How to evaluate a close-loop control during transient?
In order to evaluate the performance of a controller during transients, you can use different metrics. Two metrics you could use are

ITAE= $$\int_0^{\infty} t*|e| \,dt$$ 

ITSE = $$\int_0^{\infty} t*e^2 \,dt$$ 

where e is the difference between your reference and the measurement and t is the time since the reference change.

Basically, you want to minimize these metrics. The basic idea is that an error in the beginning won't impact the metric much while an error 1 second after the reference change will impact your metric much more.

There are probably other metrics you could use. You could also use stabilization time at 1% or 5%.

Edit : If your signal is cyclical you could limit the integral upper bound to a limited number of 2-Hz cycles.

ITAE= $$\int_0^{NT} t*|e| \,dt$$ 

ITSE = $$\int_0^{NT} t*e^2 \,dt$$ 

where N is a whole number and T is the period of your reference signal.