PID Loops

[Chris27]

Computing the derivative is easy as it is just change over time. Computing the integral is a bit more involved. You can use Fourth order Runge-Kutta to estimate the integral

http://mathworld.wolfram.com/Runge-KuttaMethod.html
http://doswa.com/blog/2009/01/02/fou...l-integration/

If you are using a PID function of some library, you probably don't need to worry about computing derivatives and integrals and will probably just need to pass it the desired set point and the current location/sensor reading (like in Labview)

[Ether]

Originally Posted by Chris27

Computing the integral is a bit more involved. You can use Fourth order Runge-Kutta to estimate the integral

"Euler's Method is the most common integration method for control systems . Control methods such as PID do not need exact integration to work well. This is because the purpose of the integral is usually to force the average error to zero to ensure that the controlled signal matches the command signal over long periods of time. Only rarely is there a need to control the integral of a signal. In those cases you may need a more accurate integration method."

Control System Design Guide
Second Edition
George Ellis
Page 82

[archaopteryx]

I'm not a mathematician, but couldn't

Pedal = K * Error

, where K is a constant, simply do without K? If pedal and error have a direct correlation, why can't you just say that pedal = error and leave it at that?

[Chris27]

Originally Posted by archaopteryx

I'm not a mathematician, but couldn't , where K is a constant, simply do without K? If pedal and error have a direct correlation, why can't you just say that pedal = error and leave it at that?

If you are trying to move your car at 50 mph and currently, the error from this target is +10 mph, does it make sense to push the pedal down at 10 mph? A correlation does not mean an equivalent 1 to 1 relation. Another example is if you are trying to drive your robot 5 feet forward and the current error is 4 inches. Does it make sense to tell the motors to drive at 4 inches? Built into the k value is unit conversion among other things.

[Ether]

Originally Posted by archaopteryx

I'm not a mathematician, but couldn't , where K is a constant, simply do without K? If pedal and error have a direct correlation, why can't you just say that pedal = error and leave it at that?

If you are trying to control position, then the error will be in inches (or feet or meters or whatever). In response to this error, you want to choose the appropriate command to your motors, which will be a voltage command... which roughly corresponds to a speed command. So the K is a scaling and gain factor to convert the error to an appropriate motor voltage (speed) command.

On the other hand, suppose you are trying to control motor speed. You want to go 2000 rpm and you are presently going 1900 rpm. So the error is 100 rpm. Would it make sense to give the motor a voltage command which is roughly equal to 100 rpm?