plant cannot be linearized for PID tune

Hello, MATLAB users.

I am using 2014a version Matlab.

I have build quadcopter linear dynamics model include state-space model of 4 motors.

input is 4. attitude phi theta psi, position z. therefore, PID also 4 and I have used PID block that simulink provide.

output is 6. attitude phi theta psi and position xyz.

but, PID tuner always give unstable response that gain not working or show the message that plant cannot be linearized.

Dynamics's equations is totally fine. there have no any errors.

If, I try re-linearize close loop, result is as follow. please, see the attached screenshot.

in this case, how could I get the good stable gains of PID contorollers ?

Could you provide some similar situation or experience, docs for me ?

Answer 1

[Jesús Zambrano]

Hi Minjae,

Even if the dynamics equations are fine, some nonlinear systems are difficult or impossible to linearize. A possible way is to use data to estimate a model of the system.

The workflow is as follows:

• In the PID Tuner tab, select Identify New Plant.
• The Plant Identification tab will open. Select Get I/O Data, then Simulate Data so to generate identification data by simulating the model.
• It will open the Simulate I/O Data tab, where you specify the input data (for example a step function) used for the plant identification.
• Click Run Simulation. Then, click Apply and Close.
• Then, the Plant Identification tab will open showing the results of the plant identification. Once in there you can modify the response by moving or adding factors (for example delay, zero, integrator).
• Select Apply. It will create a new variable in the Data Browser section of the PID Tuner.
• Go to the PID Tuner tab, select Step Plot: reference tracking plot. Here the PID is using the new identified plant. You can still improve the system response by moving the sliders.
• Click Update Block and simulate the model with the new PID parameters.

Hope this can help to solve your question.

[Minjae Yoo]

I appreciate for your kind help :)

I just throwed out that garbage linear model. Thanks you !!

[Jesús Zambrano]

Glad to hear that! All the best!

[佳玮 聂]

simulation failed,update the profile or the model to try again...why

[Sam Chak]

@佳玮 聂, Are you working on the quadcopter as well? If so, please show the mathematical model.