Method 1 . Using Step Response and Delay Time and Time Constant Parameters.
Method 2 . Using proportional controller action only. you should find critical gain and corresponding critical period.
all results come in 2 different output shape.
1- Controller with (Kp - Ti - Td)
2- Controller with (Kp - Ki - Kd)
These methods aimed at obtaining 25% maximum overshoot in step response.
>>> So the Z-N method just makes an initial PID Controller coefficients.
for a better controller you have to optimize the coefficient using many existing methods.