Consider the following state equation: A) Design an integral controller u = –Kx + Ke xn to yield a maximum overshoot Mp = 0.05, a 2% settling time ts = 2 s, and a steady-state error ess = 0 in response to a step input. Note: Place one pole in the desired characteristic polynomial at s = –100 (the other two poles are fixed by the desired Mp and 2% ts ).

Consider the following state equation: A) Design an integral controller u = –Kx + Ke xn to yield a maximum overshoot Mp = 0.05, a 2% settling time ts = 2 s, and a steady-state error ess = 0 in response to a step input. Note: Place one pole in the desired characteristic polynomial at s = –100 (the other two poles are fixed by the desired Mp and 2% ts ).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider the following state equation:

A) Design an integral controller u = –Kx + Ke xn to yield a maximum overshoot Mp = 0.05, a 2% settling time ts = 2 s, and a steady-state error ess = 0 in response to a step input. Note: Place one pole in the desired characteristic polynomial at s = –100 (the other two poles are fixed by the desired Mp and 2% ts ).

0
1
* = [ _-2₂2 _²³3] x + [9] ₁₁
u, y = [1 0]x

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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