Question 1: A given system responds to a set of inputs with the output V(t) = 5e^2tsin(4Πt). What (if anything) can you say about the stability of the system? Why?

Question 2: What is the input to our control system called?

a. manipulated variable
b. setpoint
c. controlled variable (or control variable)
d. measured variable

Question 3: If a system has an output of F(s) = 3s + 24/s(s+4)(s²+25). What would we expect its final value to be (the value as time approaches infinity)?

Find the LaPlace transform of the following:

a. f(t) = 6e^-8t + 2te^-4t

b. g(t) = 2(cos(6t) - 4u(t)]

Question 5: Which of the following statements are true? (Circle the letter of each true statement)

a.) A well-designed system with a proportional controller will have zero steady state error even without a proportional offset.

b.) The feedback loop in an open-loop system is needed to measure the controlled variable.

c.) LaPlace transforms can be used to help analyze a system described by differential equations.

d.) If a temperature sensor has self-heating, the temperature it displays will likely be lower than the actual temperature.

Question 6: A sensor output, V(T), has a static response to temperature based on the equation V(T) = 5e-^0.02T, where T is in degrees Celsius.

a. Determine the equation that linearizes the sensor's output between temperatures of 0^oC and 100^oC.

b. Using the linear approximation, what is the approximate voltage at a temperature of 50^oC?

c. What is the error in this approximation at 50^oC?

Question 7: A function f(x) is linear if and only if f(k₁x₁ + k₂x₂) = k₁f(x₁) + k₂f(x₂). Using this, show whether each of the following are linear or non-linear.

a. f(x) = -8x²

b. f(x) = 1.5 x - dx/dt

Question 8: In a given system, the output y(t) is related to the input x(t) by the equation:

2.dy/dt + 5y = 4x

a. By using LaPlace, determine Y(s)/X(s).

b. By using LaPlace, determine y(t) if the input x(t) is an impulse function, δ(t).

c. By using LaPlace, determine y(t) if the input x(t) is a unit step function, u(t).

Question 9: Consider the following transformed equation.

F(s) = 3s²+ 40s + 103 / (s+8)(s²+6s+9)

a. Perform the partial fraction expansion of this equation.

b. Determine f(t).

Question 10: Draw only the analog simulation diagram (not the op-amp implementation) of the transfer function:

Y(s)/X(s) = 2s + 3/(s + 8)(s + 2)