Smith Predictor Controller

Discrete-time Smith dead-time compensator

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Libraries:
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

$G_f\left(s\right)=G_p(s)e^{-\tau s},$

where:

• τ is the system dead time.

• G_p(s) is the process model.

• G_f(s) is prediction error filter.

Examples

DC Motor Control (Smith Predictor)

A Smith Predictor speed-control structure for a DC motor. A PWM controlled four-quadrant Chopper is used to feed the DC motor. The Control subsystem includes the Smith predictor controller, and the PWM generation. A sensor measures the rotor speed with a delay of 5ms. The total simulation time (t) is 4 seconds. At t = 1.5 seconds, the load torque increases. At t = 2.5 seconds, the reference speed is changed from 1000 rpm to 2000 rpm.

• Open Model

Ports

Input

r — Plant reference

scalar

Plant system reference signal.

Data Types: single | double

Reset — Integrator reset

scalar

External reset signal (rising edge) for the integrator.

Data Types: Boolean

y — Plant output

scalar

Plant system output signal.

Data Types: single | double

Output

u — Controller output

scalar

Control system output signal.

Data Types: single | double

Parameters

Proportional gain — K_p

1 (default) | positive scalar

Proportional gain, K_p, of the PI controller.

Integral gain — K_i

1 (default) | positive scalar

Integral gain, K_i, of the PI controller.

Integrator initial condition — Initial integrator value

0 (default) | scalar

Value of the integrator at simulation start time.

Control action upper limit — u_max

5 (default) | scalar greater than the value of the Control action lower limit parameter

Upper limit for the control output signal.

Control action lower limit — u_min

0 (default) | scalar

Lower limit for the control output signal.

Model discrete transfer function numerator — Transfer function numerator

1 (default) | scalar or vector

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.

Model discrete transfer function denominator — Transfer function denominator

[1 0.5] (default) | vector

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.

System dead time (samples) — Number of dead-time samples

2 (default) | 0 or a positive integer

Number of samples of the dead time.

Sample time (-1 for inherited) — Sampling interval

-1 (default) | default value or a positive number

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017b