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    Linear Systems and Linearized State Space

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    1. a) A system has the following model:
    x_1 = x_2
    x_2 = (-x_2)92+cos(x_1))-3sin(x_1 - u)
    y = tan(x_1 - u)

    Find the linearized state space model about the steady state with x = (0,0)^T.

    b) Draw a Simulink implementation diagram of the system in question a. The input comes from a function generator and the output and simulation time must be sent to the workspace.

    2. b) Find the natural response of the system (see attached), with input u(t) = 0 and initial condition x(0) = (-1,1)^T. Sketch your solution.

    bii) Use the Laplace transform to find the output of the system (see attached), y = (0 1)x,
    with x_0 = (1 0)^T and ut) = e^-3t.

    bii) Sketch the solution and confirm that it makes sense.

    © BrainMass Inc. brainmass.com October 9, 2019, 4:38 pm ad1c9bdddf
    https://brainmass.com/engineering/computer-engineering/linear-systems-linearized-state-space-37545

    Attachments

    Solution Summary

    This solution includes formated calculations and explanation in the attached Word document. The Simulink diagram for 1(b) is given and the .mdl model file is attached. 287 words.

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