Au - Automatic Control Systems Library

Home page and software specification

Repository

Crate registry

Documentation

State-Space representation

Creation of state-space of a linear, time indepentdent system throught the four matrices A, B, C, D.
Calculate the poles of the system.
Calculate the equiliblium point (both state and output) of the system from the given input.

System time evolution

Time response with explicit Runge-Kutta order 2 method with fixed step.
Time response with explicit Runge-Kutta order 4 method with fixed step.
Time response with explicit Runge-Kutta-Fehlberg order 4 and 5 method with adaptive step.
Time response with implicit Radau order 3 method with fixed step.

Discrete time system

Time evolution of a discrete linear system.
Discretization of a continuous linear system using forward Euler, backward Euler and Tustin methods.
Discretization of transfer functions using forward Euler, backward Euler and Tustin methods.

Transfer function representation

Sigle Input Single Output (SISO)

Creation of a single transfer function give a polynomial numerator and denominator.
Calculate the (complex) poles and (complex) zeros of the function.
Evaluation of the transfer function at the given input.

Multiple Input Multiple Output (MIMO)

Creation of a matrix of transfer functions, given a matrix of polynomials and the characteristic polynomial.
Evaluation of the matrix at the given vector of inputs.
(Mutable) Indexing of the matrix elements numerators.

Conversion between representations

SISO state-space -> transfer function
MIMO state-space -> matrix of transfer functions
Transfer function -> state-space (observable form)

Plots

Bode

Calculate the magnitude and phase for a single transfer function in an interval of frequencies.

Polar

Polar plot of a transfer function.

Root locus

Change the root of a system with the variation of the feedback gain.

Controllers

PID (Proportional-integral-derivative) controller, both ideal and real.

Polynomials

Polynomial creation from coefficients or roots.
Polynomial evaluation with Horner method.
(Mutable) Indexing of polynomial coefficients.
Polynomials addition, subtraction and multiplication.
Polynomials multiplication with fast fourier transform.
Polynomial and scalar addition, subtraction, multiplication and division.
Polynomial roots finding (real and complex).
Creation of a matrix of polynomials.

Examples

Examples of library usage can be found in the examples/ folder.