Consider the following two single-input single-output subsystems: *1 S₁: Y1 = A₁x₁ + B₁u₁ C₁x1 S₂ : J*₂ = A₂x₂ + B₂ U2 Y
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- Consider The Following Two Single Input Single Output Subsystems 1 S Y1 A X B U C X1 S J A X B U2 Y 1 (116.77 KiB) Viewed 62 times
- Consider The Following Two Single Input Single Output Subsystems 1 S Y1 A X B U C X1 S J A X B U2 Y 2 (65.71 KiB) Viewed 62 times
Consider the following two single-input single-output subsystems: *1 S₁: Y1 = A₁x₁ + B₁u₁ C₁x1 S₂ : J*₂ = A₂x₂ + B₂ U2 Y2 = C₂x₂ - where 3 A1 = 2,1 B₁ = 2-1) 9-121] * - 9 [³], = " -1 A₂ = 4, B₂ = -2, C₂ = 1. The two systems are cascaded forming an overall system S, as shown in the following block diagram. U1 U2 = y1 Y: S₁ S2 Calculate the transfer function G(s) from ₁ to y₂ of the system S. Provide the components of your answer as integers for the numerator and denominator of G Numerator of G(s) = + 82 + S+ Denominator of G(s) s+ = $3 + +
In your hand written working, include the following explanations and steps: (1) Derive the transfer function from ₁ to y₂ for the system S as a formula in terms of A₁, B₁, C₁, A2, B2, C2. Show key steps of working. (2) Write down your working in deriving the transfer function that you provided. (3) The system S has input ₁ and output y2. Explain whether the system is observable and why.