Control Systems: The Performance of Feedback Control

Control Systems Textbook Activity: The Performance of Feedback Control Instructions Handwritten solutions should be scanned and saved as a BMP, GIF, or JPG image, or scanned and pasted into this document. Questions Solve the following problems: 1. The speed control of a racing vehicle has the following block diagram: 240 where the engine transfer function is 𝐺(𝑠) = (𝑠+4)(𝑠+6) and H(s) = 1. (a) Calculate the steady-state error of the vehicle to a unit step command. (b) Calculate the overshoot of the speed to a unit step command. 2. For the same system as in problem 1 but the transfer function is G(s) = 𝐾 . (a) 𝑠(𝑠+√(2𝐾)) Determine the percent overshoot and the settling time. (b) Find K if the settling time is less than 1 second. 3. Position control of an astronaut is represented by the following block diagram: where the moment of inertia of the equipment and man is 30 kg 𝑚2 . (a) Determine the necessary gain 𝐾3 to maintain a steady-state error of 1 cm when the input is a ramp of r(t) = t meters. (b) With this gain 𝐾3 determine the necessary gain 𝐾1 𝐾2 in order to restrict the percent overshoot to 10%. 1