# Smith Predictor Controller

• Library:
• Simscape / Electrical / Control / General Control

## Description

The Smith Predictor Controller block compensates for dead time by implementing a Smith dead-time PI control structure in discrete time. This diagram shows the equivalent circuit for the block.

### Equations

The transfer function for a system with dead-time is

`${G}_{f}\left(s\right)={G}_{p}\left(s\right){e}^{-\tau s},$`

where:

• τ is the system dead time.

• Gp(s) is the process model.

• Gf(s) is prediction error filter.

## Ports

### Input

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Plant system reference signal.

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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Proportional gain, Kp, of the PI controller.

Integral gain, Ki, of the PI controller.

Value of the integrator at simulation start time.

Upper limit for the control output signal.

Lower limit for the control output signal.

Numerator of the system discretized transfer function. To determine the discrete transfer function, if you have a license for Control System Toolbox™, use the `c2d` function.

Denominator of the system discretized transfer function. To determine the discrete transfer function, if you have a license for Control System Toolbox, use the `c2d` function.

Number of samples of the dead time.

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? and Specify Sample Time.

## References

[1] Velagic. J. "Design of Smith-like Predictive Controller with Communication with Communication Delay Adaptation."International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering. Vol 2, Number 11, 2008, pp. 2447-2481.

## Version History

Introduced in R2017b