Smith predictor

| Vectorized |
in the palette on the schematic

The block implements a mathematical model of the Smith predictor.

Smith predictor shown in figure (Figure 1) consists of a main regulator and a predictor structure. The predictor part consists of a no-delay object model and a delay model.


Figure 1. Structural diagram of the closed-loop system with Smith predictor.

The output signal of the PI controller (port out of the block) is applied to the control object and to the internal model of the controller. The PI controller primarily controls the model, rather than the control object, through the summator. The signal g must match the measured signal of the regulated variable y. The y and g signals are compared to produce an error signal that includes errors from both the interference and the model. They are added to the v signal from the object model to feed the feedback signal to the PI controller block.

The transfer function of the system has the form:

where WO, WPI(z), WMO(z) are the transfer functions of the control object, PI controller and object model, respectively.

Input ports

  • ref in – setting action signal;
  • feedback – feedback signal.

Output ports

  • out – controlling action signal.

Properties

  • PI controller with a limitation
    • Proportional term – gain value of the P-term;
    • Integral term – gain value of the I-term;
    • Sampling period – block calculation sampling period;
    • Linear with saturation
      • Minimum value – the minimum value of the output;
      • Maximum value – maximum output value;
  • Object model transfer function
    • Numerator coefficients – vector b, dimension [mb];
    • Denominator coefficients – vector a, dimension [ma];
    • Initial conditions – vector of initial values yi(0) of the block output quantity;
  • Delay degree for the sampling period is the value of the degree of delay n.

Parameters

None