Computer and Control Engineering

Introduction Role of modelling in the analysis and simulation of physical processes, and in the design of the related control systems. Classification and validity limits of models in relation to linearity, time-invariance, dynamic and spatial behavior, randomness. Modelling of lumped parameter systems Ordinary differential equations, fundamental laws of mechanics, electromagnetism and fluid dynamics, conservation laws. Mechanical models: damped oscillator, pendulum, coupled oscillators, double pendulum, inverted pendulum, multi-body systems. Electrical examples: analog circuits, operational amplifiers, direct current motor, brushless motor, alternating current electric drives, satellite communication system. Examples of fluid systems: flow sensors, control valves, heat exchanger. Generalized coordinates and Lagrangian formalism, conservation of canonical momenta, examples. Electro-mechanical analogies, duality of impedance and mobility analogies, examples. Modelling of distributed parameter systems Partial differential equations, admissible boundary conditions, equation of the vibrating string, equation of the rectangular and circular membranes, equation of the bar, equation of air column tubes, stationary modes and natural frequencies, inharmonicity of natural frequencies in presence of distributed stiffness, transmission line equation. Effects of nonlinearities Harmonic distortion induced by saturations and thresholds, subharmonics induced by bifurcations, torus cycles and chaotic phenomena. Poincaré maps, fixed points and their stability. The logistic map, Feigenbaum bifurcation tree. Modelling of complex systems using probability Recall of probability theory. Bayes networks, computation of reliability, propagation of fault effects, diagnosis. Examples. Systems discretization Difference equations, signal sampling, Nyquist sampling theorem, Z-transform, ordinary differential equations discretization methods: forward and backward Euler methods, Tustin transform, prewarping, conservation of stability property, zero and first order hold based methods, wave digital filters, examples.

-Students should know the fundamental notions of calculus (in particular, the theory of linear differential equations), of linear algebra (eigenvalues, eigenvectors, canonical forms of linear operators), of physics as well as Laplace transform theory.

Teaching material available on professor's web page.

Traditional lectures

Attendance of lessons not necessary, but recommended.

Oral test

Traditional lectures