None W09A_Exercises

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Exercise: Due MONDAY, 11/1/2020 BEFORE CLASS

Controller Design: PI Controller using Angle Deficiency

Having developed a plant transfer function for the MOTOR-SPRING-LOAD configuration in Lab 5, let us assume that with the RIGID SHAFT installed instead of the flexible spring-shaft, the motor's open loop behavior is adequately represented by the FIRST ORDER PART of the MOTOR-SPRING-LOAD model you derived. If you make this assumption, you can design a PI controller on velocity for the lab rig in the MOTOR-RIGID SHAFT- LOAD configuration.

Using the angle deficiency method for controller design, design a controller such that the closed loop system's dominant eigenvalue pair is underdamped with $\zeta = 0.5$ and $\omega_n = 30 rad/s$. In this case, if you like, you could also check your solutions by designing the controller using the "direct method" because the closed loop system is only second order.

  • Place your hand calculations in the Markdown cell below using typeset equations or a picture (small file size please! Screenshots or images from a dedicated "scanning app" work best).
  • Place MATLAB code in the Octave cell below that shows a simulation of your system's closed-loop step response for a 25 rad/s step change in requested velocity, considering actual velocity as the output. Also plot a simulation of the predicted voltage u(s) sent from the Arduino to the PWMA. Indicate whether you think this design is feasible with your lab hardware. If it is feasible, what is the maximum step size you'd recommend to ensure that a linear simulation would represent actual system behavior? If it is not feasible, why not?

YOUR ANSWER HERE

In [1]:
% YOUR CODE HERE
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error: No Answer Given!