Rule #o The root Locus Crossing with the Imaginary Axis(根轨迹与虚轴的交点) The point where the locus crosses the imaginary axis may be obtained by substituting s=j@ into the characteristic equation and solving for a 1+GH(s)=0→1+GH()=0 Rell+ghg=o Im[1+GH(O=01 SP GH(s) K(S+5) 5K-402=0 S(S2+4s+8) (k+8)-02=0 S3+4s2+s(K+8)+5k=0 K=32 (5k-4o2)+f(k+8)0-3]=0 O=±6.32
• The point where the locus crosses the imaginary axis may be obtained by sunbstituting s = jω into the characteristic equation and solving for ω. Rule #6 The Root Locus Crossing with the Imaginary Axis (根轨迹与虚轴的交点） Im[1 ( ) 0] Re[1 ( ) 0] 1 ( ) 0 1 ( ) 0 + = + = + = + = G H j G H j G H s G H j 4 ( 8) 5 0 3 2 s + s + s K + + K = ( 4 8) ( 5) ( ) 2 + + + = s s s K s SP. GH s (5 4 ) [( 8) ] 0 2 3 K − + j K + − = ( 8) 0 5 4 0 2 2 + − = − = K K 6.32 32 = = K
Rule #7 The Breakaway Point of the Root Locus (t# 迹的分离点) The point at which the locus leaves a real-axis segment is found by determining a local maximum value of K. while the point at which the locus enters a real-axis segment is found by determining a local minimum value ofK(根轨迹离开实轴区段的点(分离点)由该区段的最大K值来 确定;而根轨迹进入实轴区段的点(分离点)由该区段的最小K值 来确定。)
• The point at which the locus leaves a real-axis segment is found by determining a local maximum value of K, while the point at which the locus enters a real-axis segment is found by determining a local minimum value of K.(根轨迹离开实轴区段的点（分离点）由该区段的最大K值来 确定；而根轨迹进入实轴区段的点（分离点）由该区段的最小K值 来确定。) Rule #7 The Breakaway Point of the Root Locus (根轨 迹的分离点） j − 2 −1 0 60 j − 2 −1 0