12-24-2021, 02:49 PM
Picking up after parts 1 and 2, let's imagine you are a control loop operator following a predefined set of control rules. Your boss, the master control operator with a world of experience, does periodic rounds for performance review. He looks over your shoulder to see the state of your control loop. He observes all the input and output values at the moment. What does that tell him? Aside from the instantaneous error, basically nothing. Why is that? Because your boss needs some history of past behavior in order to judge how you are doing. So he watches for a while. Then he knows how the error term tracked over a time period, but that still does not allow him to effectively grade your performance, because chances are, not much is happening.
Instead of waiting a long time while looking over your shoulder, he may reach and turn the dial to disturb your carefully balanced loop. He can then learn a lot quickly by watching your attempts to recover stability and regain the set point. To judge your skill, the master controller will then observe not only a time sequence of the error term during restabilization, but also the pattern of your dial settings while attempting that recovery. Another day, instead of scrambling your dials, the boss might dump some cold water into your temperature-controlled frying pan to see your reaction. Your loop needs to respond appropriately to both control and process disturbances.
The lesson concealed in the above is that loop control, if it is to do an expert-level job, will need to track not only a history of the error term, but also a history of the correction applied. PID control doesn't provide a control term for that. Then again, PID control is always a step behind, trying to catch up. That is why there are no ideal PID control solutions, only compromises, some better, some worse.
Going back to a variation on the helmsman analogy, think about racing car video taken from inside the vehicle showing the driver's hands on the wheel. When the track is dry and the tires are good, the driver's hands are quiet, making smooth and steady corrections. If the tires are worn out, or the track is wet, the driver's hands will be making many quick corrections. Looking from outside, the path of the car may seem the same in the two cases, but the driver is working much harder to keep the car on the road when traction is limited. As a rule of thumb, the quieter the hands, the more skilled the driver.
Your boss, looking over your shoulder, will give you a higher score if you are not cranking the dial drastically one way and another in rapid succession. The longer you wait to act, the larger the required correction. We conclude the key to better control is to act strongly and promptly, but how does that fit in the PID scheme of things? It means the gain and differential terms are going to be large, and the integral term will be very small. Experienced PID hands can tell you that is an invitation for oscillation. For a race car driver, overcorrection means going off the track. For a helmsman, it means a crooked wake. For a control operator, it means a lousy performance review.
If you think about the typical driver, having a typical off-road incident, the usual sequence is that the wheel is turned hard in order to stay on the road, or to avoid an obstacle. That part goes OK. The accident happens when the needed counter-correction is delayed. Say the car is having trouble getting around a right turn, so the driver turns harder right, and in the end, goes of the right side of the road.
In intuitive terms, the question is what, exactly, is it that the skilled operator/driver/helmsman does differently to get the better result, and how do we reduce that behavior to a generalized set of rules which a computer can follow?
A good place to start is the concept of expected error vs instantaneous error. The skilled operator knows that disturbances will take time to correct, so you take the initial corrective action, and only make additional corrections to the extent that the system is not following the expected path back to the desired state. Consider the race driver in the wet. He feels the car start to rotate off the correct line. His flick of the wheel in the corrective direction is very brief. The steering wheel is back in its original position long before the full effect of the correction is felt. How do you quantify that skill?
Driving race cars is flashier, but for basic understanding, the frying pan example will be more useful. Let's say the dial is steady and the pan temperature is at the desired point. Then, we disturb the system and look to restabilize temperature quickly without inducing oscillation. Let's say you wanted to raise the temperature N degrees, so you would need to turn up the dial. If you knew the new setting for Temperature + N, you could go straight there and wait for the pan temperature to exponentially approach the new set point. That could take a long time. Better to turn the burner up further, then turn it back down to the new setting before the temperature overshoots.
If you had experience, maybe you know that it takes XW extra watts at the burner to maintain the pan at Temperature + N. In addition, you might know the thermal mass of the pan. If it takes WH Watthours to heat the thermal mass by N degrees, then, you could crank up the burner setting until you had injected an additional WH Watthours. Afterwards, you could return the burner setting to the original setting plus XW extra watts. During the interval, you expect the temperature to be rising, but you don't expect to be making any big corrections. instead, you are waiting to see if your calculations were correct. If they were, the temperature will settle near the new value without any extra delay.
It may sound complicated, but if there is a computer in the loop, it can do all the needed calculations more than fast enough to keep up. We call this process Predictive Energy Balancing. Advanced knowledge of system behavior is a help, but is not essential. Sophisticated PEB controls can learn to optimize themselves on the fly.
To be continued.
Tom Lawson
December, 2021
Instead of waiting a long time while looking over your shoulder, he may reach and turn the dial to disturb your carefully balanced loop. He can then learn a lot quickly by watching your attempts to recover stability and regain the set point. To judge your skill, the master controller will then observe not only a time sequence of the error term during restabilization, but also the pattern of your dial settings while attempting that recovery. Another day, instead of scrambling your dials, the boss might dump some cold water into your temperature-controlled frying pan to see your reaction. Your loop needs to respond appropriately to both control and process disturbances.
The lesson concealed in the above is that loop control, if it is to do an expert-level job, will need to track not only a history of the error term, but also a history of the correction applied. PID control doesn't provide a control term for that. Then again, PID control is always a step behind, trying to catch up. That is why there are no ideal PID control solutions, only compromises, some better, some worse.
Going back to a variation on the helmsman analogy, think about racing car video taken from inside the vehicle showing the driver's hands on the wheel. When the track is dry and the tires are good, the driver's hands are quiet, making smooth and steady corrections. If the tires are worn out, or the track is wet, the driver's hands will be making many quick corrections. Looking from outside, the path of the car may seem the same in the two cases, but the driver is working much harder to keep the car on the road when traction is limited. As a rule of thumb, the quieter the hands, the more skilled the driver.
Your boss, looking over your shoulder, will give you a higher score if you are not cranking the dial drastically one way and another in rapid succession. The longer you wait to act, the larger the required correction. We conclude the key to better control is to act strongly and promptly, but how does that fit in the PID scheme of things? It means the gain and differential terms are going to be large, and the integral term will be very small. Experienced PID hands can tell you that is an invitation for oscillation. For a race car driver, overcorrection means going off the track. For a helmsman, it means a crooked wake. For a control operator, it means a lousy performance review.
If you think about the typical driver, having a typical off-road incident, the usual sequence is that the wheel is turned hard in order to stay on the road, or to avoid an obstacle. That part goes OK. The accident happens when the needed counter-correction is delayed. Say the car is having trouble getting around a right turn, so the driver turns harder right, and in the end, goes of the right side of the road.
In intuitive terms, the question is what, exactly, is it that the skilled operator/driver/helmsman does differently to get the better result, and how do we reduce that behavior to a generalized set of rules which a computer can follow?
A good place to start is the concept of expected error vs instantaneous error. The skilled operator knows that disturbances will take time to correct, so you take the initial corrective action, and only make additional corrections to the extent that the system is not following the expected path back to the desired state. Consider the race driver in the wet. He feels the car start to rotate off the correct line. His flick of the wheel in the corrective direction is very brief. The steering wheel is back in its original position long before the full effect of the correction is felt. How do you quantify that skill?
Driving race cars is flashier, but for basic understanding, the frying pan example will be more useful. Let's say the dial is steady and the pan temperature is at the desired point. Then, we disturb the system and look to restabilize temperature quickly without inducing oscillation. Let's say you wanted to raise the temperature N degrees, so you would need to turn up the dial. If you knew the new setting for Temperature + N, you could go straight there and wait for the pan temperature to exponentially approach the new set point. That could take a long time. Better to turn the burner up further, then turn it back down to the new setting before the temperature overshoots.
If you had experience, maybe you know that it takes XW extra watts at the burner to maintain the pan at Temperature + N. In addition, you might know the thermal mass of the pan. If it takes WH Watthours to heat the thermal mass by N degrees, then, you could crank up the burner setting until you had injected an additional WH Watthours. Afterwards, you could return the burner setting to the original setting plus XW extra watts. During the interval, you expect the temperature to be rising, but you don't expect to be making any big corrections. instead, you are waiting to see if your calculations were correct. If they were, the temperature will settle near the new value without any extra delay.
It may sound complicated, but if there is a computer in the loop, it can do all the needed calculations more than fast enough to keep up. We call this process Predictive Energy Balancing. Advanced knowledge of system behavior is a help, but is not essential. Sophisticated PEB controls can learn to optimize themselves on the fly.
To be continued.
Tom Lawson
December, 2021