Question: Consider a process that can be modelled with the differential equation: dx 2cx + 4axy + 6by - 8 dt where x is the dependent

Consider a process that can be modelled with the differential equation:

Consider a process that can be modelled with the differential equation: dx 2cx + 4axy + 6by - 8 dt where x is the dependent variable, a, b, and care constants, and y is an input variable. At t=0, X=Xs. a) Linearize the equation and introduce deviation variables. b) Find the Laplace transform of the equation. c) Find an expression for the time constant. d) Find an expression for the gain. e) Find an expression for the transfer function. f) Find x(t) if we introduce a step change of magnitude 1 at t=0

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