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福大电气812自动控制理论2017模拟卷

一、已知描述系统的微分方程组如下所示：

061

1521343

325

54356

0.254

X X X X X X X X X dX X X dt

dX X X dt

X X X -=-=-=+=+=+= （1）画出该系统的结构图（2）求传递函数60()()()G s X s X s =。

二、已知一控制系统的结构图如下，

（1）确定该系统在输入信号()1()r t t =下的时域性能指标：超调量%σ，调节时间S t 和峰值时间P t ；

（2）当()21(),()4sin3r t t n t t =?=时，求系统的稳态误差。

三、证明根轨迹分离点公式。

1111

j i j i d z d p ===--∑∑

四、单位反馈系统如图所示，其中21

(),0()(22)

G s a s s a s s =

>+++为待定参数。

（1）设()0C G s K =>，已知系统四条根轨迹只有一个分离点（或会合点）-1，确定参数a 并画出根轨迹图。

（2）确定根轨迹和虚轴的交点并由此确定使闭环系统稳定的K 值。（3）确定系统输出无衰减振荡分量时的闭环传递函数。

五、控制系统的结构图如图（a ）所示，其中1()G s 的频率特性如图（b ）（0,0T τ>>）

（a ）控制系统结构图

（b ）1()G s 的频率特性

（1）写出1()G s 的表达式；（2）设22

()G s s =

，求出系统的开环传递函数；（3）画出系统的幅相频率特性曲线，并用Nyquist 稳定判据分析其稳定性。

六、由实验测得某最小相位系统的幅频特性对数标图如图所示，试求：（1）系统的开环传递函数G(s)并画出系统的相频特性曲线；（2）计算系统的相角裕度γ和幅值裕度g K ；

（3）闭环系统对单位阶跃输入和单位斜坡输入的稳态误差分别是多少？

七、某火炮指挥系统是一个单位负反馈系统，其开环传递函数为

()(0.21)(0.51)

G s s s s =

++，系统最大输出速度为2r/min ，输出位置的容许误差小

于2度，求：

（1）确定满足上述指标的最小K 值，计算该 K 值下的相位裕量和幅值裕量；（2）前向通路中串联超前校正网络0.41

()0.081

c s G s s +=+，试计算相位裕量。

八、设()(1)(0.251)

o K

G s s s s =

++，设计串联校正装置，使系统满足下列性能指标：

15,40,0.5c K s γω-≥≥≥ 。

九、已知系统的结构框图如图所示。

（1）求出系统的闭环脉冲传递函数；

（2）设图中1211

(),(),()1Ts e K s G s G s H s s s K --+===+，试确定系统稳定时K 的取值范围。

已知：

111,,1(1)

T z z Tz Z Z Z s z s z e s z αα-??????

===??????-+--??????。

十、系统的方框图如图1所示，其中1,1,1,45M h θ==?== 所有的非线性特性均关于原点中心对称，2

()Ts G s s

。（1）画出负倒特性曲线和线性部分()G s 的Nyquist 图；

（2）分析当0.5T =时，系统是否存在自激振荡，如果存在自激振荡，请计算输出端的振幅和频率；

（3）讨论参数T 的变化对系统自激振荡的影响。

图中死区、饱和特性和继电特性等非线性环节的描述函数分别为：

1232

2()arcsin ,22()arcsin ,4(),K N X X X K N X X X Mh

N X j X h X ππππ??=-≥?????=≥???=

≥

图1

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