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How is the mathematical model of the control system obtained?
The mathematical model of the control system depends on the objective function and constraints of the system.

The objective function refers to the functional relationship between the concerned objective (a variable) and related factors (some variables). Simply put, it is the function you get after solving it. The function is unknown before the solution. According to your idea, using known conditions to solve the functional relationship of unknown quantity is the objective function.

When solving some linear programming problems, the known preconditions of this problem are called constraints.