Cascade Loop Specifications

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.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
ssylee wrote:

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.
--
Tim Wescott
Control system and signal processing consulting
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Tim Wescott wrote:

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 http://www.abvolt.com
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
ssylee wrote:

Inner loop -> local feedback -> less phase shift -> higher bandwidth.
VLV
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Bruce Varley wrote:

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...
--
Tim Wescott
Control system and signal processing consulting
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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
* http://www.bgu.ac.il/chem_eng/pages/Courses/oren%20courses/Chapter_10.pdf
Figure 10.4
--
Regards JCH






Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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:
* http://home.arcor.de/janch/janch/_control/20100323-system-of-order-6 /
Page 1: Process identification Page 2: PID without feedforward and compensation Page 3: With state observer techniques
That makes cascade control obsolete!
--
Regards JCH






Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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%
* http://home.arcor.de/janch/janch/_control/20100326-non-self-regulating /
This system can't be controlled better by using traditional cascade control.
--
Regards JCH




Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
groups.com...

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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

[...]
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)
* http://home.arcor.de/janch/janch/_control/20100327-non-self-regulating /
Remark: Don't argue, show comparable solution!
--
Regards JCH







Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
wrote:

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
* http://home.arcor.de/janch/janch/_control/20100327-non-self-regulating /
--
Regards JCH




Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
*PLONK*
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

What do you want? I told you the procedure I use. Do the math yourself or admit you don't really know if your method is better than cascaded closed loop control because you don't know how how to implement cascaded control properly.
The key is what I call alpha or 30 from your equation. For a critically damped response, the inner loop closed loop poles must be at -30/2 or more negative. The outer loop poles must be at 2/3 of the inner loop poles or greater in magnitude.
This shoots holes in George's ascertion that the inner loop must be 3 times greater than the outer loop. George must not do motion control. OK, we know he doesn't. George's ascertion that the inner loop must be 3 times greater than the outer loop may apply to the few types of systems that he is familiear with but not to all systems. The math must be done on a case by case basis. JCH's system is much different from a temperature control system.
The point is do the math or stop misleading by spreading false myths. Question everything. I don't believe anything until I prove if for myself. Question me too but I have posted links to pdf files for the last five years that show the techniques I use. It is time that someone else puts some effort into finding the truth because I think this news group is just a social club where people post opinions and not hard facts or math.
I have JCH's problem worked out in great detail. JCH, if the inner loop is set to the slowest response where the inner loop poles are at -30/2 and the outer loop poles are set at 2/3 of that or -10 the response is still much faster that what you have shown.
Here is my cascaded loop response using your equation with http://www.deltamotion.com/peter/Mathcad/Mathcad%20-%20t2p1%20pid2%20JCH%20cascade%204+.pdf This is pdf was made with the gains as low as possible for a critically damped response. The inner loop poles are at -30/2 or -15 and the outer loop poles are at -10. Even so the outer loop bandwith is not 1/3 of the inner loop bandwith. Even the slowest critically damped response beats JCH's best.
Now do the math your self and see if you get the same results. It should be obvious if you truly know what your are doing.
This news group should consider this a thumb in its eye for not backing up anything they said with real facts or calculations. Okay, I haven't either but atleast I have done the calculations. I am just showing the results. This can't be a one way street. Someone worthy is going to have to show me that they have put some effort into this before I spill more info.
Peter Nachtwey
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

JCH you are beat again but no one cares. It wasn't worth my time. I know that it is easy to beat your responses because they are limited by your target filter.
No one bothered to ask why the actual position is leading the target position in the sine wave simulation. ( The answer is zeros in the outer loop). I have shown my gains. It does take much to translate what I did to Scilab script to verify my gains.
I did discover a few things. The double integrator make simulating this system, using state space, prone to integration errors. The response appears to change a lot when the sample time in changed. The response is much slower at low sample times because of the integrating error. I wonder if using RK4 would be better. I will try that out. I have alway wondered which would be better,
I get exactly the same response when I don't use just a single loop when I place the closed loop poles at -10 IF I only have the P gain in the forward path. Otherwise there is a difference in the zero locations which adversely affect the sine wave significantly.
The response you see is the slowest. If I move the inner closed loop poles to -30 then the response is very quick.
Peter Nachtwey
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

Now I *PLONK* the JCH and the whole news group that gave opinions instead of hard facts and calculations.
What's wrong JCH? I haven't got a reply. Are you ever going to admit defeat and go away?
Tim, your statement "So if your "faster" means "higher bandwidth", then yes"
This is right most of the time but not all of the time. It is the times where it isn't right that bother me.
Mr Vladifilter man "Inner loop -> local feedback -> less phase shift -> higher bandwidth" This doesn't make sense and you can't justify it?
JCH "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. "
And you you posted a link to a page that said it wasn't necessarily true. I pointed that out and even then you ignored it. Apparently you to read and understand the documents you post links too.
Dr Ebert just wants to sell his e-book. It is too bad Dr Ebert didn't post something I could challenge. I love picking on PhDs.
George "To avoid interaction between the loops, the inner control loop should respond AT LEAST 3 times faster than the outer loop. " George just wants to sell expertune but I wonder where the expert in the tuning is. George, did you work through JCH's problem? It is obvious that your are wrong about the 3/1 ratio. What you say may apply to process control application but you should not say the inner loop must be faster than the outer by 3/1 as a general case. I can prove that in some cases the ratio must be greater than 10/1. It all depends on the system and the choices in how it is going to be controlled. In JCH's problem the inner loop can be slower than the outer loop.
Consider this. A hydraulic system has a outer position loop control and an inner acceleration/force loop control. The inner loop is two derivatives from the postion so don't you think the acceleation loop would be MUCH higher that 3/1?
ssylee shoud be careful about who he listens too.
The whole point of this 'thumb in the news groups eye is' that too often people repeat what they have heard or read on the web. Too often people think that their experience is true for all cases when it it not. Too often people provide opinions instead of facts.
Do the math guys. If you do it right you will find that if the inner loop for JCH's problem can have two inner loop poles at -30 then the outer loop can have just one pole at -30 and one the one pole outer loop at -30 will be faster than the two pole inner loop poles at -30.
JCH may still be saved. At least he is still willing to put some time into his posts and do some math. He only needs to listen.
Peter Nachtwey
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

Polytechforum.com is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here. All logos and trade names are the property of their respective owners.