This record defines a discrete transfer function by its zeros, poles and a gain:

product(q - z[i]) y = k*------------------- * u product(q - n[i])

where z[:] is a Complex vector of zeros, n[:] is a Complex vector of poles and k is an additional multiplicative factor. The elements of the two Complex vectors must either be real numbers or conjugate complex pairs (in order that their product results in a polynomial with Real coefficients).

In the record, the zeros and poles are transformed into a product of first and second order polynomials.

A DiscreteZeroAndPole transfer function is internally stored by the coefficients of first and second order polynomials, and by an additional multiplicative factor k:

product(q + n1[i]) * product(q^2 + n2[i,1]*q + n2[i,2]) y = k*--------------------------------------------------------- product(q + d1[i]) * product(q^2 + d2[i,1]*q + d2[i,2])

Note, the degrees of the numerator and denominator polynomials are given as:

degree of numerator = size(n1,1) + 2*size(n2,1); degree of denominator = size(d1,1) + 2*size(d2,1);

Example:

(q+0.5) dzp = 4* ------------------------------------- (p - 0.5)*(p - (0.6+j*0.3))*(p - (0.6-j*0.3))

with j = Complex.j(); is defined as

importModelica_LinearSystems2.Math.Complex;importModelica_LinearSystems2.DiscreteZerosAndPoles; j = Complex.j(); dzp = ZerosAndPoles(z = {Complex(-0.5)}, p = {Complex(0.5), 0.6+j*0.3, 0.6-j*0.3}, k=4);

Name | Description |
---|---|

'constructor' | Collection of operators to construct a DiscreteZerosAndPoles data record |

'-' | Contains operators for subtraction of discrete zeros and poles descriptions |

'*' | Contains operators for multiplication of discrete zeros and poles records |

'+' | Addition of to discrete transfer functions dzp1 + dzp2, i.e. parallel connection of two transfer functions (= inputs are the same, outputs of the two systems are added) |

'/' | Divide two discrete transfer functions in zeros and poles representation (dzp1 / dzp2) |

'^' | Integer power of DiscreteZerosAndPoles (dzp^k) |

'==' | Check whether two discreteZerosAndPoles transfer functions are identical |

'String' | Transform DiscreteZerosAndPoles transfer function into a String representation |

q | Generate the DiscreteZerosAndPoles transfer function q |

Analysis | Package of functions to analyse discrete zeros-and-poles description represented by a DiscreteZerosAndPoles record |

Design | Package of functions to design discrete zeros-and-poles controllers and observers |

Plot | Package of functions to plot discrete zeros and poles description responses |

Conversion | Package of functions for conversion of DiscreteZerosAndPoles data record |

Import | Package of functions to generate a DiscreteZerosAndPoles data record from imported data |

Internal | Package of internal material of record DiscreteZerosAndPoles (for advanced users only) |

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