PID Loops

[Chris27]

read this starting at page 23

http://www.cs.cmu.edu/afs/cs/academi...y_friction.pdf


Basically, PID is a function that takes an input a target (set point) you want to achieve and your current error to this target and outputs the motor speed to get there.

P refers to a term that is proportional to the error. It is used to achieve the desired rise time to get to the set point. However having a high P will cause
the system to oscillate around the set point.

D refers to a term that is proportional to he derivative of the error. It is used to dampen the system to reduced the oscillations. If you overly dampen the system, you may rob it of the power it needs to actually reach the set point. This is called steady state error.

I refers to a term that is proportional to the integral of the error. It is used to address steady state error. Basically, as long as error persists, the system will try harder and harder to reduce the error. This may become dangerous because of wind up. E.g. say that you disable power to a motor
for a moment. The I term will cause the speed output to rise as the error is
not going away (the motor is disabled). When the motor is finally re enabled, it will go flying.

Sometimes you can get away with just using P especially if there is a lot of
friction in the system which would make it hard to shoot past the set point.

Hope that helps.

[Ether]

Originally Posted by Chris27

D refers to a term that is proportional to he derivative of the error.

In the LabVIEW PID vi, D is the derivative of the process variable... not the error.

[theNerd]

Originally Posted by Chris27

read this starting at page 23

D refers to a term that is proportional to he derivative of the error.

I refers to a term that is proportional to the integral of the error

I still don't understand to much about the details on how to find the derivative of the error (or the integral). I understand that the derivative of an equation is e.g.: instantaneous velocity, for instance F(x)' 4x^4 = 16x^3 (not pretending anything however I don't know the in depths of the derivatives all i know from second hand learning is the power rule). However my knowledge on integrals is null. How do you find the integral and derivative?

[Ether]

Originally Posted by theNerd

I still don't understand to much about the details on how to find the derivative of the error (or the integral). I understand that the derivative of an equation is e.g.: instantaneous velocity, for instance F(x)' 4x^4 = 16x^3 (not pretending anything however I don't know the in depths of the derivatives all i know from second hand learning is the power rule). However my knowledge on integrals is null. How do you find the integral and derivative?

If you are using PID functions that came with the language you are using, you don't have to. It is done within the provided library function.

All you need supply are:

the setpoint (the target value),

the process variable (the measured - with a sensor - value of what you are trying to control),

the 3 "gains" P, I, D

and any other optional inputs to the function such as output range

See attached screenshot of LabVIEW's PID

[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?