PD controller
Student should aim for Kp and Kd value that will minimize the steady error with improved rise time and settling time. The amount of over shoot should not be more than the uncompensated system.
PI controller
Student should aim for Kp and Ki value that will provide zero steady state error with a faster rise time. If overshoot and oscillation cannot be avoided the Kp and Ki should be chosen such that the time constant of the decay and overshoot magnitude is close to the uncompensated system.
PID controller
For the PID controller the values chosen should be based on the experience provided by the PI and PD controller and should provide the best response compare to PI and PD controller. The K values should be chosen such that the system has zero steady state error, faster risetime than the original system. The amount of over shoot should be no more than the uncompensated system (zero if possible).