Tham khảo tài liệu 'essentials of control techniques and keyword stats_4', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 94 Essentials of Control Techniques and Theory -180 Figure Bode plot showing stabilization of a2 s2 using phase-advance a 3y ffl 3 a jffl . Consider a simpler example the system described by gain c s - s a when the input is e a . s a. If we turn back to the differential equation that the gain function represents we see x ax e at. Since the complementary function is now the same as the input function we must look for a particular integral which has an extra factor of t . the general solution is Frequency Domain Methods 95 w a Figure Family of response curves for various damping factors. Screen grab from 7 x te at Ae at. As t becomes large we see that the ratio of output to input also becomes large but the output still tends rapidly to zero. Even if the system had a pair of poles representing an undamped oscillation applying the same frequency at the input would only cause the amplitude to ramp upwards at a steady rate and there would be no sudden infinite output. Let one of the poles stray so that its real part becomes positive however and there will be an exponential runaway in the amplitude of the output. This page intentionally left .
