Hi,
An Operating Point of a dynamic system is the states and the inputs of the system at the specific time. It does not indicate the behaviour of the system at a specific time, rather it just indicates the states of the system at that time instant.While linearizing a plant, the operating point which we specify can be an ‘equilibrium point’ or ‘non-equilibrium point’.
- If we specify an equilibrium point, we can analyze and draw conclusions about the local stability of the system. If this linearized system is stable at that equilibrium, then there exists a neighbourhood around that point where the non linear system is also stable.
- If we specify non-equilibrium point, then we can’t draw the above conclusions as such.
If you linearize the plant for inverted pendulum at an ‘equilibrium point’, then you can perform stability analysis and controller design on the Linearized model. This analysis and design would also be valid on the non-linear plant around a small neighbourhood of that equilibrium point.
An equilibrium point is a solution to dynamical system where the states of the system do not change with time. It is a constant solution to a differential equation/ dynamical system.
Please refer to the following documentation for more details regarding the operating points;
- https://in.mathworks.com/help/slcontrol/ug/linearizing-nonlinear-models.html
- https://in.mathworks.com/help/slcontrol/steady-state-operating-points.html
- https://in.mathworks.com/help/slcontrol/ug/what-is-an-operating-point.html
I hope this is helpful.
