Discrete-time state-feedback controller with integral action

**Library:**Simscape / Electrical / Control / General Control

The State-Feedback Controller block implements a discrete-time state-feedback controller with integral action. Use this block to control linear systems with single or multiple inputs and single or multiple outputs. The integral action serves to eliminate steady-state error in the controlled outputs. You can define the controller using a precomputed optimal gain or use the state-space model of your system to generate this gain using pole placement.

The integral of the tracking error, *x _{i}*,
is an additional state that ensures zero steady-state error for the closed-loop
system. The extended state vector is

${x}_{e}=\left[\begin{array}{c}x\\ {x}_{i}\end{array}\right],$

Where:

*x*is the state vector.*x*is the integral of the tracking error._{i}*x*is the extended state vector._{e}

Therefore, the control action is

$u=K{x}_{e},$

Where:

*K*is the feedback matrix, that is, the pole placement.*u*is the controller output.

System state measurement and estimation occur outside the controller.