自控仿真作业

Nyquist Diagram10864Imaginary Axis20-2-4-6-8-10-1System: GGain Margin (dB): 6.89At frequency (rad/sec): 3.4Closed Loop Stable? YesSystem: GPhase Margin (deg): 69.4Delay Margin (sec): 0.713At frequency (rad/sec): 1.7Closed Loop Stable? Yes-0.8-0.6-0.4-0.200.20.4Real Axis

第六章 线性系统的校正

1. 6-1 设有单位反馈的火炮指挥仪伺服系统，其开环传递函数为

G0(s)?K，若要求系统最大输出速度为12?s，输出位置的容许

s(0.2s?1)(0.5s?1)误差小于2?，试求： （1）确定满足上述指标的最小K值，计算该K值下系统的相角裕度和幅值裕度；

0.4s?1（2）在前向通路中串接超前校正网络Gc(s)?，计算校正后系统的相角

0.08s?1裕度和幅值裕度，说明超前校正对系统动态性能的影响。 MATLAB程序如下： k=6;

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G0=tf(k,[conv([0.2,1,0],[0.5,1])]); Gc=tf([0.4,1],[0.08,1]); G=series(Gc,G0); G1=feedback(G0,1); G11=feedback(G,1); figure(1);

subplot(211);margin(G0);grid; subplot(212);margin(G);grid; figure(2);

step(G1,'r',G11,'b--');grid; 仿真结果如下：

Bode DiagramGm = 1.34 dB (at 3.16 rad/sec) , Pm = 4.05 deg (at 2.92 rad/sec)2000-2000-180-360-21010-1)agnitude (dB)Phase (degM100101102103)agnitude (dB)Phase (degMFrequency (rad/sec)Bode DiagramGm = 9.9 dB (at 7.38 rad/sec) , Pm = 29.8 deg (at 3.85 rad/sec)2000-2000-180-360-110100101102103Frequency (rad/sec)

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21.81.61.4ystem: G11eak amplitude: 1.431.2Overshoot (%): 43.5t time (sec): 0.7811AmplitudeSystem: G1Peak amplitude: 1.83Overshoot (%): 83At time (sec): 1.17Step ResponseSystem: G11Settling Time (sec): 3.24System: G11Final Value: 1System: G1Settling Time (sec): 42.70.8tem: G11e Time (sec): 0.3020.60.40.200102030Time (sec)405060 校正前 校正后 相角裕度 截止频率 幅值裕度 穿越频率 4.05 2.92 1.34 3.16 29.8 3.85 9.9 7.38 超调量 83.3 43.5 调节时间 42.7 3.24 分析：

由上图及表格可以看出，串联超前校正可以增加相角裕度，从而减少超调量，提高系统的稳定性，增大截止频率，从而缩短调节时间，提高快速性。 2. 6-5 设单位反馈系统的开环传递函数为G0(s)?8，若采用滞后-超前校

s(2s?1)正装置Gc(s)?(10s?1)(2s?1)对系统进行串联校正，试绘制系统校正前后的对

(100s?1)(0.2s?1)数幅频渐近特性，并计算系统校正前后的相角裕度。 MATLAB程序如下：

w=0.001:1:100;

G0=tf(8,[conv([1,0],[2,1])]);

Gc=tf([conv([10,1],[2,1])],[conv([100,1],[0.2,1])]); G=series(G0,Gc);figure(1);

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subplot(211);margin(G0); subplot(212);margin(G);

G1=feedback(G0,1);G11=feedback(G,1); figure(2);step(G1,'r',G11,'b--');grid;

仿真结果如下：

Bode DiagramGm = Inf dB (at Inf rad/sec) , Pm = 14.2 deg (at 1.97 rad/sec)1000-100-90Phase (deg)Magnitude (dB)-180-21010-1100101Phase (deg)Magnitude (dB)Frequency (rad/sec)Bode DiagramGm = Inf dB (at Inf rad/sec) , Pm = 74.5 deg (at 0.796 rad/sec)2000-200-90-180-41010-310-210-1100101102Frequency (rad/sec)

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