the simple control law u=theta_1*y_p+theta_2*r and tuning law theta_1'=-gamma1*sign(b_p)*e*y_p theta_2'=-gamma2*sign(b_p)*e*r
to make the plant
y_p'=a_p*y_p+b_p*u
to track the output of refrence model y_m'=-4*y_m+4*r
where e=y_p-y_m
It is already shown that when r is a constant, there will be infinite pairs of ultimate values of theta1 and theta2; while r=sin(3*t), the ultimate values of theta1 and theta2 must be fixed.
However, anybody knows is there any difference in the tracking performance when r is different. I find when r=sin(3*t), it takes less time for e to converge to zero. Am I right?