Very interesting history lesson! However I have to offer a slight amendment to the explanation. The prototypical fly-ball governor is not a proportional speed controller, but is itself actually a pure integral speed controller (at least in theory, for small angles, and with a zero friction balanced throttle valve, lol). The fly-ball approximates a conical pendulum. Harmonic oscillator theory tells us that a conical pendulum has one rotational speed at which the bob is stable (again, for small angles). This natural frequency is w = sqrt(g/L) in radians per second, where g is the acceleration of gravity and L is the distance from the pivot to the mass. For any speed below this speed, the balls rest all the way at the bottom of their travel. For any speed above this speed, the balls fly out to the maximum extent of their travel. When the ball angle is significant or the pivots aren’t placed in the shaft axis, the system becomes nonlinear and actually does exhibit a somewhat proportional behavior. One or both of these nonidealities is true of all the governors shown in the video. But these are all rather primitive variants, and various means were applied to more refined versions of the governor to counteract this nonideality (springs that partially modify or wholly replace the gravitational force on the balls, linkages that cause the balls to follow a paraboloidal surface, etc). There is quite a lot of period literature discussing various ways of making the governor more exactly approximate a theoretical small angle conical pendulum. The upshot of all of this is that the theoretical fly-ball governor actually exhibits an output actuator position that is a (nonlinear) function of the integrated applied torque over time, _not_ of speed. Torque is only zero at at the natural speed/frequency, and yet at this speed the actuator is stable in all positions. So the only stable equilibrium is one where the balls rotate at exactly the critical speed and the balls and throttle valve are in whatever position exactly supplies the torque required to drive the load, and the speed error is exactly zero. Hunting oscillations actually drive this point home. An ideal proportional speed controller does _not_ exhibit hunting. Acceleration is the first time derivative of speed, so a speed-proportional control law (applied torque and hence acceleration is proportional to speed error) results in a damped first order response with no overshoot. This point highlights something in the video that might bear correction or clarification. The graphs shown for proportional control at 13:05 are clearly graphs of proportional _position_ control of a system. This is _not_ the correct graph for proportional speed control. The acceleration of a mass is the second derivative of position, so in the case of proportional position control (applied torque/acceleration proportional to position error) we get overshoot and a damped harmonic oscillation, very unlike ideal proportional speed control where this does not happen. Of course I want to emphasize that most real fly-ball governors don’t actually achieve integral control. And I will be the first to recognize how many times I said the word "ideally" and "theoretically" above. However I think it’s important to state that when just using the simple equations of motion and ignoring nonidealities, it’s not correct to say that fly-ball governors exhibit proportional speed control law behavior. In fact the _core problem_ with fly-ball governors is that they are pure integral speed controllers, and it’s precisely because of this that they exhibit hunting oscillation.
Great and interesting analysis! Let me point out that the explanation I provided is specifically the one given by Maxwell in his paper (so it is 155 years old...), rather than a modern and complete explanation of governor dynamics. Also, my objective with these videos is to open up these topics beyond control experts, and I believe that a certain degree of simplification is needed (and probably the lack of it is one of the main outreach problems of the community). And thank you for your comment about the plot.
@@Prof_Gio Thank you for noticing my comment! I should have highlighted in my comment that I did not read Maxwell's treatise... which I now feel obliged to do. And I want to thank you for educating everyone about control theory, and about the fact that Maxwell had such a key part in the early history of the field. I had no idea that this was the case. Again I actually need to apologize that I didn't lead with this acknowledgement, I was too eager to get my point out and should have acknowledged the service you are doing first and foremost. I do want to know how Maxwell got to the conclusion that the flyball was a proportional controller with finite gain at zero frequency. I'm sure he was correct, in his historical context. We know for sure he was smart enough to have done the correct analysis! I didn't really think about the timeline when I wrote my original comment... my familiarity with the period literature is more around 1890 or so, after Maxwell died. So I'm guessing at the time people probably just used the off-axis pivot/large angle mode of operation which is in fact a (nonlinear) proportional controller. All of the more complex and later variants I'm familiar with were also discussed in the same breath as dashpots and other fluid dampers... probably not used in practice when Maxwell was writing? Anyway, it will be great to read the original source material that inspired your video!
So well explained, I can ALMOST grasp the ideas here. I do find the actual devices shown in operation to be more helpful in understanding their purpose - better than the drawings - but it would be even more helpful if the machinery could be run at full speed, or fast enough to see all the actions working. As an aside... It must be so exciting to actually invent something or discover something... I wish I could do that.
Superb content; thanks! It would be great if you could do a follow-up on Maxwell's contribution to color theory i.e., the basis of the RGB pixel control that allowed me to to watch you just now but which the visual arts community refused to accept initially. The more I learn about Maxwell, the more evident it becomes that he was a towering genius and kicked off much of what we take for granted in modern world. I often wonder what he would have achieved had he lived to 84 instead of just 48.
@@Prof_Gio Yes indeed ... is also a wonderful piece of industrial/academic archeology. I will come may be with further questions. Please note as well there are many bigger governor also in the Deutsche Museum in Munich. Grazie ciao.
Is there something special in the fact that the weight in the additional cylinder is immersed in a viscous fluid ? we understood that : - the first red belt (on top of spool) is making a proportional action - the second red belt (on the bottom of spool) is lifting the weight and storing potential energy for so long time the error is present so we have integral action. but what about the resistance of the viscous fluid ? a weight in a viscous fluid is giving a resistance proportional to velocity of the weight is moving in the fluid. So this last one observation seems a derivative action. Thanks and Regards.
I haven't studied this device but my explanation: It would be derivative if it were measuring the speed of the engine shaft. It is instead measuring the energy that has been stored in the feedback loop while the engine was overspeed, then viscously damping the resulting feedback torque *only from the weight*. The friction band braking effect happens to be viscous in action, but not in the control scheme that determines its magnitude. Reasonably close Professor? You could in principle have another feedback gear/shaft/weight system for underspeed condition, using friction from the governor balls when they're spinning slower than the setpoint. Not sure what it could actuate, maybe a valve for fuel/air mixture?
@Mark-sq8mh this is a good question. No, the effect is not a derivative action, but I see why you think so. The reason of the fluid is actually explained by Maxwell in his paper. The "frictions" are lumped in a coefficient Y, which also includes the viscosity of the fluid. Maxwell showed that the stability of the device depends on (B*F/M + Y)Y-G being positive. Thus, increasing the viscosity helps to make that quantity positive without mechanically changing the device. In the words of Maxwell: "To ensure this stability, the value of Y must be made sufficiently great, as compared with G, by placing the weight W in a viscous liquid if the viscosity of the lubricating materials at the axle is not sufficient." Of course the effect of Y is to damp variations of the response and in this sense it is reminiscent of a derivative action, but it not a proper one.
Why wasn't James Watt credited with the creation of control engineering, given that he invented the steam engine governor? Did he not write any treatise on the subject of governors?
Well, Watt didn't invent the governor, Christiaan Huygens did, about 100 years before to regulate the distance and pressure between millstones in windmills. Watt adapted one for steam engines. Also, governors are not even the first examples of control systems, there are examples which are thousands of years old (e.g. from Egypt). What makes the difference here is that Maxwell provided a deep analysis of what was going on, understanding the importance of the integral action, of linearisation, and setting up the basis of control engineering, which is a very formal and mathematical field. In other words, while control systems existed before, this was the first time someone recognised “control” as something important in itself, thus laying the foundation of control as an independent scientific field.
@@Prof_Gio Ah, thank you for this! I think the Watt governor is mentioned in probably every introductory control textbook and maybe that could be the reason it has stuck. Sadly, neither Maxwell nor Huygens are mentioned equally often in control. Most people only read one introductory book on the subject and, more often than not, the historical introduction is treated as filler material which is duly skipped: students have exams and homework assignments to worry about, encyclopaedic knowledge can wait for retirement!
I was wondering if there was ever a mechanical governor that was a pid Governor I actually came up with a design for one in my head. That also use the flyballs to turn an external ring to add integral into the loop. Although it had an internal ring to remove intergral from the Loop. Also had a derivative function that oddly enough Use a set of differential gears like you find in a car.
Ah, so one differential halfshaft goes to the motor, the other halfshaft goes to a flywheel, and the pinion shaft would be the derivative output with a spring to keep it centred. something like that?
@maxff123 ya. Compare the flywheel speed to the motor speed and adjust accordingly. Fluid coupling to match flywheel speed to motor, over time. Density of fluid is part of the D response.
Amazing. Engineer unlike social science or pure science don't celebrate as much the original inventor as we should. Historical context is important to know in order to learn problem solving skill. Thank you for sharing. I hope you become an engineering educator just like Neil degrasse tyson as a science educator.
If Maxwell wrote an engineering paper thusly becoming one of the forefathers of control systems engineering, does that mean there is still hope for engineers?
@@Prof_Gio Oh, I was referring to all engineers in general -- if anything, all the other types except control. You're right though: not only control is weird, it also comes with all kinds of names (for essentially the same thing) and in various flavours. It does have enough elements to qualify as a minor cult among the science/technology sector.
Very interesting history lesson! However I have to offer a slight amendment to the explanation. The prototypical fly-ball governor is not a proportional speed controller, but is itself actually a pure integral speed controller (at least in theory, for small angles, and with a zero friction balanced throttle valve, lol).
The fly-ball approximates a conical pendulum. Harmonic oscillator theory tells us that a conical pendulum has one rotational speed at which the bob is stable (again, for small angles). This natural frequency is w = sqrt(g/L) in radians per second, where g is the acceleration of gravity and L is the distance from the pivot to the mass. For any speed below this speed, the balls rest all the way at the bottom of their travel. For any speed above this speed, the balls fly out to the maximum extent of their travel.
When the ball angle is significant or the pivots aren’t placed in the shaft axis, the system becomes nonlinear and actually does exhibit a somewhat proportional behavior. One or both of these nonidealities is true of all the governors shown in the video. But these are all rather primitive variants, and various means were applied to more refined versions of the governor to counteract this nonideality (springs that partially modify or wholly replace the gravitational force on the balls, linkages that cause the balls to follow a paraboloidal surface, etc). There is quite a lot of period literature discussing various ways of making the governor more exactly approximate a theoretical small angle conical pendulum.
The upshot of all of this is that the theoretical fly-ball governor actually exhibits an output actuator position that is a (nonlinear) function of the integrated applied torque over time, _not_ of speed. Torque is only zero at at the natural speed/frequency, and yet at this speed the actuator is stable in all positions. So the only stable equilibrium is one where the balls rotate at exactly the critical speed and the balls and throttle valve are in whatever position exactly supplies the torque required to drive the load, and the speed error is exactly zero.
Hunting oscillations actually drive this point home. An ideal proportional speed controller does _not_ exhibit hunting. Acceleration is the first time derivative of speed, so a speed-proportional control law (applied torque and hence acceleration is proportional to speed error) results in a damped first order response with no overshoot.
This point highlights something in the video that might bear correction or clarification. The graphs shown for proportional control at 13:05 are clearly graphs of proportional _position_ control of a system. This is _not_ the correct graph for proportional speed control. The acceleration of a mass is the second derivative of position, so in the case of proportional position control (applied torque/acceleration proportional to position error) we get overshoot and a damped harmonic oscillation, very unlike ideal proportional speed control where this does not happen.
Of course I want to emphasize that most real fly-ball governors don’t actually achieve integral control. And I will be the first to recognize how many times I said the word "ideally" and "theoretically" above.
However I think it’s important to state that when just using the simple equations of motion and ignoring nonidealities, it’s not correct to say that fly-ball governors exhibit proportional speed control law behavior. In fact the _core problem_ with fly-ball governors is that they are pure integral speed controllers, and it’s precisely because of this that they exhibit hunting oscillation.
Great and interesting analysis! Let me point out that the explanation I provided is specifically the one given by Maxwell in his paper (so it is 155 years old...), rather than a modern and complete explanation of governor dynamics. Also, my objective with these videos is to open up these topics beyond control experts, and I believe that a certain degree of simplification is needed (and probably the lack of it is one of the main outreach problems of the community). And thank you for your comment about the plot.
@@Prof_Gio Thank you for noticing my comment! I should have highlighted in my comment that I did not read Maxwell's treatise... which I now feel obliged to do.
And I want to thank you for educating everyone about control theory, and about the fact that Maxwell had such a key part in the early history of the field. I had no idea that this was the case. Again I actually need to apologize that I didn't lead with this acknowledgement, I was too eager to get my point out and should have acknowledged the service you are doing first and foremost.
I do want to know how Maxwell got to the conclusion that the flyball was a proportional controller with finite gain at zero frequency. I'm sure he was correct, in his historical context. We know for sure he was smart enough to have done the correct analysis!
I didn't really think about the timeline when I wrote my original comment... my familiarity with the period literature is more around 1890 or so, after Maxwell died. So I'm guessing at the time people probably just used the off-axis pivot/large angle mode of operation which is in fact a (nonlinear) proportional controller. All of the more complex and later variants I'm familiar with were also discussed in the same breath as dashpots and other fluid dampers... probably not used in practice when Maxwell was writing?
Anyway, it will be great to read the original source material that inspired your video!
So well explained, I can ALMOST grasp the ideas here. I do find the actual devices shown in operation to be more helpful in understanding their purpose - better than the drawings - but it would be even more helpful if the machinery could be run at full speed, or fast enough to see all the actions working. As an aside... It must be so exciting to actually invent something or discover something... I wish I could do that.
Thanks! As a control engineer I haven’t dug much into the history so this was really fascinating.
Thanks for your support. I have some ideas for more videos like these in future. Stay tuned ;)
Superb content; thanks! It would be great if you could do a follow-up on Maxwell's contribution to color theory i.e., the basis of the RGB pixel control that allowed me to to watch you just now but which the visual arts community refused to accept initially. The more I learn about Maxwell, the more evident it becomes that he was a towering genius and kicked off much of what we take for granted in modern world. I often wonder what he would have achieved had he lived to 84 instead of just 48.
I'll consider this for a future video. Thank you for the tip!
Thanks a lot. I tried many times to find one explanation of the integral action in the mechanical governor.
Very happy that you found this video of help. I was lucky to have such wondeful exhibit next door. It all makes much more sense when you see it!
@@Prof_Gio Yes indeed ... is also a wonderful piece of industrial/academic archeology. I will come may be with further questions. Please note as well there are many bigger governor also in the Deutsche Museum in Munich. Grazie ciao.
amazing video. I will be tuned if you want to made some about N. Wiener contributions.
Thanks! I'll definitely do more videos like this (when I find the time -_-')
Will you do a follow-up video on adding the Derivative Term to make the D in PID controllers?
Is there something special in the fact that the weight in the additional cylinder is immersed in a viscous fluid ?
we understood that :
- the first red belt (on top of spool) is making a proportional action
- the second red belt (on the bottom of spool) is lifting the weight and storing potential energy for so long time the error is present so we have integral action.
but what about the resistance of the viscous fluid ? a weight in a viscous fluid is giving a resistance proportional to velocity of the weight is moving in the fluid. So this last one observation seems a derivative action.
Thanks and Regards.
I haven't studied this device but my explanation:
It would be derivative if it were measuring the speed of the engine shaft. It is instead measuring the energy that has been stored in the feedback loop while the engine was overspeed, then viscously damping the resulting feedback torque *only from the weight*. The friction band braking effect happens to be viscous in action, but not in the control scheme that determines its magnitude. Reasonably close Professor?
You could in principle have another feedback gear/shaft/weight system for underspeed condition, using friction from the governor balls when they're spinning slower than the setpoint. Not sure what it could actuate, maybe a valve for fuel/air mixture?
@Mark-sq8mh this is a good question. No, the effect is not a derivative action, but I see why you think so. The reason of the fluid is actually explained by Maxwell in his paper. The "frictions" are lumped in a coefficient Y, which also includes the viscosity of the fluid. Maxwell showed that the stability of the device depends on (B*F/M + Y)Y-G being positive. Thus, increasing the viscosity helps to make that quantity positive without mechanically changing the device. In the words of Maxwell: "To ensure this stability, the value of Y must be made sufficiently great, as compared with G, by placing the weight W in a viscous liquid if the viscosity of the lubricating materials at the axle is not sufficient."
Of course the effect of Y is to damp variations of the response and in this sense it is reminiscent of a derivative action, but it not a proper one.
@@Prof_Gio thanks again.
Transferring the rotational speed, not the torque. That would be a different measurement, requiring a different sort of measuring device.
Thanks for pointing this out. I added a correction card at 03:16.
Why wasn't James Watt credited with the creation of control engineering, given that he invented the steam engine governor? Did he not write any treatise on the subject of governors?
Well, Watt didn't invent the governor, Christiaan Huygens did, about 100 years before to regulate the distance and pressure between millstones in windmills. Watt adapted one for steam engines. Also, governors are not even the first examples of control systems, there are examples which are thousands of years old (e.g. from Egypt).
What makes the difference here is that Maxwell provided a deep analysis of what was going on, understanding the importance of the integral action, of linearisation, and setting up the basis of control engineering, which is a very formal and mathematical field. In other words, while control systems existed before, this was the first time someone recognised “control” as something important in itself, thus laying the foundation of control as an independent scientific field.
@@Prof_Gio Ah, thank you for this! I think the Watt governor is mentioned in probably every introductory control textbook and maybe that could be the reason it has stuck. Sadly, neither Maxwell nor Huygens are mentioned equally often in control. Most people only read one introductory book on the subject and, more often than not, the historical introduction is treated as filler material which is duly skipped: students have exams and homework assignments to worry about, encyclopaedic knowledge can wait for retirement!
I was wondering if there was ever a mechanical governor that was a pid Governor I actually came up with a design for one in my head. That also use the flyballs to turn an external ring to add integral into the loop. Although it had an internal ring to remove intergral from the Loop. Also had a derivative function that oddly enough Use a set of differential gears like you find in a car.
Ah, so one differential halfshaft goes to the motor, the other halfshaft goes to a flywheel, and the pinion shaft would be the derivative output with a spring to keep it centred. something like that?
@maxff123 ya. Compare the flywheel speed to the motor speed and adjust accordingly. Fluid coupling to match flywheel speed to motor, over time. Density of fluid is part of the D response.
It would be nice to have a decent auto tune function for PID parameters for betaflight. It takes me 8 hours to really dial in a drone.
Amazing. Engineer unlike social science or pure science don't celebrate as much the original inventor as we should. Historical context is important to know in order to learn problem solving skill. Thank you for sharing. I hope you become an engineering educator just like Neil degrasse tyson as a science educator.
Thanks for the appreciation!
If Maxwell wrote an engineering paper thusly becoming one of the forefathers of control systems engineering, does that mean there is still hope for engineers?
Difficult to say, control engineers are weird engineers to begin with...
@@Prof_Gio Oh, I was referring to all engineers in general -- if anything, all the other types except control.
You're right though: not only control is weird, it also comes with all kinds of names (for essentially the same thing) and in various flavours. It does have enough elements to qualify as a minor cult among the science/technology sector.