After you kill the troops / wall defences in a city. you need to do the so-called ''loyalty waves''. What is that? you keep attacking the guy to get loyalty down to the 15 by this. Then once the city your hitting reaches 15loyalty you stop the constant hitting, instead your gonna hit him once every 6minutes as after 15loyalty it take public grievance to get loyalty further down and that will only go down by 1 every 6mins and by that 1 hit every6 mins you keep public grievance high enough to drop that 1 point every 6 mins...

Hope this helped you ; )

Cheers