Pole-Zero Map10.80.60.4Imaginary Axis0.20-0.2-0.4-0.6-0.8-1-2System: GPole : -2Damping: 1Overshoot (%): 0Frequency (rad/sec): 2System: GPole : -1Damping: 1Overshoot (%): 0Frequency (rad/sec): 1System: GPole : 0Damping: -1Overshoot (%): 0Frequency (rad/sec): 0-1.8-1.6-1.4-1.2-1Real Axis-0.8-0.6-0.4-0.20

图2-1 零、极点分布图

实验2.1所作曲线5432Imaginary Axis10-1-2-3-4-5-7-6-5-4-3-2-1012Real Axis

图2-2 根轨迹图

16 实验2.1所作曲线5432System: GGain: 6.25Pole: 0.0128 + 1.44iDamping: -0.00893Overshoot (%): 103Frequency (rad/sec): 1.44Imaginary Axis10-1-2-3-4-5-7System: GGain: 0.384Pole: -0.442Damping: 1Overshoot (%): 0Frequency (rad/sec): 0.442System: GGain: 6.03Pole: 0.00303 - 1.42iDamping: -0.00214Overshoot (%): 101Frequency (rad/sec): 1.42-6-5-4-3-2-1012Real Axis

图2-3 根轨迹图（2）

%求临界稳定时的根轨迹增益Kgl z=[];p=[0 -1 -2];k=1;G=zpk(z,p,k); rlocus(G)

title('实验2.1 临界稳定时的根轨迹增益Kgl'); [k,p]=rlocfind(G) 运行结果：

Select a point in the graphics window selected_point = 0.0059 + 1.4130i k = 6.0139 p =

-3.0013 0.0006 + 1.4155i 0.0006 - 1.4155i

17 实验2.1 临界稳定时的根轨迹增益Kgl5432Imaginary Axis10-1-2-3-4-5-7-6-5-4-3-2-1012Real Axis

图2-4 根轨迹图（3）

%求取根轨迹的分离点与相应的根轨迹增益 z=[];p=[0 -1 -2];k=1;G=zpk(z,p,k); rlocus(G)

title('实验2.1 根轨迹的分离点与相应的根轨迹增益曲线图'); [k,p]=rlocfind(G) 运行结果：

Select a point in the graphics window selected_point = -0.4226 k = 0.3849 p = -2.1547 -0.4227 -0.4226

18 实验2.1 根轨迹的分离点与相应的根轨迹增益曲线图5432Imaginary Axis10-1-2-3-4-5-7-6-5-4-3-2-1012Real Axis

图2-5 根轨迹图（4）

2．

要求：确定系统具有最大超调量时的根轨迹增益；

解：当Kg=5.5时，系统具有最大超调量=3.89% ，如图2-6所示。 % Matlab程序

num=5.5*[1 3];den=[1 2 0];G0=tf(num,den);G=feedback(G0,1,-1); step(G) title('实验2.2 系统阶跃响应曲线');

19 实验2.2 系统阶跃响应曲线1.4System: GPeak amplitude: 1.04Overshoot (%): 3.89At time (sec): 0.7211.21Amplitude0.80.60.40.2000.5Time (sec)11.5

图2-6 实验2.2 系统阶跃响应曲线

3．绘制下列各系统根轨迹图。 %Matlab计算程序

x1=[1 0];x2=[1 4];x3=[1 6];x4=[1 4 1];y1=conv(x1,x2);y2=conv(x3,x4);z=conv(y1,y2) 运行结果： z =

1 14 65 106 24 0 %绘制系统根轨迹图。

num=[1 2 4];den=[1 14 65 106 24 0];G0=tf(num,den); G=feedback(G0,1,-1);rlocus(G) title('实验2.3系统根轨迹图');

20