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What are the limitations of using transfer function as mathematical model?
Solution:

1. Different from the structure diagram, it can be used for nonlinear systems, and the transfer function is limited to linear time-invariant systems.

2. It is suitable for SISO system description, that is, MIMO (MIMO system is not applicable).

3. If the initial condition of the system is not 0, it is not applicable, because from differential equation to transfer function, zero initial state is needed.

4. It can only reflect the external characteristics of the system, and the internal state of the specific system is opaque.

Therefore, nonlinear systems and state space analysis methods are explained in the textbook of automatic control principle.

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