If you have a sensor with a constant bias you can integrate that as another state in an expanded state-space model. The constant sensor bias can be denoted by (). It is then added to the existing states and matrices to create a new system
\dot{x} \\ \dot{b} \end{bmatrix}= \begin{bmatrix} A & 0 \\0 & 0 \end{bmatrix} \begin{bmatrix} x \\ b \end{bmatrix}+ \begin{bmatrix} B \\ 0 \end{bmatrix}u$$ The sensor bias model adds a pure integrator at the origin. Adding a sensor bias increases the order of the system by 1. In some cases the sensor bias might not always be observable. You need an unbiased measurement of the integral of a biased sensor to estimate the sensor bias. [[Tachometer]] - Biased sensor measurement. [[Superaugmentation Architecture]] - $1/\Big(\hat{T}_{\theta_2}s+1\Big)\int Uq\ dt,\ G_{wo}q\rightarrow \delta_e$ mechanization removes accelerometer bias issues [[A320 Lateral Control Law]] - shows sensor/actuator lags added to a basic state-space plant model #bevlyMECH4420Lectureb