Управление качеством переходных процессов в многосвязных системах. Задание на курсовое проектирование, страница 13

Приращения параметров режима через их частные производные записываются следующим образом:

          ¶U            ¶U                                                                                          DU = —— Dd + —— DE_q                                                                   (2.63)                    ¶d             ¶E_q

          ¶w_u                ¶w_u                                                                                    Dw_u = —— pDd + ——– pDE_q                                                           (2.64)                    ¶pd              ¶pE_q

Используя эти выражения, выразим DEr через Dd и DE_q:

                   ¶U                 ¶U                   ¶w                     ¶w                           DE_r = ( W_U —– Dd + W_U —– DE_q + W_w —– pDd + W_w —— pDE_q +                                     ¶d                  ¶E_q                  ¶pd                  ¶pE_q

+ W_Eq) W_ok                                                                                         (2.65)

Вынося за скобки Dd и DE_q, имеем:

                          ¶U                    ¶w                              ¶U                                DE_r = ( W_UW_OK —– + W_wW_OK —– p)Dd + (W_UW_OK —– +                                                           ¶d                    ¶pd                              ¶E_q

                  ¶w                                                                                                   + W_wW_OK ——– + W_EqW_OK) DE_q                                                        (2.66)                          ¶pE_q

Обозначим:

                        ¶U                                                                                             W_Ud = W_UW_OK—–                                                                              (2.67)                                  ¶d

                        ¶w                                                                                     W_wd = W_wW_OK —–  (2.68)                                                                                                                           ¶pd

                            ¶U                                                                                 W_UEq = W_UW_OK —— + W_EqW_OK                                                                                          (2.69)                                     ¶Eq

                           ¶w                                                                                          W_wEq = W_wW_OK ——                                                                           (2.70)                                    ¶pE_q

С учетом (2.67) – (2.70) выражение (2.66) примет вид:

DE_r = ( W_Ud + W_wdp )Dd + (W_UEq +W_wEqp )DE_q

                                                                                                          (2.71)

                                                 Dd                    Dd                                                                                             —— (p)                                                                           DE_r                              DE_r