Final answer:
A PID controller can be tailored to meet the design requirements of zero steady-state error and a settling time of less than 0.4 seconds for a DC motor with the given parameters. The design starts with a reduced model and is then verified using the full model, ensuring performance adherence to the inductive effects in real scenarios.
Step-by-step explanation:
To design a suitable position control for a DC motor that guarantees zero steady-state error and a settling time of no more than 0.4 seconds, a common approach is to use a proportional-integral-derivative (PID) controller. Given the parameters K = 0.1, R = 1, L = 1mH, B = 0.001 N.m. sec/rad, J = 0.001 N.m.sec²/rad, the reduced model of the motor will be used initially for simplicity during design since it ignores the inductance L, which is small and causes the system to have a faster response.
The transfer function of the reduced motor model can be derived from the motor's electrical and mechanical equations. Assuming a unity feedback system, the PID controller will be designed such that the closed-loop transfer function meets the given performance specifications. A root locus or frequency response method can be used to tune PID parameters until the desired specifications are met. Afterward, the performance of the controller must be tested against the full model including inductance L to ensure the design is adequate.
Moreover, since a zero steady-state error is required, the integral part of the PID ensures the error integral over time is minimized to zero. The settling time requirement will also dictate the speed at which the controller must respond to changes, influencing the proportional and derivative terms of the PID controller.