Explore BrainMass

Explore BrainMass

    Control Systems, State Space Form and Convolution Integrals

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A control system is represented in the state space form by the following equations in the attached file.

    a) Solve for the state vector using the convolution integral
    b) Find the output, y(t)

    © BrainMass Inc. brainmass.com March 4, 2021, 8:14 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/control-systems-state-space-convolution-integrals-154235

    Attachments

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    Problem:

    A control system is represented in the state space form by the following equations:

    a) Solve for the state-transition matrix
    b) Solve for the state vector using the convolution integral
    c) Find the output y(t)

    Solution:

    a) For a simple linear differential equation with constant coefficients of form
    , a = constant (1)
    and with initial condition
    (2)
    the solution is given by
    (3)
    This formula can be written in another form, using the convolution integral:
    (4)
    where
    ...

    Solution Summary

    Control Systems, State-Space Form and Convolution Integrals are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

    $2.49

    ADVERTISEMENT