You are given a system with the following transfer function: Y(s) 1 G(s) = = U(s) 10+ s a. Write an ordinary differential equation (ODE) describing the relationship between the output and input. b. Find the steady-state gain (K) and time constant (T) c. The process input, u(t), is shown in the graph below. 3 process input 2.5 2 1.5 19 0.5 0 -0.5 -1 -1 0 1 2 3 4 5 time (min) Write an expression for u(t) in terms of S(t) [the unit step function], and S(t-1). d. Use the principle of superposition and your answer from part c to determine U(s). e. Simulate the response, y(t), of the system to the input, u from parts c and d.