图 4-144　图 4-143 所示各系统单位阶跃响应曲线（MATLAB）

(a)

• System: sys
• Settling Time (sec): 0.391

(b)

• System: sys
• Settling Time (sec): 1.96

(c)

• System: sys
• Settling Time (sec): 2.3

(d)

• System: sys
• Peak amplitude: 1.16
• Overshoot (%): 16.3
• At time (sec): 1.21
• System: sys
• Settling Time (sec): 2.69

(e)

• System: sys
• Peak amplitude: 1.3
• Overshoot (%): 29.9
• At time (sec): 0.81
• System: sys
• Settling Time (sec): 2.5

(f)

• System: sys
• Peak amplitude: 1.43
• Overshoot (%): 42.7
• At time (sec): 2.68
• System: sys
• Settling Time (sec): 13.6

4-43　已知单位反馈系统的开环传递函数 \(G(s)=\dfrac{K^{*}(s+a)}{s(s+1)}\)，试绘制 \(a>1\)，\(K^{*}\) 从 \(0\to+\infty\) 时系统的闭环根轨迹图。

解　系统的开环传递函数为

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