Question

Given that the derivative gain kv=5 , find the proportional gain kp (up to two decimal places) such that the rise time is less than 1s and overshoot less than 5%​

a) (kₚ = 1.50)
b) (kₚ = 2.00)
c) (kₚ = 2.50)
d) (kₚ = 3.00)

Answer 1

Without a specific system type or transfer function, it is impossible to provide a correct value of the proportional gain kp that would achieve the desired rise time and overshoot characteristics with the given derivative gain kv = 5.

Step-by-step explanation:

The question is asking to determine the proportional gain kp in a control system with a derivative gain kv = 5 such that the system has a rise time of less than 1 second and an overshoot of less than 5%. This problem involves understanding control system dynamics and using the given specifications to find a suitable kp value. Typically, this would involve using the transfer function of the system and applying standard control theory methods such as damping ratio and natural frequency to meet the design criteria for rise time and overshoot. However, without further information on the type of system or its transfer function, providing an accurate value for kp is not possible. To give an explicit answer, the characteristics of the system and its mathematical model are necessary.