Motor Position Control for Master-Slave Robotic System

I am trying to design a master-slave robotic system, in which a slave robot mimics the motion of a master arm. The position control of the slave needs to be designed such that it follows a constantly changing desired position function, that comes from the master. PID would be the obvious choice for position control but it can not compensate for the rapid change in setpoint values. How can i tune the PID to make it better at this or what other options do I have?
PS - First-time poster so please forgive any formatting mistakes. Thanks