In a homeostatic control system, when a variable is not changing, but energy must be added continuously to maintain this variable constant, it is called:

Steady state

Explanation:

Steady-state refers to the nonequilibrium state of any system. The system in the steady-state exhibits flow of matter and maintains a constant concentration of all the components.

Given that the system under study maintains the variable constant, the system is in steady-state. To maintain the variable constant, the system in the steady-state spends energy.

For example, the blood glucose level remains nearly constant since the rate of its synthesis and consumption balances each other. These metabolic processes require input of energy.

true, i don't really know what you're asking but from the info you provided im guessing the answer is true.