A controller action in which there is a con-tinous relation between the values of controlled variable and the rate of change of conrolled output signal is called the __________ action.

ANS:B - integral

Integral action, also known as integral control or reset action, is one of the three basic types of control actions used in feedback control systems, alongside proportional and derivative actions. Integral action is designed to eliminate the steady-state error in a control system. Steady-state error occurs when there is a difference between the desired setpoint and the actual output of the system once it has reached a stable condition. This discrepancy can be caused by various factors such as disturbances, nonlinearities, or inaccuracies in the system. The integral action continuously accumulates the error signal over time and uses this accumulated error to adjust the control signal. This accumulation process helps to gradually reduce the steady-state error until it reaches zero. Mathematically, the integral action involves integrating the error signal over time. The integral term in a control algorithm is often represented by ∫ e(t) dt, where e(t) is the error signal at time t. By integrating the error signal, the integral action effectively considers both the magnitude and duration of the error. Integral control is particularly effective in systems where there is a constant disturbance or offset that needs to be corrected. It provides robustness and stability to the control system by continuously adjusting the control signal to maintain the desired setpoint despite external influences. In summary, integral action in a controller ensures that the steady-state error in a control system is minimized by continuously integrating the error signal over time and using the accumulated error to adjust the control signal.