Sensitivity (control systems)

The controller parameters are typically matched to the process characteristics and since the process may change, it is important that the controller parameters are chosen in such a way that the closed loop system is not sensitive to variations in process dynamics. One way to characterize sensitivity is through the nominal sensitivity peak M s {displaystyle M_{s}} : The controller parameters are typically matched to the process characteristics and since the process may change, it is important that the controller parameters are chosen in such a way that the closed loop system is not sensitive to variations in process dynamics. One way to characterize sensitivity is through the nominal sensitivity peak M s {displaystyle M_{s}} : M s = max 0 ≤ ω < ∞ | S ( j ω ) | = max 0 ≤ ω < ∞ | 1 1 + G ( j ω ) C ( j ω ) | {displaystyle M_{s}=max _{0leq omega <infty }left|S(jomega ) ight|=max _{0leq omega <infty }left|{frac {1}{1+G(jomega )C(jomega )}} ight|} where G ( s ) {displaystyle G(s)} and C ( s ) {displaystyle C(s)} denote the plant and controller's transfer function in a basic closed loop control system using unity negative feedback. The sensitivity function S {displaystyle S} , which appears in the above formula also describes the transfer function from external disturbance to process output. In fact, assuming an additive disturbance n after the output