Consider a system response, , with one dominant pole, and other real-axis poles, and zeros such that                                 H s( ) A0 Π 1 s ωzi + ------ ⎝ ⎠ ⎛ ⎞ × 1 s ωp1 + ------- ⎝ ⎠ ⎛ ⎞ Π...

Consider a system response, , with one dominant pole, and other real-axis poles, and zeros such that

                                H s( ) A0 Π 1 s ωzi + ------ ⎝ ⎠ ⎛ ⎞ × 1 s ωp1 + ------- ⎝ ⎠ ⎛ ⎞ Π 1 s ωpi + ------ ⎝ ⎠ ⎛ ⎞

Also consider an approximating function, , given by

                                Happ( ) s Ao 1 s ωp1 + ------- ⎝ ⎠ ⎛ ⎞ 1 s ωeq + -------- ⎝ ⎠ ⎛ ⎞

Show that, when is approximated by such that the phase of the two systems are approximately equal at of , should be equal to

                                  1 ωeq -------- 1 ωpi ∑------ 1 ωzi