Dear researchers, how can can I simulate nonlinear disturbance observer for UAV on Simulink?

I want to model this nonlinear disturbance observer - - on Simulink, in order to estimate the disturbance. Any relevant help is well appreciated.

Answer 1

[Sam Chak]

Hi @ALABA PHILIP OPAYEMI

As you didn't provide sufficient explanations for the problem and I don't know what it is, so I just integrated the given differential equation in the blue NDO Fcn block as usual, and this is the simplest example I can make with the disturbance :

Hope it works out for you.

[UASLAB]

@Sam Chak

Thank you. I am sorry this is the detail about the problem I am trying to solve:

Nonlinear funtion is: (of the form )

The NDO is:

I am particularly interested in how to solve and model this NDO in Simulink?

[Sam Chak]

No worries, @ALABA PHILIP OPAYEMI. I'm no UAV expert but I guess you got confused by the symbol z in UAV dynamics with another symbol z in the NDO , where the former refers to altitude (layman's terms: height of the UAV above ground), and the latter refers to internal state of the NDO in estimating the disturbance. So, pick your symbols wisely during coding.

Anyhow, I think my example should be simple enough for you to follow. In my example, I made , , and . Just type out the right-hand side of your NDO differential equation in the blue Fcn block (or multiple Fcn blocks if NDO order is higher than 1) and hook it up to an Integrator block (or corresponding Integrator blocks) with the intial condition with .

Also, since I assumed in my example, then naturally , where I labelled the signal as dhat. In your case, you should probably multiply the sum with the matrix .

If you find my simple NDO demo example in Simulink is helpful, please consider accepting ✔ and voting 👍 the Answer. Thanks!

[UASLAB]

@Sam Chak

Alright. The NDO is of order 2.

To clear my doubt,

1. is NDO FCN block a standard ready made block in Simulink or if not, could you please show me how to make NDO fcn?

2. My A, C p(x) and l(x) are matrices...will the fcn be able to handle it?

Thank you

[Sam Chak]

Hi @ALABA PHILIP OPAYEMI

Actually I copied the Fcn block from the old versions of a Simulink file. Also, Fcn handles only a single scalar equation. In my NDO Fcn block, I have shown the equation that I entered in the block:

- 10*1*u(3) - 10*(1*10*u(2) + 0 + 1*u(1))

where u(1) refers to the u input, u(2) refers to the x input, and u(3) refers to the input.

In the latest Simulink, you can use Interpreted MATLAB Function block as a substitute.

Since your NDO order is 2, then you will need two Interpreted MATLAB Function blocks plus two Integrator blocks to get the internal states and . Of course, you also need to do a little math to resolve the NDO matrix equation form () into two NDO scalar equations ( and ).

Else, if you are relatively good and comfortable at coding, you can use the S-Function block directly. S refers to System, and since the NDO is a system described by the differential equation, then it is 100% possible to write the compact NDO matrix equation form () in the S-function.

The S-function approach is generally preferred and more efficient for higher order systems ().

[UASLAB]

Thank you very much.

[UASLAB]

@Sam Chak

Please help me check, this is the result I am getting when I simulate disturbance d and its estimatimation dhat. I do not know the reason for the gap between d and dhat?

The NDOB model:

A = 2*pi/10, C = 1, k = 30

[Sam Chak]

Hi @ALABA PHILIP OPAYEMI

Technically, it looks like you have successfully estimated the disturbance, but with an offset of . What could that be? I can't determine from the image of a block diagram. My mathematical instinct tells me it probably comes from the input u if it has a constant term.

[UASLAB]

Hello sir @Sam Chak

U is the control input for altitude and computed by the altitude controller...

okay, please can I send you the simulink file then?

Thank you.

[Sam Chak]

Hi @ALABA PHILIP OPAYEMI

Edit: New stuff:

By the way, I noticed this circled in RED. Maybe this is the culprit.

Old stuff:

I don't know what your control input u is. But if it is some kind of simple mathematics, then I think you can check and find out of whether or not there is a constant in u.

Do not fret about it! As mentioned previously, your NDO has successfully estimated the amplitude and frequency of the sinusoidal disturbance. A workaround for this is simply add back to , something like

Let me know the outcome! 😉

[UASLAB]

@Sam Chak Thanks.

g is the acceleration due to gravity, and g = 9.81, there is no constant add in U...okay I will follow your guide and tell you the outcome.

[UASLAB]

Hello @Sam Chak

It worked...

this is the outcome

Thank you

[Sam Chak]

Great to see that it works out. @ALABA PHILIP OPAYEMI

Anyhow, you should understand that any constant term that goes into the NDO (to be integrated) can be a "suspect".

And the is just one of the prime suspect if it does not get cancelled out by your control input u.

[UASLAB]

@Sam Chak

alright sir, thank you.

[Alfa]

@Sam Chak I'm sorry sir, i still confuse about p(x). I have read in the journal that p(x) is the nonlinear function to be designed, but i don't know where is p(x) from. How can i get p(x) ??

Answer 2

[Sam Chak]

Hi @ALABA PHILIP OPAYEMI

There are two Dryden Wind Turbulence Model blocks: one is continuous and the other is discrete. Check out the links:

1. https://www.mathworks.com/help/aeroblks/drydenwindturbulencemodelcontinuous.html
2. https://www.mathworks.com/help/aeroblks/drydenwindturbulencemodeldiscrete.html

You can also see this example on how the disturbance model is implemented.

https://www.mathworks.com/help/aeroblks/nasa-hl-20-lifting-body-airframe.html

If you find the guidance is helpful, please consider voting 👍 the Answer. Thanks!

[UASLAB]

Thank you @Sam Chak, my main challenge is how to implement this for simulation as I want to model wind disturbance for a quadrotor. These are my concerns:

1. how to get DCM for a Quadrotor?
2. what Airspeed input to use, as I am performing a simulation and no means to measure airspeed?

I will appreciate if you can put me through on this...

Thank you.

[Sam Chak]

@ALABA PHILIP OPAYEMI, Thanks for your clarification. Looks like this is beyond NDO. NDO is simply pure math, just a single line of equation. But your new questions are Engineering and Physics problems. It's not even a MATLAB/Simulink problem.

• Can you find out the DCM formula for your Quadrotor?
• When I say it's Physics, it's because I think we need to imagine what the Airspeed is defined according to the Aerodynamics. I presume that you are Aeronautical Engineering Guy based on the project you did above (correct me if I'm wrong). Sure this is only simulation and you cannot measure the real Airspeed. But you can definitely estimate them (via mathematical formula) from the states of your Quadrotor.

MathWorks Help Center Search results show that there are blocks in the Aerospace Blockset for you to compute and obtain the DCM. See link:

https://www.mathworks.com/help/aeroblks/axes-transformations-1.html

If you don't have the Blockset, you can write the code to compute DCM. I've checked with a lecturer in the Department of Mechanical & Aerospace Engineering. DCM is commonly taught in Flight Dynamics and Control, or Motion of Mechanical Systems.

Stay calm because the challenge is not as big as you think. Do 1 thing at at a time. I'd suggest that your put the Simulink simulation on hold. Sort out the mathematical formulas that you need to compute the Quadrotor DCM and Airspeed. If you still needs help, then ask a new question on how to put those formulas in the Simulink Block.

[UASLAB]

Thank you @Sam Chak

...I presume that you are Aeronautical Engineering Guy...No, you are not...

I will work on the insights you have given.

Thank you.

[UASLAB]

Dear sir @Sam Chak,

I have tried to incorporate the DCM and other necessary input parameters into the model but did not work. I am yet to understand how to implement it...

However, I have been using this model(https://www.mathworks.com/help/simulink/slref/aircraft-longitudinal-flight-control.html) below and it works; except that I do not know how to vary the parameter to get different desired wind speeds as I am yet to come accross any documentation on it.

Thank you.

Answer 3

[UASLAB]

Dear @Sam Chak,

please, I need help on how to implement Dryden wind model for simulating wind disturbance in Simulink.

Thank you.