# State-Feedback Controller

Discrete-time state-feedback controller with integral action

• Library:
• Simscape / Power Systems / Simscape Components / Control / General Control

## Description

The State-Feedback Controller block implements a discrete-time state-feedback controller with integral action.

### Equations

The integral of the tracking error, xi, 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.

• xi is the integral of the tracking error.

• xe is the extended state vector.

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.

### Assumptions

System state measurement and estimation occur outside the controller.

## Ports

### Input

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Plant system reference signal.

Data Types: `single` | `double`

Measured or estimated system state vector.

Data Types: `single` | `double`

External reset signal (rising edge) for the integrator.

Data Types: `Boolean`

Plant system output signal.

Data Types: `single` | `double`

### Output

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Control system output signal.

Data Types: `single` | `double`

## Parameters

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Controller feedback matrix. To determine the controller matrix, if you have a license for Control System Toolbox™, use the `lqr` or `lqi` function.

Upper limit for the control output signal.

Lower limit for the control output signal.

Time interval between samples. If the block is inside a triggered subsystem, inherit the sample time by setting this parameter to `-1`. If this block is in a continuous variable-step model, specify the sample time explicitly. For more information, see What Is Sample Time? (Simulink) and Specify Sample Time (Simulink).

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