AUTOMATIC CONTROL A

1) Fundamental concepts: systems and mathematical models. Block diagrams. Feedforward and feedback. Robustness of feedback with respect to feedforward. Mathematical modelling of physical systems: examples from electric networks, mechanical systems, and thermal systems.
2) Analysis methods of LTI (linear time-invariant) systems. Ordinary differential equations and Laplace transform. Inverse Laplace transform of rational functions. Generalized derivatives and elements of impulse function theory. Relations between the initial conditions of a differential equation. First and second order linear systems.The concept of dominant poles.
3) Frequency-domain analysis: the frequency response function. Relation between the impulse response and the frequency response. Bode’s diagrams. Nyquist’s or polar diagrams. Asymptote of the polar diagrams. Bode’s formula and minimum-phase systems.
4) Stability to perturbations and BIBO (bounded-input bounded-output) stability of LTI systems: definitions and theorems. The Routh criterion. Properties of feedback systems. The Nyquist criterion. Phase and magnitude margins: traditional definitions and their extensions. The Padé approximants of the time delay.
5) The root locus of a feedback systems: properties for the plotting. Generalization of the root locus: the “root contour”. Examples. Stability degree on the complex plane of a stable systems.
6) Control system design: the approach with fixed-structure controllers. Specification requirements and their compatibility. Phase-lead and phase-lag compensation. Pole-zero cancellations and the internal stability of a feedback connection. The PID regulator. The inversion formulae for the synthesis of lead and lag compensators. Synthesis with Diofantine equations.