(a) For the project topic that you have selected, design a model reference adaptive controller with an adaptation law based upon the "MIT rule", and evaluate and discuss its performance and stability through simulation studies.

(b) Repeat the model reference adaptive controller design in part (a), but now based upon stability methods (e.g, Lyapunov, SPR), and evaluate and discuss its performance and stability through simulation studies.

For a frictionless servo, consider the plant and reference model transfer functions:

G(s) = Y(s)/U(s) = (1/Js); and Gm(s) = Ym(s)/R(s) = (1/(s+1))

The J is an unknown inertia, y is the output velocity, u is the control input, and r is the reference input. The subscript m refers to the reference model, and the controller (proportional) is given by:

u = K(r-y)

(a) Use Lyapunov theory to design a model reference adaptive controller, that adapts the controller gain K.

(b) Let r be a constant reference, and investigate what happens to the adaptive controller from part (a) in the presence of a load disturbance input v at the input to the plant, i.e.,

dy/dt = (u + v)/J

Problem 6.1 from your textbook

Problem 6.3 from your textbook

Problem 6.10 from your textbook