5 ms·

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 t

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
  - jbay808 5y ago
    Yeah, hysteresis control aka "bang bang" control can also be unreasonably effective. It's a natural choice when your furnace can't throttle, or can but operates most efficiently at one output level anyway. Since the system always pushes as hard as it can, it automatically reaches the setpoint in the minimum possible time. It's almost like a PID controller with infinite gain. But the tradeoff is jitter -- all the error gets pushed up to the highest frequency bands. As long as you don't care about that in your system, it's a great choice and effortless to tune. It can also be a bad choice if there's any cost to changing or toggling the output, like if your furnace wears out from switching on and off a lot.
    - sokoloff 5y ago
      Many hot water circulating heating systems use bang-bang for the call-for-heat actuation but vary the circulating water temperatures in response to the outdoor temperature (via an “outdoor reset” input to the system). Properly set, this dampens the swings of temperature in the rooms as the heat gain is more closely matched to the heat loss, increasing comfort and economy of the system. https://en.m.wikipedia.org/wiki/Hot_water_reset https://en.m.wikipedia.org/wiki/Hot_water_reset
  - shawnz 5y ago
    On-off or "bang-bang" control actually makes a lot of sense for home thermostats. For example consider: - With a home thermostat you probably want it to reach the desired temperature as quickly as possible. PID will never reach the setpoint as fast as bang-bang control since bang-bang control will always use the maximum possible power. - PID might help you avoid overshooting the desired temperature but that's not really an important issue for a home furnace. In fact it might be better if it overshoots the desired temperature a bit on very cold days. - The air in the home acts like a big thermal battery that helps negate the need for a sophisticated controller. PID works very good for a wide variety of situations but it's important to remember it is not always the best tool for every job. In that way it is kind of like "quicksort".
tzs 5y ago
Another thing the integral handles is a systematic error in the controls. For example, suppose you have a vehicle that is suppose to automatically follow a straight line painted on the road. You have a sensor that can tell you how far you are from the line, and you can set the steering angle. The car is supposed to go straight when the steering angle is 0, but if there is a misalignment so that to go straight you actually have to set the steering angle to some constant non-zero value, if you just do PD you can end up with the car following a fixed distance to the side of the line instead of centered on the line like you want. Make it a PID controller instead of just PD, and the I term will fix this.

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
- jbay808 5y ago
  Yeah, hysteresis control aka "bang bang" control can also be unreasonably effective. It's a natural choice when your furnace can't throttle, or can but operates most efficiently at one output level anyway. Since the system always pushes as hard as it can, it automatically reaches the setpoint in the minimum possible time. It's almost like a PID controller with infinite gain. But the tradeoff is jitter -- all the error gets pushed up to the highest frequency bands. As long as you don't care about that in your system, it's a great choice and effortless to tune. It can also be a bad choice if there's any cost to changing or toggling the output, like if your furnace wears out from switching on and off a lot.
  - sokoloff 5y ago
    Many hot water circulating heating systems use bang-bang for the call-for-heat actuation but vary the circulating water temperatures in response to the outdoor temperature (via an “outdoor reset” input to the system). Properly set, this dampens the swings of temperature in the rooms as the heat gain is more closely matched to the heat loss, increasing comfort and economy of the system. https://en.m.wikipedia.org/wiki/Hot_water_reset https://en.m.wikipedia.org/wiki/Hot_water_reset
- shawnz 5y ago
  On-off or "bang-bang" control actually makes a lot of sense for home thermostats. For example consider: - With a home thermostat you probably want it to reach the desired temperature as quickly as possible. PID will never reach the setpoint as fast as bang-bang control since bang-bang control will always use the maximum possible power. - PID might help you avoid overshooting the desired temperature but that's not really an important issue for a home furnace. In fact it might be better if it overshoots the desired temperature a bit on very cold days. - The air in the home acts like a big thermal battery that helps negate the need for a sophisticated controller. PID works very good for a wide variety of situations but it's important to remember it is not always the best tool for every job. In that way it is kind of like "quicksort".

tzs 5y ago

Another thing the integral handles is a systematic error in the controls. For example, suppose you have a vehicle that is suppose to automatically follow a straight line painted on the road. You have a sensor that can tell you how far you are from the line, and you can set the steering angle. The car is supposed to go straight when the steering angle is 0, but if there is a misalignment so that to go straight you actually have to set the steering angle to some constant non-zero value, if you just do PD you can end up with the car following a fixed distance to the side of the line instead of centered on the line like you want. Make it a PID controller instead of just PD, and the I term will fix this.