1) In general there are two situation in which compensation is required.
2) In 1st case, the system is absolutely unstable & the compensation is required to stabilize, if as well as to achieve a specified performance.
3) In 2nd case the system is stable, but the compensation is required to obtain the desired performance.
4) The system which are type 2 or higher are usually absolutely unstable, for these type of system clearly load compensator increase the margin of stability.
5) In type 0, type 1 system stable operation is always possible, if the gain if sufficiently reduced. In Such cases any of the 3 compensator lead, lag and Lead lag may be used to obtained the desired performance.