Long Question 2 (Total 20 points) Tests the Core outcomes 2…
Long Question 2 (Total 20 points) Tests the Core outcomes 2 Problem 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. Procedure Work neatly on paper showing all the steps needed to get to the final K(s).Neat + clean + organized = extra credit! Then show your papers to camera. Just type your final C(s) (and if needed F(s) ) below, rest all will be graded based on paper work submitted after the exam. After exam, submit your work as a pdf on canvas. Answer the following parts. Be SUPER organized and neat. What do you need and C(s) (and if needed F(s))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) What do you need and C(s) (and if needed F(s)) to ensure u(t) shall be finite for ramp r(t). (4 points) By plotting the root locus explain what type of controller is needed to meet ALL the specifications.i.e., what symbolic controller poles and zeros (if any) are needed to meet all the specifications. (6 points) Perform the closed-loop calculations to find your final transfer functions C(s) and F(s) to meet ALL the specs. i.e. find the numerical values of gain/pole/zeros of C(s) and F(s) to get their transfer functions. (4 points)
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