Answer to Question #226327 in Electrical Engineering for Romz

Question #226327

For the 2nd order system given Ts =7 sec and Tp= 3 sec find the value of % OS and location of poles.


1
Expert's answer
2021-08-16T02:19:52-0400

"T_s= \\frac{4}{\\xi w_n}\\\\\nw_n= \\frac{0.571}{\\xi}\\\\\n\\xi= \\frac{\\pi}{\\frac{0.571}{\\xi} \\sqrt{1-\\xi^2}}\\\\\n\\sqrt{1- \\xi^2}=(\\frac{\\pi}{3(0.571)}) \\xi\\\\\n1-4363 \\xi^2\\\\\n\\xi= 0.479\\\\\n\\therefore w_n= \\frac{4}{7*0.479}= 1.193 rad\/sec\\\\\ns^2+(2*0.479*1.193)s+1.193)s+1.193^2=0\\\\\ns= -\\frac{1.143\u00b1\\sqrt{1.143^2-4*1.423}}{2}\\\\\ns=-0.542\u00b1j0.903"


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