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Carm controller motor Potentiometer Input knob Angle sensor Controller Motor Joint Angle + K,/R Position Knob Kc Position J,3²+(KK,/R+b)s b a) How many integrators (1/s terms) are there in the forward path of this unity gain feedback system? What is the system type? b) Assume Jm = 1 kg m², b Kt = 1Nm, Kb = Vsrad-1 , R =10 and a controller gain of Kc =10. By hand, show that the steady state error for a step input is zero. c) Confirm this result in Matlab (using the step input) or Simulink by plotting the error signal versus time. d) Instead of moving the robot arm to a given position, you decide to continually rotate the joint at a constant velocity with an input r(t) = t. What is the steady state error in this case? e) Confirm this result in Matlab or Simulink by plotting the error signal versus time. f) Find a value of Kc that will reduce ess below 0.1 rad. A more realistic servomotor block diagram is shown below. In this case, the block next to the input represents a gain of V rad=1 for the knob input and the block in the feedback path represents a sensor gain of Input Gain Controller Motor Joint Angle + K,/R Position Knob Kinput Kc Position Sensor Gain Ksensor g) Find the equivalent unity gain feedback system using block diagram simplification. h) What is the system type? i) Calculate the steady state error for a step input? Assume Kinput =5 V rad - 1 and K, sensor . j) Confirm this result in Matlab or Simulink.

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