MIT rule predicts the controller parameters as given in the below equation:

, where γ is design parameter (It is going to be called "gamma" for the rest of this tutorial), e is the error between the output of the plant and the output of the reference model, and finally the last term (It is going to be called "sens" for the rest of the tutorial) is called the sensitivity derivative. MIT rule predicts the controller parameters by comparing the output of the plant and a reference model whose behavior MIT rule is imposing on the plant. The output of the plant, suspended pendulum is taken as the linear combination of the angular position and velocity. Hence

MIT rule of Model reference adaptive control implies

  where k₁, k₂, and k₃ are controller parameters that are going to be predicted by the MRAC MIT rule. k₁ is the gain on the command, k₂ and k₃ are the output feedback gains.

The equations of motion of the suspended compound pendulum is:

This gives us the following equation:

Applying the MRAC (MIT rule) to the system given by the above equation, following is obtained:

k₁, k₂ and k₃ must be adapted with the following equation:

.