A robotic surgical system has a robot arm holding an instrument for performing a surgical procedure, and a control system for controlling movement of the arm and its instrument according to user manipulation of a master manipulator. The control system includes a filter in its forward path to attenuate master input commands that may cause instrument tip vibrations, and an inverse filter in a feedback path to the master manipulator configured so as to compensate for delay introduced by the forward path filter. To enhance control, master command and slave joint observers are also inserted in the control system to estimate slave joint position, velocity and acceleration commands using received slave joint position commands and torque feedbacks, and estimate actual slave joint positions, velocities and accelerations using sensed slave joint positions and commanded slave joint motor torques.