Solution:The value of Kₚ, the proportional gain, in different controllers helps in adjusting the control system's response.
(a) For a simple proportional controller, Kₚ might be given by T/L, where T and L are constants associated with the system dynamics.
(b) In a Proportional-Integral (PI) controller, the Kₚ may often be slightly modified to account for the integral action. The given value suggests Kₚ = 0.9 T/L.
(d) PID controllers, incorporating proportional, integral, and derivative actions, might have another value for Kₚ. Here, Kₚ = 1.2 T/L is given.
Tuning these constants appropriately ensures optimal performance of control systems in various applications, from industrial systems to home appliances.