Consider the following linear, time-invariant system
Consider the following linear, time-invariant system
Consider the following linear, time-invariant system:
Where
The vector x = [x1 x2] T is known as the state vector. The parameter k0 is a constant. The input to the system is u. Develop a script using MathScript to perform the following computations:
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(a) For 0 ≤ k0 ≤ 5, compute the eigenvalues of A. The eigenvalues can be complex (imaginary) numbers. Generate a plot of the real part of the eigenvalues versus the imaginary part.
(b) With the input u = 2 for t ≥ 0 and k = 0.5, find the solution using numerical integration and plot x versus t for 0 ≤ t ≤ 20. Use the initial conditions x(0) = [1 0] T
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Consider the following time-invariant linear system.
Consider the following time-invariant linear system.
Consider the following time-invariant linear system:
Where
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x = [x1 x2] is a vector. T is referred to as the state vector. The parameter k0 is a fixed value. The system’s input is u. Create a MathScript script to conduct the following computations:
(a) For 0 k0 5, find the eigenvalues of A. Complex (imaginary) numbers can be used as eigenvalues. Generate a plot of the real part of the eigenvalues versus the imaginary part.
(b) With the input u = 2 for t ≥ 0 and k = 0.5, find the solution using numerical integration and plot x versus t for 0 ≤ t ≤ 20. Use the initial conditions x(0) = [1 0] T
