In trigonometric function, the point where the second derivative takes zero value is the zero point of trigonometric function.
For example, the research object is a temperature control system. We have an ideal temperature x and an actual temperature y, both of which are functions of time t, and xy satisfies some differential equation. If a controller can be set to make the relationship between X and Y closer to our needs, then ensuring the stability of this controller is the premise.
For example, the indoor temperature is Y, the set temperature of air conditioner is X, and xy is a function of time T, which satisfies a certain differential equation. Now we need to control the refrigeration and heating system of air conditioner, so that Y can approach X faster in a shorter time or the air conditioner is the most energy-saving.
First of all, we must ensure the stability of this control system, especially for this kind of system with time delay. The unstable situation is this: if the indoor temperature is 35 degrees, the set temperature is 26 degrees.
If the model is unstable, it may be supercooled to 23 degrees, then heated to 30 degrees, then cooled to 23 degrees, then heated to 30 degrees, and continue to work indefinitely. This is critical stability. Even in the case of absolute instability, the temperature fluctuation is farther and farther away from the equilibrium position of 26 degrees.
Extended data
Equilibrium points can be divided into stable equilibrium points and unstable equilibrium points. The stable equilibrium point is the point where chestnuts will oscillate near the equilibrium point after small disturbance, and the unstable equilibrium point is the point where small disturbance will destroy the equilibrium state.
Take cosx as an example, its potential energy is -sinx, which is a potential field with peaks and valleys. The valley is a stable equilibrium point, and the peak is an unstable equilibrium point.