How to use System Identification to estimate System Model with Process Variable (PV), Set Point (SP), and Output (OP) actual data over certain period?

Hello, I am new in Control System subject. Here I have a dataset from a Level Controller consist of: Timestamp, PV, SP, OP with 1 minute sampling time. It looks like this

I need to estime the system model and I want to use System Identification. What is the best approach that I should use in order to process this data to obtain the system model? I already read and watched some references where they use input and output as an example, but what is the input and output of my system based on my data? And is there any effect on timestamp which maybe I should treat my data as a time series? Thank you very much for your help

Answer 1

[Sam Chak]

Hi @Kiky Agustina Putri

According to this article, a control system has three variables: the setpoint (SP), the process variable (PV), and the output (OP). The PV is the parameter to be controlled (Level in your case), the SP is the desired value for the PV, and the OP is the value sent from the controller to the control element.

So, OP should be the input, and PV is the output. Here, I take care of the hard work and type out the data for you.

%% Data
OP  = [29.5887 22.3842 43.3046 41.4478 10.9213 25.4135 52.8004 38.4974 21.8591 31.3099];
PV  = [20.1326 19.2233 22.3332 21.6243 17.2468 19.2986 23.7606 21.2787 19.0127 20.5806];

%% Input and Output
in  = OP;
out = PV;

[Kiky Agustina Putri]

Hello @Sam Chak

Thank you for your answer, I would like to ask a further question. The OP that I have comes from a controller with PID in it. Is it okay if I use these data of my system which is controlled by the PID, or shoud I use the data where my system is in uncontrolled condtion (without PID controller)?

[Sam Chak]

Hi @Kiky Agustina Putri

As long as the input and output are bounded signals, it is okay to use a control signal as an input. If the system is known to be open-loop stable, then many people tend to inject a sinusoidal signal as input and measure the system's frequency response.

OP  = [29.5887 22.3842 43.3046 41.4478 10.9213 25.4135 52.8004 38.4974 21.8591 31.3099];
PV  = [20.1326 19.2233 22.3332 21.6243 17.2468 19.2986 23.7606 21.2787 19.0127 20.5806];

subplot(211)
plot(OP, '-o', 'color', '#2596be'), grid on, title('Input: OP')
subplot(212)
plot(PV, '-o', 'color', '#db703a'), grid on, title('Output: PV')