- Linear algebra review (6 hours).
Linear Algebra: Calculation of the Inverse Matrix. Definition of the exponential of a matrix.
- Representation of dynamic systems (12 hours).
Dynamic systems and mathematical models. Input and output variables. Algebraic systems and dynamic systems. State variables. Representation in the state-space form. Linear and non-linear systems, time-variant and time-invariant, SISO and MIMO. Equilibrium state and output. Stability of an equilibrium state. Linearization of non-linear systems around a state of equilibrium.
- Time domain analysis of linear time-invariant systems (LTI), discrete time and continuous time (22 hours).
Representation of LTI systems. Equivalent representations. Superposition principle. Free evolution and forced evolution. Free evolution modes. Dominant modes. Calculation of forced response to impulse and step. Parameters of the step response. Steady-state response and transient response. Stability of LTI systems. Routh's criterion.
- Analysis in the Laplace domain of LTI systems with continuous time (16 hours).
The Laplace transform: definition and main properties. Inverse Laplace transform. Definition of transfer function. Zeros and poles. Calculation of the evolution of an LTI system in the Laplace domain. From the transfer function representation to an i-s-u representation. Block diagrams. Series connections, parallel and feedback.
- Analysis in the frequency domain of LTI systems with continuous time (16 hours).
The harmonic response function and its interpretation. Steady-state response to sinusoidal signals. Filtering action of dynamic systems. Bode diagrams: asymptotic diagrams and corrections. Main parameters of the harmonic response.
- Use of scientific software such as Matlab or Octave for the analysis of dynamic systems (24 hours).
Brief introduction to Matlab / Octave. Main commands for the manipulation of vectors and matrices. Main graphic commands. Analysis of LTI systems with the aid of Matlab / Octave.