Blog

Free response question 2 (Total 20 points) Tests the Core ou…

Free response question 2 (Total 20 points) Tests the Core outcomes 2 START ON A NEW PAGE. Work in a neat, clean, and organized way (and get extra credit!) You’ll submit your written work as a pdf after the exam is over.  Briefly show your page(s) to the camera during the exam for academic integrity.    Consider a feedback system below to control a standing robotThe TF from input torque u to robot angle y (in rad) is G = 1/(s^2  – 4). Note: this TF has poles at +2 and -2. The TF of the angle sensor from the angle y (in rad) to measured angle ym (in rad) is H = 1/(s+3).  You want the robot to lean uniformly at the rate of 0.1 rad/s. Thus, r = 0.1*t . Design a controller C(s) and prefilter F(s) to meet all of the following specifications.  if r=0.1*t (i.e., a ramp) then y has no steady state error in following it.  The settling time of the system should be less than 2s. Torque u(t) should remain finite. The overshoot is not a problem, anything is fine.  Don’t cancel the unstable plant pole at +2, it would lead to bad disturbance response. There is a huge penalty for cancelling it.  Disturbance du = 0.  Answer the following parts neatly and separately on a new page: What do you need to meet the error specification?Explain briefly and mathematically.  (3 points) What region in the 2D complex plane should the closed loop poles be so that the settling time specifications is met?Explain briefly and mathematically. ( 3 points) By plotting the root locus explain what type of controller is needed to meet all the specifications.i.e., what controller poles and zeros (if any) are needed to meet all the specifications. (5 points) Perform the closed-loop calculations to find your final transfer functions C(s) and F(s).i.e. find the numerical values of gain/pole/zeros of C(s) and F(s) to get their transfer functions. (5 points) Ensure that your u(t) shall be finite. Explain briefly and mathematically how did you do that. (4 points)   No need to type anything below.Just work on paper, show to camera during exam, and submit pdf after exam.