how can I get a model from system identification toolbox for three tank system

I want to get different models for three tank system imagining that it is a blackbox system as input we have 2 step signals which represent 2 waterflows to thtee tank system and h1 h2 h3 are the heights of the system which are out put of the system . my question is how i should apply these parameters to toolbox system identification to get the models . the problem is the input is signal which is time domain and h1 h2 h3 are 3 different value it means 3 outputs in the same time how i must apply the data to get models ?

Answer 1

[Shubham]

Hi Tannaz,

To model a three-tank system as a black-box system using the System Identification Toolbox in MATLAB, you need to prepare your input-output data properly and then use the toolbox to estimate a model that fits your data. Here's a step-by-step guide on how to achieve this:

Step 1: Prepare Your Data

1. You have two input signals representing water flows into the system. These should be organized as a matrix where each column represents a different input signal.
2. You have three output signals representing the heights ( h_1, h_2, ) and ( h_3 ). These should also be organized as a matrix where each column represents a different output signal.
3. Ensure you have a time vector that corresponds to your input and output data. This is especially important if your data is not sampled at regular intervals.

Here's a basic example of how your data might be structured in MATLAB:

% Example data
time = (0:0.1:10)'; % Time vector
u1 = stepfun(time, 2); % Example step input 1
u2 = stepfun(time, 5); % Example step input 2
h1 = rand(length(time), 1); % Example output 1
h2 = rand(length(time), 1); % Example output 2
h3 = rand(length(time), 1); % Example output 3

% Input matrix
U = [u1, u2];

% Output matrix
Y = [h1, h2, h3];

Step 2: Create an iddata Object

The iddata object in MATLAB is used to store input-output data for system identification.

% Create iddata object
data = iddata(Y, U, 0.1); % 0.1 is the sample time

Step 3: Choose a Model Structure

You can choose from several model structures, such as:

• ARX (AutoRegressive with eXogenous inputs): Simple and fast to estimate.
• State-Space Models: More flexible and can handle multiple inputs and outputs.
• Transfer Function Models: Useful if you have some insight into the system dynamics.
• For a multi-input multi-output (MIMO) system like yours, state-space models are often a good choice.

Step 4: Estimate the Model

Use the ssest function to estimate a state-space model:

% Estimate a state-space model
model = ssest(data, 3); % The number 3 is an initial guess for the number of states

Step 5: Validate the Model

After estimating the model, validate it by comparing the model's output to the measured data:

% Compare the model output to the actual data
compare(data, model);

Step 6: Refine the Model

• Adjust Model Order: If the model doesn't fit well, try adjusting the model order (number of states).
• Try Different Structures: Experiment with different model types (e.g., ARX, transfer function) to see which fits best.
• Cross-Validation: Use a portion of your data for validation to ensure the model generalizes well.