Quiz 1 - 2005

Name_________________________

        Here is the step response of a system.

• This is the unit step response of the Actuator + Plant (i.e. the open loop system).
• This system is embedded in a feedback control loop - as shown below.

• What is the open loop DC gain - i.e. the DC gain of the Actuator + Plant?
• Open Looop DC Gain = 5.  The output reaches a steady state of 5 in response to a unit step input.  (That's a step with a magnitude of 1.0.
• Determine the relationship between the steady state output and the steady state input
• Y_ss/U_ss = Closed Loop DC Gain = [K x Kp]/[1 + (K x Kp)] (Using the sheet passed out in class.)
• Assuming that you want 2% Steady State Error or less, what value should you use for the proportional gain, K_p?
• Proportional gain for 2% SSE or less = _______________
• Error% = 100/[1 + (K x Kp)]
• For 2% SSE, you need 1 + (K x Kp)] = 50.  Since K = 5, that means the proportional gain, Kp, has to be at least 9.8.
• Assuming that you want 1% Steady State Error or less, what value should you use for the proportional gain, K_p?
• Proportional gain for 1% SSE or less = _______________
• For 1% SSE, you need 1 + (K x Kp)] = 100.  Since K = 5, that means the proportional gain, Kp, has to be at least 19.8.