Question

A unity negative feedback control system has the process transfer function 1 G(s) = 1/ s(s+3)(8 +6) Your task is to design a lag compensation Gc(s) = s+z/s+n to meet the following specifications:

• The step response 2% settling time is to be at most 5 sec
• The step response overshoot is to be at most 17%.
• The steady-state error to a unit ramp input must not exceed 10%.

Answer 1

To design a lag compensation for the unity negative feedback control system, we need to consider the settling time, overshoot, and steady-state error. By following specific guidelines, we can design the lag compensation.

Step-by-step explanation:

To design a lag compensation for a unity negative feedback control system, we need to find values for the parameters n and z in the transfer function Gc(s) = (s+z)/(s+n). To meet the given specifications, we can use the following guidelines:

1. To ensure 2% settling time is at most 5 sec, we need to choose values of n and z that result in a dominant pole with a time constant less than 5/4.
2. To limit step response overshoot to 17%, the damping ratio of the dominant pole should be around 0.45.
3. To ensure the steady-state error to a unit ramp input does not exceed 10%, we need to choose values of n and z that result in a gain of at least 10.

By following these guidelines, we can design a suitable lag compensation for the given control system.