In this publication, parameter sets for PID controllers are presented, which can be used to control systems with time-delayed stable step responses. These parameter sets minimize the quality criteria in the time domain, IAE, ITAE and ISE. They also take into account the controller output limitation, which is relevant in practice. The parameter sets are scalable with the time constant and the static gain of the system. Therefore they can be used to control all systems with a time delay behavior.