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| Vectorized | |
| in the palette | on the schematic |
The block implements a mathematical model of an adaptive regulator with a reference model.
The block is a submodel, the structural diagram of which as part of the closed-loop system is shown in the figure (Figure 1):
Рисунок 1. Structural diagram of a closed-loop system and an adaptive regulator with a reference model.
The output signal of the PID controller with saturation compensation is:
- if D-term filtering is not used, then:
- if D-term filtering is used, then:where Kp, Ki, Kd are the gains of the proportional, integrating and differentiating terms of the regulator, respectively, T is the sampling period, Tdif is the derivative time constant, e is the error signal, k is the simulation step number.
The reference model reflects the desired behavior of the closed-loop system. The transfer function of the reference model is as follows: 
where N(z), L(z) are the polynomials of the numerator and denominator of the transfer function, determined by the coefficients ai, b i (i = 0..n, j = 0..m, n ≥ m, an ≠ 0).
The regulator corrects the control action based on the error between the output data of the control object and the output data of the reference model: 
where y is the output of the control object, ym is the output of the reference model, γ is the learning rate coefficient, an increase in the value of which leads to a faster adaptation of the model to changes.
The control corrected output signal is: 
Input ports
- ref in – setting action signal;
- feedback – feedback signal.
Output ports
- out – controlling action signal.
Properties
- Discrete PID controller with saturation compensation
- Sampling period – block calculation sampling period;
- Initial conditions – vector of initial values yi(0) of the block output quantity;
- Proportional term – gain value of the P-term;
- Integral term – gain value of the I-term;
- Differential term – the value of the gain of the D-term;
- Use D-term filtering – checkbox (flag) that includes additional D-component settings;
- Derivative time constant – the property is available if the "Use D-term filtering" item is activated;
- Linear with saturation
- Minimum value – the minimum value of the output;
- Maximum value – maximum output value;
- Feedback gain – scalar multiplier for the input value;
- Reference model
- Numerator coefficients – vector b, dimension [m];
- Denominator coefficients – vector a, dimension [n];
- Initial conditions – vector of initial values yi(0) of the block output quantity;
- Learning rate coefficient – a real number, the speed coefficient of adaptation to changes in the control object.
Parameters
None
