How to programmatically tune this closed loop system with desired response time and robustness?

I have a closed loop system with a transfer function:

I can pid tune using the tuner app and specify robustness and response time or bandwidth and phase margin. I would like to do this programmatically so it can retune for slightly different input coeffiecients in the transfer function. The tranfer function coefficients are applied programmatically, I have linearized the system and saved it to a variable ClosedPID. I can output the step response of this system using step(ClosedPID). I am trying to use the pidTuner function to open to tuner and update the block but it I don't know how to programmatically change phase margin and bandwidth and apply it to the block. On top of this the plant it uses is slightly different and doesn't produce the same PID values even after manualy entering in the phase margin and bandwidth values. I am wondering what I am doing wrong.

TLDR; How can I programmatically automate the process of:

Clicking on the PID controller in simulink

Clicking Tune... (next to Transfer Function Based)

Entering Xrad/s for bandwidth and Ydeg for phase margin (where X and Y are numbers I choose)

Update block

Answer 1

[Siddharth Jawahar]

Hi Jack,

You can do the list of actions you mentioned by using the pid, pidtuneOptions, pidtune functions. As an example, using a similar third order system you have shown, you can do something like this:

sys = tf(1,[1 3 3 1]);
C_0 = pid(1,1,1); % Parallel form PID controller object with initial gains
gm = 0.80 % Gain margin
pm = 45   % Phase margin
opts = pidtuneOptions('PhaseMargin',pm,'DesignFocus','disturbance-rejection');% Set your tuning options
[C,info] = pidtune(sys,C_0, gm,opts);

>> C

C =

1

Kp + Ki * --- + Kd * s

s

with Kp = 1.99, Ki = 1.11, Kd = 0.885

Continuous-time PID controller in parallel form.

>> info

info =

struct with fields:

Stable: 1

CrossoverFrequency: 0.8000

PhaseMargin: 45

[Jack York]

Thank you. I will use this and update the simulink model using setPar with the parameters that this finds.

[Siddharth Jawahar]

Hi Jack,

Regarding setting the tuned parameters back in the model, the controller object has fields to access the gains. As in, you can use the variables C.Kp,C.Ki and C.Kd in the PID block and they will directly apply once you have tuned the controller. This would be easier compared to set_param.

Best,

Sid

[Jack York]

Thanks again. I will give that a try :)

[Jack York]

That does work better and is faster than set_param however I realised that for my particular application I need the simulink model to work independently after tuning without the original Matlab script being present or being ran and set_param works for this.

[Siddharth Jawahar]

Sure Jack! Good to know that worked for you