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By Wan E.A.

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Extra info for Control systems.Classical,neural,and fuzzy

Sample text

The transfer function from a plant noise to the system error will not have the zero, and thus, disturbance transients can be very long in duration in a system with lag compensation. 3 The "Stick on a Cart" example O m u After normalization, we have: ; =u 49 (87) ) s2 (s) ; (s) = U (s) (88) (s) 1 U (s) = s2 ; 1 (89) This results in the following model of the system: The root locus diagram is shown below. The u θ 1/(s^2 - 1) Figure 10: X -1 X 1 Figure 11: above gure indicates an unstable system, irrespective of the gain.

Z = 0:1 and p = 0:01). Since z > p, the phase is negative, corresponding to a phase lag. It improves the steady-state error by increasing the low-frequency gain. Lag compensation however decreases the stability. 1 Illustration Again, consider the transfer function, as in equation 84. Include the lead compensation D1 (s) = (s + 2)=(s + 20) that produced the locus as in gure . Raise the gain until the closed-loop roots correspond to a damping ratio of = 0:707. At this point, the root-locus gain is found to be 31.

This indicates an integration at nearzero frequencies, and is achieved by lag compensation. Lag compensation approximates PI control. A pole is placed near s = 0 (low frequency). But, usually a zero is included near the pole, so that the pole-zero pair, called a dipole does not signi cantly interfere with the dynamic response of the overall system. , z = 0:1 and p = 0:01). Since z > p, the phase is negative, corresponding to a phase lag. It improves the steady-state error by increasing the low-frequency gain.

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