实验三 频率特性分析一·实验目的1.掌握频率特性的基本概念，尤其是频率特性的几种表示方法。

2.能熟练绘制极坐标频率特性曲线（奈奎斯特曲线）和对数频率特性曲线，尤其要注意的是在非最小相位系统时曲线的绘制。

3.正确应用频率稳定判别方法，包括奈奎斯特稳定判据和对数稳定判据。

4.熟练正确计算相位裕量和幅值裕量。

5.掌握闭环频率特性的基本知识以及有关指标的近似估算方法。

二·实验内容1增加开环传递函数零极点个数对奈奎斯特图的影响 1）改变有限极点个数n ，使n=0,1,2,3Nyquist DiagramReal AxisI m a g i n a r y A x i s-2-101234-3.5-3-2.5-2-1.5-1-0.500.511.52n=0n=1n=2n=32）改变原点处极点个数v ，当v=1,2,3,4,Nyquist DiagramReal AxisI m a g i n a r y A x i s-2-1.5-1-0.500.511.52-2-1.5-1-0.500.511.52System: sysP hase Margin (deg): -32.9Delay Margin (sec): 4.41At frequency (rad/sec): 1.3Closed Loop Stable? No System: sysP hase Margin (deg): -121Delay Margin (sec): 3.49At frequency (rad/sec): 1.2Closed Loop Stable? NoSystem: sysP hase Margin (deg): 150Delay Margin (sec): 2.28At frequency (rad/sec): 1.15Closed Loop Stable? NoSystem: sysP hase Margin (deg): 51.8Delay Margin (sec): 0.575At frequency (rad/sec): 1.57Closed Loop Stable? Yesv=1v=2v=3v=43）改变有限零点个数m ，使m=1,2,3,4Nyquist DiagramReal AxisI m a g i n a r y A x i s-2-1.5-1-0.500.51 1.52-2-1.5-1-0.50.51System: sysP hase Margin (deg): 103Delay Margin (sec): 3.25At frequency (rad/sec): 0.55Closed Loop Stable? YesSystem: sysP hase Margin (deg): 20.6Delay Margin (sec): 0.499At frequency (rad/sec): 0.721Closed Loop Stable? Yesm=1m=2m=3m=42奈奎斯特判据与对数频率稳定判据 )1)(1()1()()(321s T s T s s T K s H s G v+++=1） 根据传递函数，由根轨迹图设定参数，使该系统成为条件稳定系统。

（K=1，v=1，T1=0.1，T2=0.2，T3=0.5）。

2） K 的取值范围。

3） 分别使K1小于，K2等于，K3大于临界稳定值，观察奈氏图与伯德图的变化，总结频率响应的稳定判别方法。

4） 在奈氏图和伯德图上分别读出幅值裕度和相角裕度，指明他们的对应关系。

K=1Root LocusReal AxisI m a g i n a r y A x i s-10-8-6-4-202-20-15-10-55101520System: sys Gain: 24.2P ole: 0.00586 + 5.87i Damping: -0.000998Overshoot (%): 100Frequency (rad/sec): 5.87奈氏图Nyquist DiagramReal AxisI m a g i n a r y A x i s-2-1.5-1-0.500.511.52-2-1.5-1-0.50.511.52System: sys2P hase Margin (deg): -2.2Delay Margin (sec): 0.966At frequency (rad/sec): 6.46Closed Loop Stable? NoSystem: sys1P hase Margin (deg): 60.7Delay Margin (sec): 1.18At frequency (rad/sec): 0.901Closed Loop Stable? YesSystem: sys3P hase Margin (deg): 178Delay Margin (sec): 0.48At frequency (rad/sec): 6.46Closed Loop Stable? NoK1=1K2=30K3=-30伯德图Bode DiagramFrequency (rad/sec)-100-5050System: sys2Gain Margin (dB): -2.18At frequency (rad/sec): 5.77Closed Loop Stable? NoSystem: sys1Gain Margin (dB): 27.4At frequency (rad/sec): 5.77Closed Loop Stable? YesM a g n i t u d e (d B )10-1100101102-270-180-9090System: sys3P hase Margin (deg): 178Delay Margin (sec): 0.48At frequency (rad/sec): 6.46Closed Loop Stable? NoSystem: sys2P hase Margin (deg): -2.2Delay Margin (sec): 0.966At frequency (rad/sec): 6.46Closed Loop Stable? NoP h a s e (d e g )System: sys1P hase Margin (deg): 60.7Delay Margin (sec): 1.18At frequency (rad/sec): 0.901Closed Loop Stable? Yes3非最小相位系统的奈奎斯特图 )4)(3)(2)(1()5(25)()(11s s s s s s H s G +++++=)4)(3)(2)(1()5(25)()(22s s s s s s H s G ++++--=Nyquist DiagramReal AxisI m a g i n a r y A x i s-6-4-20246-5-4-3-2-1012345System: sys2Phase Margin (deg): 150Delay Margin (sec): 1.12At frequency (rad/sec): 2.34Closed Loop Stable? NoSystem: sys1Phase Margin (deg): 20.5Delay Margin (sec): 0.153At frequency (rad/sec): 2.34Closed Loop Stable? YesBode DiagramFrequency (rad/sec)-150-100-5050System: sys1Gain Margin (dB): 4.71At frequency (rad/sec): 3.05Closed Loop Stable? YesM a g n i t u d e (d B )10-210-1100101102103-270-180-90090180System: sys2P hase Margin (deg): 150Delay Margin (sec): 1.12At frequency (rad/sec): 2.34Closed Loop Stable? NoP h a s e (d e g )System: sys1P hase Margin (deg): 20.5Delay Margin (sec): 0.153At frequency (rad/sec): 2.34Closed Loop Stable? Yes4闭环频率特性曲线与系统动态性能的关系系统如下：1)(,)4(4)(=+=s H s s s G ζ444)()(2++=s s s R s C ζ 观察当)1,0(∈ζ取不同值时系统的闭环频率响应与时域响应之间的关系。

当ζ=0.2时-100-5050100M a g n i t u d e (d B )系统开环伯德曲线的变化Frequency (rad/sec)10-210-110101102-180-135-90P h a s e (d e g )System: sysP hase Margin (deg): 22.6Delay Margin (sec): 0.205At frequency (rad/sec): 1.92Closed Loop Stable? Yes-80-60-40-20020M a g n i t u d e (d B )系统闭环伯德曲线的变化Frequency (rad/sec)10-110101102-180-135-90-450P h a s e (d e g )System: sys1P hase Margin (deg): 32.8Delay Margin (sec): 0.211At frequency (rad/sec): 2.71Closed Loop Stable? Yes系统阶跃响应的变化Time (sec)A m p l i t u d e0510150.20.40.60.811.21.41.6System: sys1P eak amplitude: 1.53Overshoot (%): 52.7At time (sec): 1.6System: sys1Settling Time (sec): 9.8当ζ=0.5时-80-60-40-2002040M a g n i t u d e (d B )系统开环伯德曲线的变化Frequency (rad/sec)10-110101102-180-135-90P h a s e (d e g )System: sysP hase Margin (deg): 51.8Delay Margin (sec): 0.575At frequency (rad/sec): 1.57Closed Loop Stable? Yes-80-60-40-20020M a g n i t u d e (d B )系统闭环伯德曲线的变化Frequency (rad/sec)10-110101102-180-135-90-450P h a s e (d e g )System: sys1P hase Margin (deg): 90Delay Margin (sec): 0.785At frequency (rad/sec): 2Closed Loop Stable? Yes系统阶跃响应的变化Time (sec)A m p l i t u d e01234560.20.40.60.811.21.4System: sys1P eak amplitude: 1.16Overshoot (%): 16.3At time (sec): 1.82System: sys1Settling Time (sec): 4.04当ζ=0.7时-80-60-40-2002040M a g n i t u d e (d B )系统开环伯德曲线的变化Frequency (rad/sec)10-110101102-180-135-90P h a s e (d e g )System: sysP hase Margin (deg): 65.2Delay Margin (sec): 0.877At frequency (rad/sec): 1.3Closed Loop Stable? Yes-80-60-40-20020M a g n i t u d e (d B )系统闭环伯德曲线的变化Frequency (rad/sec)10-110101102-180-135-90-450P h a s e (d e g )System: sys1P hase Margin (deg): 164Delay Margin (sec): 7.15At frequency (rad/sec): 0.4Closed Loop Stable? Yes系统阶跃响应的变化Time (sec)A m p l i t u d e00.51 1.52 2.53 3.540.20.40.60.811.21.4System: sys1P eak amplitude: 1.05Overshoot (%): 4.6At time (sec): 2.21System: sys1Settling Time (sec): 2.995开环频率特性与时域性能指标之间的关系 （1）低频段 vj Kj G )()(ωω≈当K=20，v=0时-60-40-2002040M a g n i t u d e (d B )Bode DiagramFrequency (rad/sec)10-110101102103-180-135-90-450P h a s e (d e g )System: sys1P hase Margin (deg): 27.4Delay Margin (sec): 0.0156At frequency (rad/sec): 30.6Closed Loop Stable? Yes当K=20，v=1时Bode DiagramFrequency (rad/sec)10-110101102103-270-225-180-135-90System: sys2P hase Margin (deg): 90Delay Margin (sec): 0.0785At frequency (rad/sec): 20Closed Loop Stable? YesP h a s e (d e g )System: sys1P hase Margin (deg): -7.52Delay Margin (sec): 0.757At frequency (rad/sec): 8.13Closed Loop Stable? No -150-100-5050M a g n i t u d e (d B )System: sys1Gain Margin (dB): -2.5At frequency (rad/sec): 7.07Closed Loop Stable? No当K=20，v=2时Bode DiagramFrequency (rad/sec)10-1100101102103-360-315-270-225-180System: sys1P hase Margin (deg): -58.6Delay Margin (sec): 1.37At frequency (rad/sec): 3.85Closed Loop Stable? NoSystem: sys2P hase Margin (deg): 0Delay Margin (sec): 0At frequency (rad/sec): 4.47Closed Loop Stable? No P h a s e (d e g )-200-150-100-50050100System: sys2Gain Margin (dB): 0At frequency (rad/sec): 4.47Closed Loop Stable? NoM a g n i t u d e (d B )（2）中频段)12)(1()()(22+++=n nssTs Ks H s G ωζω已知系统如上，设定参数K ，)1,0(∈ζ，要求改变交接频率1/T 和Wn 观察系统的相对稳定性与伯德图幅频特性在穿越频率处斜率的关系。