Compensators can be designed to give zero steady-state error in tracking arbitrary periodic or repetitive reference signals. The previously presented technique for design of the compensator has a limited convergence rate for the decay of tracking errors and a limited region of stability. Several alternative design approaches are presented which yield improvements in high-frequency convergence rate while some designs also improve stability. The design approaches are in two classes, designs based on adding periodic correction to an existing controller and total designs for transient and periodic performance. The approaches include FIR and IIR filter design by pole placement and linear quadratic control design.