Refer to "Phase-Locked Loops/Roland E. Best", Chapter 4: Higher Order Loops.
The main problem - stability of the loop. You should choose the proper phase margin at the transit frequency ωT. The phase margin is correlated with damping factor in the second-order systems. What about the third-order PLLs, I can't say, maybe there is no such concept in these systems. Instead the phase margin is used. (see Figure 4.1 in the book).
Refer to "Phase-Locked Loops/Roland E. Best", Chapter 4: Higher Order Loops.
The main problem - stability of the loop. You should choose the proper phase margin at the transit frequency ωT. The phase margin is correlated with damping factor in the second-order systems. What about the third-order PLLs, I can't say, maybe there is no such concept in these systems. Instead the phase margin is used. (see Figure 4.1 in the book).