请问各位大大们三题有关根轨迹设计的问题 第一题： 画出系统特徵方程式的跟轨迹，其中 L(s) = (s+1) / [s(s+1)(s+2)] 然後计算跟轨迹的增益使共轭复数极点有阻尼比0.5 第二题： 数值控制工具机的定位伺服机构有正规化和缩放後的转移函数 G(s) = 1/ [s(s+1)] 在单位负回授，若闭回路极点位於 s = -1±j√3 处，系统就可符合性能规格。 （a）证明只用比例控制 D(s) = Kp 时，不可能符合规定。 （b）设计能符合规格的超前补偿 D(s) = K[(s+z)/(s+p)] 第三题 假设单位负回授的闭回路系统有前馈转移函数 G(s) = 1 / [s(s+2)] 设计落後补偿使得闭回路系统的主极点位於 s = -1±j 处并且对单位斜坡 输入的稳态误差低於0.2 谢谢～ 不好意思,我忘记要放答案 第一题答案 This must be a typo! The roots at -1 cancel and the second order system will have damping of 0.5 at K = 4. A more interesting case occurs for num = s+3. In this case, the roots are at ..42+j.7 and the gain is 0.47 第二题答案 (a) With proportional control, the poles have real part at s = ..5. (b) To design a lead, we select the pole to be at p = .10 and compute the zero and gain to be z = .3, k = 12. 第三题答案 The poles can be put in the desired location with proportional control alone, with a gain of kp = 2 resulting in a Kv = 1. To get a Kv = 5, we add a compensation with zero at 0.1 and a pole at 0.02. D(s) = 2[(s + 0.1)/（s+ 0.02）]

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