Proportional Control
   Without realizing it you were applying proportional control to the car speed. In other words the corrective action you took in response to an incorrect speed was in proportion to the amount of error.  A large drop in speed caused you to floor the accelerator and, as your speed came up, you gradually eased off the pedal until achieving the target of 30mph. So much easier than the switch, but more complex control. With the switch control, your input (reading the speedometer), only had to decide above or below the target. Now you have to know how much above or below.  Your output was a simple on-off, now its a pedal position.  Is it worth it for controlling the car? Of course it is. Would you use it for central heating control? Probably not. Knowing where it is appropriate to apply specific control techniques is as important as knowing how to apply them.

   
 

 

 
     
     
     
     
     
     
     
     
                   
   

   Let’s adjust our car control environment a little more to examine a limitation in proportional control. We are driving along a flat road with our proportional control of the pedal responding to changes in the speedometer reading when suddenly we start to climb a steep hill.  The speed drops very quickly and we match the drop by a carefully proportioned depression of the accelerator. The net result is that eventually we get back up to 30mph but only after we have dropped right down to about 10.    We could see the speed dropping quickly but we constrained ourselves to only apply a fixed proportion of accelerator based on the difference between actual speed and target speed. What we feel we needed to do is produce a lot more accelerator power than we actually needed for a short duration to counteract the sudden decrease in speed followed by a more proportioned response.  How do we relate this “gut” feeling to control theory? The answer is derivative control.

   
       
       
       
       
         

Next:  Derivative Control

     
   
     
   
 

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