This is a question in Persian related to identifying a system using classical methods, with a specific focus on simulating the system in SIMULINK.

Translation of the text:

Question 1: The goal of this question is to identify a system using classical methods. For each student, a specific system is considered, and a SIMULINK file is provided to conduct the required experiments (applying the input signal and collecting input-output data). The required tasks are:

Part A: Apply a step signal with a unit amplitude to the system (in the SIMULINK environment) and obtain its step response. Use the obtained response to appropriately describe the system's dynamic behavior over time. Determine if the system model is acceptable using the $R^2$ criterion. Verify if the obtained model is acceptable using this criterion.

Approach:

1. SIMULINK Simulation:

   • In SIMULINK, design a system where a step signal (with amplitude 1) is applied to the system under consideration.
   • Obtain the system's response to this step input and observe key features such as settling time, overshoot, steady-state error, etc.

2. System Identification:

   • Analyze the system's behavior by fitting a transfer function model (possibly using methods like least squares).
   • Measure the fit quality using the $R^2$ statistic. A high $R^2$ value (close to 1) would indicate that the model fits well.

3. Verifying Dynamics:

   • You would need to compare the system’s time-domain response (step response) to classical dynamics (like first or second-order systems) to ensure proper system identification.

Tip:

While working on SIMULINK, ensure that you properly configure the simulation time and step size for accurate results, especially when dealing with continuous-time systems.

Let me know if you need assistance with SIMULINK implementation or model identification, or if you'd like details on the $R^2$ criterion.

Related Questions:

1. What are the key characteristics of a system's step response?
2. How can you compute the $R^2$ statistic for a system model?
3. How does a unit step input help in identifying a system's dynamics?
4. What are the typical methods to model system dynamics in SIMULINK?
5. How does one assess overshoot, settling time, and steady-state error in a response?

Tip: When using classical system identification methods, it’s helpful to have a clear understanding of the physical meaning of transfer function parameters (like poles and zeros) and how they affect system behavior.