In a cascade control architecture with an inner and outer loop, assuming the reference and disturbances are step-like signals, is it fairly common for the inner loop to be running much faster than the outer loop? If so, why is this the case? Thanks in advance.
Define "faster".
The inner loop often has a higher bandwidth, and in a sampled-time system has a greater need for a high sampling rate. In some systems it is convenient to have a high bandwidth, high sample rate, simple loop surrounded by a low bandwidth, low sample rate, complex loop.
So if your "faster" means "higher bandwidth", then yes. If your "faster" means "higher sampling rate" -- well, maybe not as often, but it's still going to be a valid technique.
When this is the case it is because one has a system that just plain needs two loops, either because it has two inputs to the plant or because it has two measurements of the plant behavior. Often these are arranged as they are because you'd really like to have the fine control that the 'slow' input or output offers, but things just plain won't work without the coarse -- and fast -- control that the 'fast' input or output offers.
Nested loops are everywhere: almost every sensor or actuator has inside a control loop of its own. In nested loop configurations, a seemingly paradoxical result can happen: if the inner loop gain is reduced, then the outer loop can loose stability.
Vladimir Vassilevsky DSP and Mixed Signal Design Consultant
Inner loop -> local feedback -> less phase shift -> higher bandwidth.
VLV
Theory aside, it's common for outer loops in industry to scan more slowly than inner loops. An inner flow controller may have a process response time of a few seconds, and require a control scan rate of < 1 second, whereas a level controller that writes to the flow controller setpoint may have a response time of an hour or more, and be able to function fine with a scan rate of a minute or so.
Slower scan rates are more commonly seen when controlling 'complex' variables, where there may be a large amount of computing involved. Processor load can be conserved by only running calculations as often as necessary.
Remember that one of the key functions of cascade controls is to buffer them from *fast* disturbances.
"ssylee" schrieb im Newsbeitrag news: snipped-for-privacy@z1g2000prc.googlegroups.com...
The inner loop must have faster dynamics and is used to pre-control the system using an auxiliary process value that leads to improved performance. Disturbance d2 is instantly feed-back controlled.
See
Heh.
What you say here is pretty much in line with what I was trying to express in my post. The only real difference in my experience is that my 'fast' loops are often sampled at or above 10kHz, and my 'slow' loops (except for the odd thermal control) are sampled no lower than 100Hz.
Same theory, different worlds...
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Did you read the bottom of page 257 in the pdf file you posted a link to? It said otherwise. Now who is right? Better yet who can prove it one way or the other so that ssylee has the right answer. One example is not a proof. Would this work on my favorite type 1 under damped second order systems?
Peter Nachtwey
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I refered to 'Figure 10.4 Traditional cascade block diagram'.
Traditional! Nothing else.
For more difficult systems I would use State Observer techniques.
EXAMPLE
Real process transfer function of 6th order:
That makes cascade control obsolete!
To avoid interaction between the loops, the inner control loop should respond AT LEAST 3 times faster than the outer loop. We cover cascade controls, and tuning of cascade loops, in this recorded webinar:
Thanks for your replies. The link to the book certainly helped me with more resources to better understand the operation of cascade architectures.
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I haven't read the paper but lets think about the alternative. If the inner loop was slower than the outer loop then the outer loop would be trying to correct at higher frequencies than the inner loop was conditioned for. This might lead to forcing unconsidered inner loop poles being forced active; resulting in control thrashing. While you might deal with it; it would be more complex. The only case where I could imagine it is if your trying to reject high frequency disturbances in the inner loop; and avoid saturation effects. Even in that case making the outer loop faster should be done only in the context of a full system analysis to avoid problems.
Ray
Because it simply works out that way mathematically. At least in one case. I can prove that for a single pole system, such as a motor with a velocity loop and a position loop, that the position loop must have a lower bandwidth than the inner loop. This is not a general proof but for a single pole system a few things should be obvious. First, the closed loop transfer function of the inner loop will have two poles. One for the system and on for the integrator that comes with the inner loop integrator gain. The output loop will have 4 poles. There will be two from the inner velocity loop. One for integrating velocity to position and one from the outer loop integrator gain. It should be obvious that the inner loop two poles system will be much faster than the outer loop four pole systems unless the outer loop poles are very fast relative to the inner loop poles. So how much faster can the outer loop poles be made relative to the inner loop poles? The answer is not fast enough. I tried an example where the inner loop was tuned to be critically damped with the characteristic equation being (s+lambda)^2 and then tried to chose outer loop poles that would be faster. I chose a desired characteristic equation of (s
+mu)^2*(s+delta)*(s+gamma) and found the symbolic solutions for them. I found there was a narrow range for mu relative to the inner loop poles at -lambda. mu cannot be made to be greater than lambda without moving delta and gamma to the right hand side and therefor unstable. Also, mu had to be less than 1/3*lambda for Ki to be positive and mu had to be less than 1/2*lambda for Kp to be positive. By taking the derivative of either the formula for Ki or the formula for Kp I found the relative value of mu compared to lambda that provided the highest gains is about 0.21132*lambda. This is less than 1/3 lambda. As it turned out gamma=3D0.21132*lambda too but delta turned out to be 1.366*lambda so the characteristic equation for the outer loop turned out to be (s+0.21132*lambda)^3*(s+1.366*lambda) which is much slower than the inner loop's characteristic equation of (s+lambda)^2.I don't consider this a proof but just one example but I can show symbolically that the inner loop is going to be much faster than the outer loop. I am pretty sure that more complicated systems will have similar results for similar reasons. I don't agree with with the statement on page 257 in the document JCH posted a link too. I can prove the statement is wrong at least in this case.
Note, as a by product of this work it was found that inner loop AND the outer loop can be tuned once I know the system gain and bandwidth and by choosing inner closed loop pole locations at -lambda. The outer loop Ki=3D0.01289*lambda^2 and outer loop Kp=3D0.192459*lambda
Peter Nachtwey
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Be aware that my solutions are not simulations. They are 'solved' differential equations on the basis of process identification methods.
EXAMPLE
Non-self regulating difficult system 3rd order:
Process: 0,001 v1''' + 0,03 v1'' + 0 v1' + 0 v1 = v2 Disturbance: 50%
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First, there is no point in using cascade control because there aren't multiple feed back devices. Second, you still haven't learned how to tune a PID. Let alone two PIDs in cascaded loop. Third, that is a simulation unless real hardware is being controlled. System identification is never perfect and your simulations shows a system where the acceleration or second derivative is being controlled and that is being integrated to provide velocity. There is no viscous damping term for v1', the velocity. Now what REAL system doesn't have friction? Fourth, what do you do when the set point is an arbitrary function of time or something other than a step change?
Peter Nachtwey
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[...]
Sometimes you can neglect small values or superfluous digits. (No one uses pi with infinity digits.)
Compare Page 1 (without) with Page 2 (with friction)
JCH, do you really want me to embarras you again? I don't think any body cares or really wants to move beyond the myths.
Peter Nachtwey
No one is obliged to accept my solution. I'd just like to see YOUR solution! Don't just argue.
AGAIN
Process transfer function and benchmark: Example Page 2
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I am not arguing. I simply know your statement about not doing better with cascaded loop is wrong, so why bother? What is in it for me? You never seem to learn from what I have posted before or even admitted that you were beat. You keep on posting your nonsense.
If you are willing to do the math yourself then this is how I approach problems like this. The outer closed loop transfer function has 3 poles if I don't use an integrator and four poles if I do. I simply place the three or four poles on the negative real axis and move them far enough in the negative direction to get a faster response than what you have. You have seen this before. I always get a faster response than what you do because I am not limiting the response with a target generator filter like you do. The inner loop , velocity, is just another system to be tuned in a similar manner but obviously the inner loop is tuned first.
Peter Nachtwey
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