Consider a fan to which an electric current is provided as input and the rotational speed of its shaft is the output. Then, if one wants to find the current required to achieve a desired rotational speed, then one is solving the problem of synthesis prediction control modelling

Yes, you are correct. In this scenario, you are dealing with a problem of synthesis prediction control modelling. Here are the steps you would typically follow:

1. System Identification: The first step is to understand the system, i.e., the fan in this case. You need to identify how the input (electric current) affects the output (rotational speed of the shaft). This can be done through experiments or by using physical laws.

2. Model Development: Once you have identified the system, the next step is to develop a mathematical model that describes the relationship between the input and output. This model can be derived from physical laws or from experimental data.

3. Control Design: After the model has been developed, you can design a control system that will adjust the input (electric current) to achieve the desired output (rotational speed). This is typically done by developing a control law or algorithm.

4. Implementation: The final step is to implement the control system. This involves applying the control law or algorithm to the actual system (the fan) and adjusting the input (electric current) based on the control system's instructions.

5. Testing and Validation: After the control system has been implemented, it should be tested to ensure that it is working correctly. This involves providing the system with a desired output (rotational speed) and checking whether the system is able to achieve this output.

In summary, to find the current required to achieve a desired rotational speed, you would need to understand the system, develop a model, design a control system, implement this system, and then test and validate it.