Introductory Control System Problems
Problem Intro1P02
Name_________________________

Dr. Abner Mallity has been working on a little consulting job with River City Circuits Corporation  (RC3).  He has a motor-amplifier combination and he has measured the step response of the system when he puts in a step of one volt.  Here is a sample plot of one of his measurements.  And you can listen here to the sound of the motor speeding up.

Note the following about his measurements.
• The input was a step of one (1) volt.
• The output is measured in radians/sec.
• There is some noise in his measurements.
Ever the cautious one, Mallity has taken several measurements of the same response.  They don't seem to come out the same.  Here is another measurement taken later the same day under the same circumstances.

Finally, when he noticed that things were different, he took a third set of measurements three days later.  That's shown below.

Mallity has been charged by the department head at RCCC - Helen Highwater - to produce a system that controls the speed of the motor.  He needs to be able to specify a speed and have the system respond accurately.  In particular, he needs to do the following.
• When a speed is specified the eventual speed attained should be within 3% of the specified speed.
• He needs to predict how the eventual speed is attained.
• Helen Highwater requires a plot of rotational speed vs. time for the complete system.
• She wants to ensure that the system does not overshoot by more than 15% when a step change in speed is requested.
• Mallity must also be able to give limitations on the performance due to variation in the system.