Mathematical Model Consider the following mathematical model of a physical system + (M? + sin(/))y?...

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Mathematical Model Consider the following mathematical model of a physical system ÿ + (M? + sin(/))y? + (log10(m) + k})ÿ + JBy = yù + cos(a) u? Parameter Values M = 1.5,] =,m = 50, kr = 6, B = 9,y = 1, a = 12 Task 1 [10 points] Linearize the given system after substituting the appropriate parameter values (use u' = B). Write down the corresponding linearized system for each equilibrium point. Convert the linearized system(s) into transfer function Task 2 [4 points] Calculate the poles of the linearized system(s) and determine the stability property. Task 3 [6 points] Verify the stability property of the linearized system(s) using Routh Hurwitz criteria. Mathematical Model Consider the following mathematical model of a physical system ÿ + (M? + sin(/))y? + (log10(m) + k})ÿ + JBy = yù + cos(a) u? Parameter Values M = 1.5,] =,m = 50, kr = 6, B = 9,y = 1, a = 12 Task 1 [10 points] Linearize the given system after substituting the appropriate parameter values (use u' = B). Write down the corresponding linearized system for each equilibrium point. Convert the linearized system(s) into transfer function Task 2 [4 points] Calculate the poles of the linearized system(s) and determine the stability property. Task 3 [6 points] Verify the stability property of the linearized system(s) using Routh Hurwitz criteria.

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