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# hw2 - If the steady state value of the input is u s = 0...

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Home Assignment Note: All the problems below have MULTIPLE steady-state solutions. Make sure you get all of them. For example, Problem 1 has steady states (+0.781, +1.603) and (-0.781, +1.603). It is a good idea to plug in your solutions into the original equations and make sure that each equation is equal to zero. Problem 1 : Consider the following dynamic system: d dt " x 1 x 2 # = " x 2 1 - x 2 + u e x 2 - 5 # If the steady state value of the input is u s = 1, what are the steady state values of the states, x 1 s and x 2 s . Linearize the system around these steady state values. Problem 2 : Consider the following dynamic system: d dt " x 1 x 2 # = " x 1 x 2 2 - x 2 + u x 3 1 - x 2 2 # If the steady state value of the input is u s = 0, what are the steady state values of the states, x 1 s and x 2 s . Linearize the system around these steady state values. Problem 3 : Consider the following dynamic system: d dt x 1 x 2 x 3 = x 2 1 + 2 x 1 + 1 2 x 2 - x 1 + u x 1 + x 2
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Unformatted text preview: If the steady state value of the input is u s = 0, what are the steady state values of the states, x 1 s , x 2 s and x 3 s . Linearize the system around these steady state values. Problem 4 : Consider the following dynamic system: d dt " x 1 x 2 # = " x 2 1 + x 1 + 1 2 x 1 + x 2 + u # If the steady state value of the input is u s = 0, what are the steady state values of the states, x 1 s and x 2 s . Linearize the system around these steady state values. Problem 5 : Consider the following dynamic system: d dt " x 1 x 2 # = " x 2 1 + 2 x 1 + u 1 x 1-x 2 2 + u 2 # If the steady state value of the inputs are u 1 s = 1 and u 2 s = 1, what are the steady state values of the states, x 1 s and x 2 s . Linearize the system around these steady state values. 1...
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