# Automatic Control Lab 05-Ait

May 12th, 2015
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Solve the following problem with the help of Matlab as much as possible. All the Matlab command inputs used in this problem should be listed in the report in accordance with the command results. Only the commands studied in the class are allowed to use.

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Automatic Control Lab 05-AitASIAN INSTITUTE OF TECHNOLOGYCONTROL THEORYName: Dilesha HerathID.No: st20000297Date 13/03/2013ExerciseSolve the following problem with the help of Matlab as much as possible. All the Matlab command inputs used in this problem should be listed in the report in accordance with the command results. Only the commands studied in the class are allowed to use. Problem Assume that the relation between input, u, and output, y, of a system shown below is represented by the transfer function, s?3 . G( s) ? 4 3 s ? 12s ? 49s 2 ? 78s ? 40U(s)G(s)Y(s)(a) By Routh-Hurwitz stability criteria, determine that the system under consideration is stable or not. >> alpha3=b1/c1; >> d1=b2; >> alpha4=c1/d1; >> alpha5=d1; >> alpha1, alpha2, alpha3, alpha4, alpha5 alpha1 = 0.0833 alpha2 = 0.2824 alpha4 = 1.6676 alpha5 = 401ASIAN INSTITUTE OF TECHNOLOGYCONTROL THEORYSince alpha1, alpha2, alpha3, alpha4, alpha5 are positive the system is stable. (b) Dominant time constant is a number determined when the system is stable. This number informs about speed of system response. It is defined as absolute inverse of real part of the root locating the nearest with the imaginary axis. Find the system's dominant time constant. >> [x y z] = residue([1 3], [1 12 49 78 40]); >> r = max(y); >> time_constant = 1/(-r) time_constant = 1.0000 (c) For this problem, a choice to improve the system's dominant time constant is done by equipping an adjustable

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