The same plant was controlled by the following controllers P

The same plant was controlled by the following controllers P, PD, PI, PID. In all cases the tuning controllers was carefully adjusted considering the following criteria:
1-The error of the regime to step is the smallest possible
2-The smallest possible overshoot
3- gain not too high to prevent the situation of output controllers

Figure 6.41 presents response y (t) to unit steps applied in reference systems in closed loop with each of the controllers. Join the graphics to the corresponding controllers and justify your choice.

Solution

Figure (a) represent response of a PID controller, because improvement in transient and steady state.

Figure (b),here steady state response improved, hence PI controller

Figure(C), improvement is only in transient response ,hence PD controller

Figure(d) is P controller