自动控制理论-I-ch7.pptVIP

At real axis, So the system is stable when Example 7.5 So the system is stable when Tt, and is unstable when Tt. Example 7.6 non-minimum phase system Conclusion： Nyquist diagram encircles the –1 point one time in the direction of counter-clockwise. N=1,P=1，Z=P-N=0, so the system is stable. The system is stable when K3. Example 7.7：The open-loop TF is 　 　 Determine the changing range of K.　　　　 The －1 point located on A or C, the system is stable. The –1 point located on B or D, the system is unstable. We can get： 　－1 locus on A, K19.2, stable 　－1 locus on B, 19.2K334, unstable 　－1 locus on C, 334K13200, stable 　－1 locus on D, K13200, unstable So the changing range of K is 0 K19.2 and 334K13200.　 7.4 Stability Margin of System The closeness of the L(jw) curve to “-1” is a measure of the relative stability of the system. There are two measures of relative stability ----- Gain Margin and Phase Margin. Phase Margin (PM): Definition：the phase angle through which the L(jw) locus must be rotated so that the unity magnitude |L(jw)|=1 point will pass through the (-1, 0) point in the L(jw)-plane. wc : the gain crossover frequency 　 　PM0(PM0) indicates a stable (an unstable) system. Gain Margin(GM): Kg Definition：the reciprocal of the gain |L(jw)| at the frequency at which the phase angle reaches -180°. wg: the phase crossover frequency 　GM1(0 dB) indicates a stable closed-loop system and the system will remain stable if the loop gain increase is less than GM. GM1(0 dB) indicates an unstable closed-loop system and a reduction of loop gain at least GM is required for the system to become stable. 0 phase margin Gain margin Kg Gain and Phase Margins on Bode plots. 7.5 Dynamics performance of closed-loop from open-loop frequency characteristic 1. System type and steady state error System type Slope of the low frequency asymptote type 0 0. type 1