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ball beam project 1 chris hulbert redesign

# ball beam project 1 chris hulbert redesign - Since the...

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Analysis of the Continuous Linear System Through the design in project 1, the plant with the servo system was calculated as 2 3 4 7 . 20 5 . 6 88 . 12 s s s + + . Figure 1 shows the frequency response of this system. Figure 1 Due to the required response time of the system, we chose a high crossover frequency, approximately 70 rad/s, and calculated the lead controller to have the following zero and

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pole: 79 . 3 = = α ϖ c z 1292 = = c p . From this information, we could then plot the response of the controller as shown in Figure 2. Figure 2 The next step was to simulate this system. Since as project one’s report proved Simulink’s results to be the same as Matlab’s step response, Figure 3 shows the response of the system, 2 3 4 5 6 7 3 3 010 464 . 4 010 412 . 1 009 189 . 2 006 033 . 5 3883 012 18 . 8 012 98 . 6 012 842 . 1 011 62 . 1 s e s e s e s e s s e s e s e s e + + + + + + + + , to Matlab’s step command.
Figure 3 Using this system with the non-linear system in the lab proved the design was flawed due to the lack of consideration of several properties such as the limited voltage of the motor.

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Unformatted text preview: Since the motor could only handle 10 volts and our system gain was extraordinarily high, a saturation block had to be placed between the controller and the lead. With these factors then in mind, we re-evaluated our original design and decided to pick a much lower crossover frequency in the range of 1.6 rad/s. We also lowered the gain of our system to approximately 0.2 and moved the pole and zero closer to each other. After numerous iterations, we got very good results as shown by Figure 4. Since the error never crosses the zero mark, the system does not have an overshoot, but rather an under shoot. Also noted is the fact that the low frequency crossover affected the settling time, which almost doubled the given specifications. Figure 4...
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ball beam project 1 chris hulbert redesign - Since the...

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