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.