Lambda tuning is another name for pole placement. If you look at my videos you can see I use the Greek lambda to indicated the location of the closed loop poles.
Here is a simple first order example
http://deltamotion.com/peter/Mathcad/Mathcad - t0p1 pi NG.pdf
Here is a video tuning roughly the same system. I have other videos showing how to use pole placement on more complicated systems.
https://www.youtube.com/watch?v=lTRhuU_oQes
It bothers me that this is not obvious in my videos.
The other question is how do you do lambda tuning or pole placement if you don't have a transfer function for the plant? You can't. Please see the videos on system identification.
Multiple loops that interact with one another
My tank level control has an inner and outer loop example.
https://www.youtube.com/watch?v=d_twlM8VDuM
I have a pdf of speed and position control of a DC motor
I start out with speed control then I add position control.
Some of my calculations get geeky. I was trying to debunk some people on LinkedIn that said the inner loop has to be 10 to 15 times faster than the outer loop.
http://deltamotion.com/peter/Mathcad/Mathcad - DC Motor Velocity.pdf
I got the example from
http://ctms.engin.umich.edu/CTMS/index.php?example=MotorSpeed§ion=SystemModeling
Do you have another example?
Video your conversation with the process engineer when you ask for one extra sensor, and he says "but you can calculate that from the other sensors". This is a tough one for control system engineers.
That would be entertaining for you guys. I get involved with lots of motion control not process control. I have had many heated arguments with idiots that kludge together systems without regards to how it will be controlled. I try to be nice and keep my cool. I know I have posted my opinion about mechanical and hydraulic engineers many time here. There are those that kludge together systems. There are those that evolve systems starting with someone else's work. There are few that design systems. None have provided me with a transfer function yet and I have been doing control for a long time.
Observers are used to estimate states or feedback when feed back devices are not available. There are limits though. Our controller can do a very good job of estimating the acceleration. We do that without an acceleration sensor. However, it is unreasonable to expect a PLC programmer to do this for one system. It would cost too much and it can't be done in the PLC. It is cheaper to buy the sensor.
The tank level control video and the hammer from hell are non-linear.
such as moving average + dead time
I don't using moving average for control. To crude. I have used moving averages and standard deviations for quality control purposes. That project was done over 25 years ago. I don't have any data that and I don't have the presses. The project was at Coors in Golden, CO. We made a die press monitor that did quality control on the making of beer and pop can ends ( tops ).
If have examples of how to compensate for dead time. Here. I just haven't made the video.
In this pdf I derive the Internal Mode Control equations for a second order plus dead time , SOPDT, temperature system. The data came from Ron Beaufort's hotrod training units long ago.
I show how to derive the controller parameters that compensate for dead time IF the dead time isn't too large.
http://deltamotion.com/peter/Mathcad/SOPDT/Mathcad - SOPDT_HOTROD.pdf
Here I simulated lots of dead time so that it would be uncontrollable using a simple PID.
I used a Smith Predictor.
http://deltamotion.com/peter/Mathcad/SOPDT/Mathcad - SOPDT SP.pdf
How to 'know' how much a process gain might change under different conditions, and how you can measure the robustness of your tuning to satisfy yourself that your tuning is acceptable.
The tank level control shows this. I show how the gains change as the tank levels go up and down. If the tank doesn't have vertical sides the gains will change. If the outflow is through an orifice then the outflow will be proportional to the square root of the pressure/level. I also show that time "constants" may not be really constant. Again, the tank level control was done to help a student on LinkedIn.
On LinkedIn so many engineers suggested estimating the tank time constant by filling the tank and measuring the time for the tank to empty 63% for one time constant. That is so wrong due to the reasons I pointed out above. The 63% rule works well if there is just ONE pole or time constant to measure and the system is otherwise linear. This is what you are taught in class.
However, reality is that the time constants may change. If your want to know the instantaneous value of a time "constant" then you must use this rule. The instantaneous time "constant" is something/rate_of_change_something. You don't hear instructors say that. You don't see that in the text books. This is what my rant is about. In the case of the tank level control video the time constants are updated every scan. The time constants are calculated by the level divided by the rate of change in level.
If I were teaching a class I would use the Tank Level Control example. I can make so many good points. BTW, you don't pass unless you can write the differential equations for the two tanks. That is my starting point.