PID Servo Tuning / Troubleshooting

There are generally three settings you must adjust to make a PID based controller work correctly:

• Proportional constant: Also called "gain". This value is multiplied by the error between where you want the servo to be and where it is. A larger value gets the servo to the desired position faster and makes even small errors matter more… but it may also cause the unit to overshoot the correct position and oscillate back and forth without ever stopping. A smaller value will stop oscillations, but may not generate enough drive when the error is small to actually overcome friction and move the unit all the way to the correct position.
   
• Integral constant: This value amplifies the accumulated error over time. It makes even a small position error eventually matter enough to get the motor to the exact right place, and increases the speed of long runs… but it really makes overshoot and oscillation a certainty. It should generally be proportioned to the amount of friction in the system.
   
• Derivative constant: This value amplifies the difference between the prior position and the current position. It compensates for inertia and can really help reducing oscillations, but too much will make the system "shudder" and shake violently as it comes to a stop at a new position.

Ziegler / Nichols Starting Point: There are several ways to tune a PID controller, these steps present the Ziegler / Nichols closed loop method as a starting point. Further "trial and error" tuning should certainly be used: (Commands for the BOB PID system will be shown in parenthesis after each step... your systems commands may vary. For e.g. Arduino or other hard coded systems, adjust the parameters in the sketch before programming each time.)

1. No I or D, Little P Start with the I and D terms set to 0 and P set to a very small value. (0i0d1p)
    
2. Power up, set desired position to 1 (1{enter}) and make sure you have direction set correctly (216w or 286w) and enable the driver (e), If the servo just spins and spins, it's doing a zig when it should zag... the direction is probably wrong; disable the driver ({space}) and try the other direction before enabling again.
    
3. While(!Oscillating) P++; Slowly increase the P constant while moving from one point to another and back until the unit starts to oscillate with a consistent motion, back and forth the same amount. (1p100{enter}1{enter}2p100{enter}1{enter}...) To save time, you can use an exponential and then binary search. Start with 1, then 10, then 100, then 1000, etc… until you get oscillation. Then divide that number in 2; if it still oscillates, divide by two again, otherwise, add half the current value back. E.g. from 100, try 50, if it oscillates, try 25, if not, try 75 = 50/2+50. And so on.
    
4. This setting for P is called the Ku or "ultimate gain". Record it, and count the number of oscillations per second, which is called the frequency or Tu. Be sure to then change Tu into units matching the sample time used in the controller. E.g. the BOB PID uses ¼ second updates, so divide your measurement by 4.
    
5. Now you can use these values to calculate good starting points for the P, I, and D terms:
    
   • P/=2; In general P should be about half of Ku, so if your system started oscillating when P was 12, try setting it to 6 to start. (6p)
      
   • D=Tu/(8*t); Set D to about Tu/8. For example, 0.125, with BOB PID at 4 Hz. (.125d). We are setting D before I here to keep for getting into out of control oscillation.
      
   • I=Tu/(2*t); Set I to less than Tu/2. For example, if your system oscillated at 4 cycles per second, and you use the BOB PID with ¼ second updates, set I to .1. (.1i)

Now try moving back and forth and see how the system reacts. Make both short and long jumps, small and large movements. e.g. (10{enter}1{enter}200{enter}1{enter}...) If it starts oscillating out of control, disable the motor and continue with troubleshooting below. ({space}) Be sure to give it time to settle at each point, and ensure it really does make it to exactly the desired point (mark the shaft if you can).

Once you have the tuning done, save the values to non-volatile memory {321w}

PID Troubleshooting

Oscillation: If you have a very heavy shaft, meaning a lot of mass turning on the shaft especially away from the center of rotation; this has nothing to do with the weight of the load being moved unless that load is spinning with the shaft, then increase D until you start to hear shuddering or vibration as it approaches a new setpoint. If you have a lot of overshoot when approaching a new setpoint, decrease I. Otherwise, decrease P.

Slow approach to setpoint: If you have a lot of friction in the system, increase I. If the system "grinds" or "shudders" or vibrates as it approaches the setpoint, decrease D. Otherwise increase P.

Overshoot (without oscillation): Decrease P.

See also:

• https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method
• http://www.mstarlabs.com/control/znrule.html
• https://controls.engin.umich.edu/wiki/index.php/PIDTuningClassical (archived)

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