# How to evaluate a close-loop control during transient?

I have implement a close-loop control in order to perform the tracking of the desired signal R. The basic scenario shall be summarized as follow:

I have to evaluate the performance of my control G with a moving average value of the Error E.
When there is no transient the error E shall be less then a certain threshold.

But, how to relax the threshold during transient ?

• Frequency of R is limit to 2 HZ
• Rising time is 200ms
• Control G has a 1 Hz band (but this is not a problem)
• I can acquire R E U and Y
• Real-time FFT of R is not possible during execution.

My idea is to find a threshold as function of r signal which is small when reference is stationary (constants from at least 200 ms) and high when the reference is fast changing.

Thank you all
Regards

• What kind of transient? Disturbances? Reference change?
– Ben
Sep 30 '19 at 14:03
• Reference change Sep 30 '19 at 14:06
• You mention "tracking" below. You need to have a type one or two system (or alternate control design) look at the boxes in the middle of ctms.engin.umich.edu/CTMS/index.php?aux=Extras_Ess for descriptions. If somebody has a better descriptive Type I II link please post and I will delete this. Oct 1 '19 at 21:08
• If your reference is sufficiently continuous and you have a good model of the system you can probably reduce the transient by adding feedforward. Oct 2 '19 at 6:21

In order to evaluate the performance of a controller during transients, you can use different metrics. Two metrics you could use are

ITAE= $$\int_0^{\infty} t*|e| \,dt$$

ITSE = $$\int_0^{\infty} t*e^2 \,dt$$

where e is the difference between your reference and the measurement and t is the time since the reference change.

Basically, you want to minimize these metrics. The basic idea is that an error in the beginning won't impact the metric much while an error 1 second after the reference change will impact your metric much more.

There are probably other metrics you could use. You could also use stabilization time at 1% or 5%.

Edit : If your signal is cyclical you could limit the integral upper bound to a limited number of 2-Hz cycles.

ITAE= $$\int_0^{NT} t*|e| \,dt$$

ITSE = $$\int_0^{NT} t*e^2 \,dt$$

where N is a whole number and T is the period of your reference signal.

• Dear Ben Thank you, I have already test and implement your approach. But this is a tracking problem so (in general) the desired signal continues to change value with a max 2 Hz band. Sep 30 '19 at 14:52