Sensitivity (control systems)

The controller parameter 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 $M_{s}$ :

$M_{s}=\max _{0\leq \omega <\infty }|S(j\omega )|=\max _{0\leq \omega <\infty }|{\frac {1}{1+G(s)C(s)}}|,$

where $G(s)$ and $C(s)$ denote the plant and controller's transfer function in a basic closed loop control System, using unity negative feedback. The quantity $M_{s}$ is the inverse of the shortest distance from the Nyquist curve of the loop transfer function to the critical point $-1$.

The sensitivity function $S$, which appears in the above formula also describes the transfer function from measurement noise to process output, where measurement noise is fed into the system through the feedback. Hence, lower values of $|S|$ suggest further attenuation of the measurement noise.

A basic closed loop control System, using unity negative feedback. C(s) and G(s) denote compensator and plant transfer functions, respectively.

It is important that the largest value of the sensitivity function be limited for a control system and it is common to require that the maximum value of the sensitivity function, $M_{s}$, be in a range of 1.3 to 2.

See also

• Control theory
• Control engineering
• Robust control
• PID controller