u_{\alpha,max} & = & 50V,\\ 456 u_{\beta,max} & = & 50V.\end{eqnarray*} 457 458 \end_inset 459 460 461 \end_layout 462 454 463 \begin_layout Section 455 464 Control … … 475 484 \end_inset 476 485 477 is the chosen penalization of the inputs. 486 is the chosen penalization of the inputs, in this case 487 \begin_inset Formula $\psi=0$ 488 \end_inset 489 490 . 478 491 479 492 \end_layout … … 530 543 \begin_inset Formula \begin{eqnarray*} 531 544 \hat{\isa{}} & = & 0,\,\hat{\isb{}}=0,\hat{\omega}=1,\th=\frac{\pi}{2},\\ 532 P_{t} & = & \mathrm{diag}([0.01,0.01, 1,1]).\end{eqnarray*}545 P_{t} & = & \mathrm{diag}([0.01,0.01,0.01,1]).\end{eqnarray*} 533 546 534 547 \end_inset … … 541 554 \begin_inset Formula \begin{eqnarray*} 542 555 \hat{\isa{}} & = & 0,\,\hat{\isb{}}=0,\hat{\omega}=1,\th=\frac{\pi}{2},\\ 543 P_{t} & = & \mathrm{diag}([0.01,0.01, 1,10]).\end{eqnarray*}556 P_{t} & = & \mathrm{diag}([0.01,0.01,0.01,10]).\end{eqnarray*} 544 557 545 558 \end_inset … … 550 563 \begin_layout Standard 551 564 The requested value 552 \begin_inset Formula $\overline{\omega}_{t}=3.$ 553 \end_inset 554 555 565 \begin_inset Formula $\overline{\omega}_{t}=1.0015.$ 566 \end_inset 567 568 569 \end_layout 570 571 \begin_layout Conjecture 572 It is sufficient to consider hyper-state 573 \begin_inset Formula $H=[\hat{i}_{\alpha},\hat{i}_{\beta},\hat{\omega},\hat{\vartheta},P(3,3),P(4,4)]$ 574 \end_inset 575 576 . 577 \end_layout 578 579 \begin_layout Conjecture 556 580 \begin_inset CommandInset bibtex 557 581 LatexCommand bibtex
