State Space and Modeling

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Question description

onsider the following differential equation:

d 2 y + 3 dy + 2 y = u dt2 dt

  1. Write the state equations for this system

  2. Add a new state in which x&3 = y − yd where yd is the unit step and represents the desired output of the system. Write the new state equations treating yd as another input.

  3. Now,pickavector k=[k1,k2,k3]suchthatifu=−kx,thenewstateswillhaverootsofthe

    characteristic equation at ‐2, ‐3, and ‐4.

  4. Simulate the system and observe the output y and compare the response for yd = step input

    to the step response of the system without control. 

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