5 ms·

PID Controller: A Simple Control Loop Mechanism

115 points by vackosar 5y ago

Animats 5y ago
Wasn't there an HN article recently which linked to a useful site on PID controller tuning? That was interesting. PID controllers are easy to create but hard to tune.
- shawnz 5y ago
  See https://news.ycombinator.com/item?id=27273399 https://news.ycombinator.com/item?id=27273399
valbaca 5y ago
I worked with a PID controller in college. It's a concept that's stuck with me to this day. https://en.wikipedia.org/wiki/PID_controller https://en.wikipedia.org/wiki/PID_controller Proportional–integral–derivative P: proportional, this one is obvious. Water is WAY too cold, turn the knob WAY up I: integral, how long does it take for feedback to take effect. You don't want to turn the knob up and up each second if it takes 10 seconds for the change to take effect. D: derivative, a bit trickier. What's really interesting is seeing how humans apply these concepts, which are so intuitive to things like balance, we don't even think about them. In face we'll apply them to where they don't apply or are faulty. You'll see it when people learn to back up a car for the first time or start winning at blackjack.
- chowells 5y ago
  Your description for Integral is how the Derivative term is used. Proportional: set the control based on a multiple of the difference between the current and the target. Integral: adjust that setting based on cumulative difference over time. This handles the case where the proportional setting isn't providing enough of a change. Derivative: adjust the setting based on how fast the current value is approaching the target value. This provides damping when the error is decreasing rapidly to minimize overshoot and oscillation around the target. What's interesting is that a lot of controllers leave out the derivative term. Car cruise controls are often only PI, for instance. This works best when it's ok to approach the target slowly anyway, so oscillation is minimal.
  - jbay808 5y ago
    > What's interesting is that a lot of controllers leave out the derivative term This is because a PD controller controlling system X is equivalent to a PI controller for the system (dX/dt). For example, a PI controller adjusting force to control velocity is equivalent to a PD controller adjusting force to control position. If your system has a strong "momentum-like" term (larger than its damping), you need a derivative term to stabilize it. So a force-position controller needs D, but a room heater does not, because when you stop heating the room, the temperature doesn't keep coasting upwards (usually - there can be some phase lag if your sensor is far from your heater, or if your room is on fire). A force-velocity controller (cruise control) also does not have "momentum", as you can see from the fact that if you stop applying force, velocity stops increasing immediately.
    - thrdbndndn 5y ago
      Speaking of room heater, I remembered when I was studying on control theory in university and learned PID, I was thinking "this thing is so simple and yet so effective, it gotta be everywhere!". It's a little bit disappointing when I later realized that most of heater/air conditioner basically just use on/off control with a deadband. I guess the limiting factor here isn't the controller but the actuator part, but still a let-down to see them being so primitive.
      - bumby 5y ago
        On larger hydronic systems, you’ll occasionally see a PI controller on the mixing valve. The burner is kept near constant and the mixing valve is used to maintain water temp setpoint by tempering boiler water temp
      - jay3ss 5y ago
        From what I can recall from my optimal controls course using on/off is actually an optimal controller. Edit: It's called a bang-bang controller [0] [0]: https://en.wikipedia.org/wiki/Bang%E2%80%93bang_control https://en.wikipedia.org/wiki/Bang%E2%80%93bang_control
      - 5y ago
- weaksauce 5y ago
  another way to think of it: P some value multiplied by how far off you are from the setpoint. Integral term is just that from calculus... adding stuff up over time. some value (gain) multiplied by the error every N (min/milliseconds/seconds) and sent to the output. usually clamped at some value to avoid runaway errors. aka turn up the heat a little more periodically to eventually reach the setpoint. another math term(derivative being the rate of change of something with respect to something else basically)... the derivative term is supposed to be a way to dampen the output so you don't overshoot it and oscillate around the output value. if you can critically dampen the output you hit the setpoint without overshooting it and quickly. the trick is knowing which to use when because all systems are a little bit different with differing responses to the outputs and some systems are cascading and rely on other pid loops which is another bag of worms.
- elteto 5y ago
  Another interpretation: P is a spring (the spring equation is k * delta x, same as the P term, but in terms of the error). Adding a P term will make the controller “want” to eliminate any error. D term is a mass damper (again, equation is the same). It will fight oscillations, but it is extremely sensitive to noise in your input (calculating discrete derivatives in noisy signals is hard). The I term makes your output converge to the desired value. Your system will have an inherent friction or stiction which can’t be overcome with just a P term. The I helps with that but introduces other issues like windup.
oceanghost 5y ago
If I may recommend "PID without a PHD" https://www.wescottdesign.com/articles/pid/pidWithoutAPhd.pdf https://www.wescottdesign.com/articles/pid/pidWithoutAPhd.pd...
xupybd 5y ago
I'm tempted to try this for our logistics forecasting. PID seems perfect but it really breaks the KISS principle.
- vackosar 5y ago
  Why it breaks the KISS principle?
cardosof 5y ago
Saw PID in college and as a course project designed one to control room heating systems. Years later worked on one to control ads spending.
- pillefitz 5y ago
  Ad spending, very interesting application!
- sgc 5y ago
  What parameters were trying to control and using as controlling factors using PID on ad spending? Would you have done it differently if you were selling a different product/service?
zubspace 5y ago
I've used PID controllers for some things in game development, but mostly for simple stuff like specifying a target velocity. What I always have problems with, is using pid controllers for angular movements. Like turning an object to a desired angle or approaching a desired angular velocity. Are PID controllers suited for this task? For example: You want to turn right and specify a large angular velocity. But now, after a few turns the integral part adds up to a huge value. Then you want to turn back, but now the response is very slow, because of the large integral part. Never got around this problem. How would you approach this?
- meheleventyone 5y ago
  PID controllers are used to do exactly this with quadcopters. There is a lot of finesse on top to deal with oddities and problems like I term windup. Common ones are zeroing it out when it’s no longer valid or clamping it within specific bounds. For games you might just get away with a PD controller and not need to worry about the I term at all.
- leafario2 5y ago
  1) this is the same problem like controlling the angle of a quad copter, for which I have used PID. You can calculate the error of the position, which is in the range -180..179. Applying one PID stage to the error of the orientation yields a "desired rate of change" - it increases if the error is large or held for a long time and it's sign describes the direction of the rate of change of orientation. You can use another PID stage to give a step count power iteration (how much to turn the object). 2) integral windup is commonly prevented by just capping it. You can also use a smoother capping function which bounds the size of the integral, or lowers it on each iteration.
  - zubspace 5y ago
    Capping and/or gradually lowering the the integral part seems like an elegant solution. Thanks for your input! This is something which is never told but should be part of every PID controller resource on the web.
lazzlazzlazz 5y ago
There's an interesting crypto protocol called Reflexer[1] that uses a PID loop to alter interest rates and incentives to maintain the stability of a stablecoin/debt coupon called Rai. This allows the asset to remain relatively stable[2] in response to actual market forces. At the time of posting there are over $35m worth of Rai in circulation[3]. [1]: https://reflexer.finance/faq https://reflexer.finance/faq [2]: https://stats.reflexer.finance/ https://stats.reflexer.finance/ [3]: https://coinmarketcap.com/currencies/rai/ https://coinmarketcap.com/currencies/rai/
mbilal 5y ago
I remember using https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method in college to tune PID controllers in C. Fun times.
lamontcg 5y ago
When you've figured out PIDs then its time to try a Linear Quadratic Regulator: https://twitter.com/The___Missile/status/1378190268520927234 https://twitter.com/The___Missile/status/1378190268520927234
- juangburgos 5y ago
  LQR does not include integral action by default
  - lamontcg 5y ago
    Extending it to LQI is not difficult

115 points by vackosar 5y ago

Wasn't there an HN article recently which linked to a useful site on PID controller tuning? That was interesting. PID controllers are easy to create but hard to tune.

shawnz 5y ago
See https://news.ycombinator.com/item?id=27273399 https://news.ycombinator.com/item?id=27273399

valbaca 5y ago

I worked with a PID controller in college. It's a concept that's stuck with me to this day. https://en.wikipedia.org/wiki/PID_controller https://en.wikipedia.org/wiki/PID_controller Proportional–integral–derivative P: proportional, this one is obvious. Water is WAY too cold, turn the knob WAY up I: integral, how long does it take for feedback to take effect. You don't want to turn the knob up and up each second if it takes 10 seconds for the change to take effect. D: derivative, a bit trickier. What's really interesting is seeing how humans apply these concepts, which are so intuitive to things like balance, we don't even think about them. In face we'll apply them to where they don't apply or are faulty. You'll see it when people learn to back up a car for the first time or start winning at blackjack.

chowells 5y ago
Your description for Integral is how the Derivative term is used. Proportional: set the control based on a multiple of the difference between the current and the target. Integral: adjust that setting based on cumulative difference over time. This handles the case where the proportional setting isn't providing enough of a change. Derivative: adjust the setting based on how fast the current value is approaching the target value. This provides damping when the error is decreasing rapidly to minimize overshoot and oscillation around the target. What's interesting is that a lot of controllers leave out the derivative term. Car cruise controls are often only PI, for instance. This works best when it's ok to approach the target slowly anyway, so oscillation is minimal.
- jbay808 5y ago
  > What's interesting is that a lot of controllers leave out the derivative term This is because a PD controller controlling system X is equivalent to a PI controller for the system (dX/dt). For example, a PI controller adjusting force to control velocity is equivalent to a PD controller adjusting force to control position. If your system has a strong "momentum-like" term (larger than its damping), you need a derivative term to stabilize it. So a force-position controller needs D, but a room heater does not, because when you stop heating the room, the temperature doesn't keep coasting upwards (usually - there can be some phase lag if your sensor is far from your heater, or if your room is on fire). A force-velocity controller (cruise control) also does not have "momentum", as you can see from the fact that if you stop applying force, velocity stops increasing immediately.
  - thrdbndndn 5y ago
    Speaking of room heater, I remembered when I was studying on control theory in university and learned PID, I was thinking "this thing is so simple and yet so effective, it gotta be everywhere!". It's a little bit disappointing when I later realized that most of heater/air conditioner basically just use on/off control with a deadband. I guess the limiting factor here isn't the controller but the actuator part, but still a let-down to see them being so primitive.
    - bumby 5y ago
      On larger hydronic systems, you’ll occasionally see a PI controller on the mixing valve. The burner is kept near constant and the mixing valve is used to maintain water temp setpoint by tempering boiler water temp
    - jay3ss 5y ago
      From what I can recall from my optimal controls course using on/off is actually an optimal controller. Edit: It's called a bang-bang controller [0] [0]: https://en.wikipedia.org/wiki/Bang%E2%80%93bang_control https://en.wikipedia.org/wiki/Bang%E2%80%93bang_control
    - 5y ago
weaksauce 5y ago
another way to think of it: P some value multiplied by how far off you are from the setpoint. Integral term is just that from calculus... adding stuff up over time. some value (gain) multiplied by the error every N (min/milliseconds/seconds) and sent to the output. usually clamped at some value to avoid runaway errors. aka turn up the heat a little more periodically to eventually reach the setpoint. another math term(derivative being the rate of change of something with respect to something else basically)... the derivative term is supposed to be a way to dampen the output so you don't overshoot it and oscillate around the output value. if you can critically dampen the output you hit the setpoint without overshooting it and quickly. the trick is knowing which to use when because all systems are a little bit different with differing responses to the outputs and some systems are cascading and rely on other pid loops which is another bag of worms.
elteto 5y ago
Another interpretation: P is a spring (the spring equation is k * delta x, same as the P term, but in terms of the error). Adding a P term will make the controller “want” to eliminate any error. D term is a mass damper (again, equation is the same). It will fight oscillations, but it is extremely sensitive to noise in your input (calculating discrete derivatives in noisy signals is hard). The I term makes your output converge to the desired value. Your system will have an inherent friction or stiction which can’t be overcome with just a P term. The I helps with that but introduces other issues like windup.

oceanghost 5y ago

If I may recommend "PID without a PHD" https://www.wescottdesign.com/articles/pid/pidWithoutAPhd.pdf https://www.wescottdesign.com/articles/pid/pidWithoutAPhd.pd...

xupybd 5y ago

I'm tempted to try this for our logistics forecasting. PID seems perfect but it really breaks the KISS principle.

vackosar 5y ago
Why it breaks the KISS principle?

cardosof 5y ago

Saw PID in college and as a course project designed one to control room heating systems. Years later worked on one to control ads spending.

pillefitz 5y ago
Ad spending, very interesting application!
sgc 5y ago
What parameters were trying to control and using as controlling factors using PID on ad spending? Would you have done it differently if you were selling a different product/service?

zubspace 5y ago

I've used PID controllers for some things in game development, but mostly for simple stuff like specifying a target velocity. What I always have problems with, is using pid controllers for angular movements. Like turning an object to a desired angle or approaching a desired angular velocity. Are PID controllers suited for this task? For example: You want to turn right and specify a large angular velocity. But now, after a few turns the integral part adds up to a huge value. Then you want to turn back, but now the response is very slow, because of the large integral part. Never got around this problem. How would you approach this?

meheleventyone 5y ago
PID controllers are used to do exactly this with quadcopters. There is a lot of finesse on top to deal with oddities and problems like I term windup. Common ones are zeroing it out when it’s no longer valid or clamping it within specific bounds. For games you might just get away with a PD controller and not need to worry about the I term at all.
leafario2 5y ago
1) this is the same problem like controlling the angle of a quad copter, for which I have used PID. You can calculate the error of the position, which is in the range -180..179. Applying one PID stage to the error of the orientation yields a "desired rate of change" - it increases if the error is large or held for a long time and it's sign describes the direction of the rate of change of orientation. You can use another PID stage to give a step count power iteration (how much to turn the object). 2) integral windup is commonly prevented by just capping it. You can also use a smoother capping function which bounds the size of the integral, or lowers it on each iteration.
- zubspace 5y ago
  Capping and/or gradually lowering the the integral part seems like an elegant solution. Thanks for your input! This is something which is never told but should be part of every PID controller resource on the web.

lazzlazzlazz 5y ago

There's an interesting crypto protocol called Reflexer[1] that uses a PID loop to alter interest rates and incentives to maintain the stability of a stablecoin/debt coupon called Rai. This allows the asset to remain relatively stable[2] in response to actual market forces. At the time of posting there are over $35m worth of Rai in circulation[3]. [1]: https://reflexer.finance/faq https://reflexer.finance/faq [2]: https://stats.reflexer.finance/ https://stats.reflexer.finance/ [3]: https://coinmarketcap.com/currencies/rai/ https://coinmarketcap.com/currencies/rai/

mbilal 5y ago

I remember using https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method in college to tune PID controllers in C. Fun times.

lamontcg 5y ago

When you've figured out PIDs then its time to try a Linear Quadratic Regulator: https://twitter.com/The___Missile/status/1378190268520927234 https://twitter.com/The___Missile/status/1378190268520927234

juangburgos 5y ago
LQR does not include integral action by default
- lamontcg 5y ago
  Extending it to LQI is not difficult