Create a function block at the command line

Hi @Hisham Hussein ,

To address your query regarding, “Actually, I want to create my whole system model and work only in the command line. I don’t want to work in Simulink at all. The who system model is a 2 input, 1 output system. The plant model looks as in the following: sqrt(u2/u1), Where u1 is the first input/output TF, u2 is the measured disturbance from the 2nd input/output TF. My problem is that I don’t know how to express the plant model in the command line ( I need to run my simulation only in the command line and No simulink). I have attached the system model how it looks”

Please see my response to your comments below.

To model the described system labeled as “IMG_1602.jpeg” shared by you in MATLAB's command line, you will need to define the various components using MATLAB's built-in functions for control systems and signal processing. Below is a step-by-step breakdown of how to express your system model:

Define the Transfer Functions

First, you need to represent the first and second-order transfer functions as well as the PID controller. Here is how you can define them in MATLAB:

   s = tf('s'); % Define s as a transfer function variable
   tau1 = 1; % Example time constant for G1
   G1 = 1 / (tau1 * s + 1); % First-order transfer function
   omega_n = 1; % Natural frequency for G2
   zeta = 0.5; % Damping ratio
   G2 = (omega_n^2) / (s^2 + 2*zeta*omega_n*s + omega_n^2); % 
   Second-order transfer function
   Kp = 1; Ki = 1; Kd = 1; % PID gains
   PID = Kp + Ki/s + Kd*s; % PID controller

Summation and Feedback Implementation

Then, you can implement the summation block and feedback connections using MATLAB functions. For instance, you may use the feedback function to incorporate the feedback from the manipulated variable u1 into the summation.

     % Define the sum block (assuming subtraction for feedback)
     feedback_signal = feedback(G1 * PID, 1); % Feedback loop

For more information on “feedback” function, please refer to

https://www.mathworks.com/help/control/ref/inputoutputmodel.feedback.html?s_tid=doc_ta

Plant Model Definition

The plant model can be implemented using a function that calculates the square root of the ratio of outputs from the two transfer functions. Here’s how you might express this:

     % Define u1 as the output from G1 and u2 as the output from G2
     u1 = G1 * PID; % Output from the first input
     u2 = G2; % Output from the second input

     % Implement the plant model
     plant_model = @(u1, u2) sqrt(u2 / u1);

Simulation Setup

Use a time vector and simulate the step response using the lsim function, which allows you to simulate the system's response to various inputs over time.

   t = 0:0.01:10; % Time vector
   step_input = ones(size(t)); % Step input for the simulation

   % Simulate the system response
   [y, t] = lsim(feedback_signal, step_input, t); % Response to 
   step input

For more information on “lsim” function, please refer to

https://www.mathworks.com/help/control/ref/dynamicsystem.lsim.html?s_tid=doc_ta

Visualize the Output

Finally, you can plot the output to analyze the system's response.

   figure;
   plot(t, y);
   title('System Response');
   xlabel('Time (seconds)');
   ylabel('Output y');
   grid on;

Please see attached.

After simulating the system, you might want to tune the PID parameters for optimal performance, which can be done using various techniques, including Ziegler-Nichols or software tools like pidTuner. I would advise to validate your model against known responses or benchmarks to ensure accuracy. By following this structured approach, you can successfully model and simulate your control system entirely through the MATLAB command line, achieving the desired functionality without relying on Simulink.

Please let me know if following above mentioned steps resolved your problem.