北方工业大学 2013 年自动控制原理真题答案
一、
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D, 2. B, 3. D, 4. C, 5. A, 6. B, 7. D, 8. A, 9. C, 10. A, 11. A, 12. D,
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B, 14. B, 15. C
二、
(1)
\[G(s) = \frac{2k}{s(s+p)} \Rightarrow D(s) = s^2 + ps + 2k = 0 \Rightarrow 2k = \omega_n^2, p = 2\omega_n \xi\]
\[\xi = 0.5 \Rightarrow \omega_n = \sqrt{2k}, p = \sqrt{2k} \Rightarrow \Phi(s) = \frac{2k}{s^2 + \sqrt{2k}s + 2k}\]
\[\sigma\% = e^{\frac{-\pi\xi}{\sqrt{1-\xi^2}}} \times 100\% = e^{\frac{-\sqrt{3}\pi}{3}} \times 100\% \Rightarrow\]
则 \(C_{max} = 1 \times (1+\sigma\%) = 1 + e^{\frac{-\sqrt{3}\pi}{3}}\)
(2)
\[t_s = \frac{3.5}{\xi \omega_n} < 0.5, \xi = 0.5 \Rightarrow p = \omega_n > 14\]
三、
(1)
\[G(s) = \frac{K}{(s+2)(s^2+2s+2)}\]