《自动控制原理(双语)》标准答案及评分标准.PDF
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长安大学 2007 -2008 学年第 1 学期 试题( B )卷 《自动控制原理 (双语)》标准答案及评分标准
一、(5 points )A control system is given in following figure ,Determine the transfer
function C(s)/R(s).
解: G (s)G s +G (s)G (s) C(s) 1 2 ( ) 2 3 R (s ) 1+G (s )H (s ) +G (s )G (s )H (s ) 2 1 1 2 2
二、(10 points )A unit-feedback system has the forward transfer function * K G(s) s(s +1)(s +3) 1)Draw the root of the system . 2)Evaluate the range of values of K for which the system is stable and the critically damped stable.
解: 1)a)开环极点 p 1 0, p 2 −1, p 3 =−3
b)实轴上的根轨迹:[-10],[- ∞,-3] n m p − z ∑ ∑ i j 0 1 3
c)渐进线 σa i 1 j 1 − − −1.33 2 3 d) 计算分离点: D(s)=1+D(s)=0 K ∗ 即 1+ 0 s(s 1)(s 3) + + K ∗ =−(s 3 +4s 2 +3s ) dK ∗ 2 由 0 , 得3d +8d+3=0 ds s d 解得d =-0.452,d =-2.215(舍),所以d=-0.452 1 2 * ∗ K d K d d =+1 d +3 0.63 ,K 0.21 d d 3 e)与虚轴的交点 3 2 * D