The dynamics of a process with one input 'u' and one state 'y' are described by the following nonlinear ordinary differential equation: dy = ue" - y dt It is desired to study this process using an equivalent linearized equation. If the process is originally at steady state and u=0, perform the following steps: a. Obtain a linearized model in terms of deviation variables. b. Obtain a first order transfer function model relating Y(s) to U(s). c. Calculate the gain and time constant of the transfer function model developed. d. If u is changed suddenly to u=0.1, (step change), solve for y(t). Calculate the new steady state value of y according to this transfer function model, and according to the original nonlinear equation (solved at st. st.). Calculate the error in the linearized prediction. e. Repeat part (d) if the step change was to u=1. Calculate the error. f. Assume the process was initially at steady state at u=1, obtain a new transfer function model at this steady state. What are the new values of gain and time constant? g. Šummarize and explain your findings. My we here to dleciole m is nen ineer Ove

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