Teacher

prof. Stefano MIANI

Credits

9 CFU

Language

Italian

Objectives

Dynamical systems input-state-output modeling. Representation of nonlinear system dynamics at equilbirium points. Determination of linear input-output systems response to canonical inputs (pulses, steps, and sinusoids) and harmonic response graphing. Synthesis of PID, lead, lag and lead-lag controllers for SISO systems.

Acquired skills

- Input-state-output represntation of dynamical systems.
- Evaluation of free and forced response.
- Determination of equilbiria of nonlinear systems and linearization.
- Frequency response and Bode plots graphing.
- Controller synthesis.
- Use of software tools for the analysis, synthesis and simulation of dynamical systems.
- Evaluation of dynamical properties of input-output dnamical systems.

Lectures and exercises (topics and specific content)

Introduction and examples: control problems, process intrumentation, transducers and actuators, modeling (4 hours).
Dynamical systems examples and algebra: 2nd order mechanical systems, algebra, eigenvalues and eigenvectors, matrix powers and matrix exponential; Laplace transforms (8 hours).
Input-state-output representation. Equilibrium:  state of a dynamical system; input to state and (state,input) to output maps; motion and equilibrium (8 hours).
Linear time-invariant systems: matrix exponential, Euler formula, base change, matrix exponential for block diagonal matrices, state space trajectories (4 hours).
Exercises, software tools: eigenvalues, eigenvectors, matrix exponential and Laplace transforms; Matlab software (8 hours).
Linearization. Input output behaviour: linearization and Lyapunov functions; transfer function; step response for first and second order systems; frequency response; Matlab control toolbox (8 hours).
Realization, frequency response: state space representation of a given transfer function; frequency response; Bode and Nyquist diagrams; Fourier series expansion (10 hours).
Feedback systems analysis: graphic representation of series, parallel and feedback connections; Nyquist and Bode criterion (8 hours).
Controller synthesis: frequency based synthesis; PID and lead lag controllers (8 hours).
Tools for controller synthesis: root locus; software tools for controller synthesis (10 hours).
Exercises: transfer functions; step response; Laplace anti transform (4 hours).
Labs (8 hours).
Tutorials/Seminars (2 hours).

References

- Paolo Bolzern, Riccardo Scattolini, Nicola Schiavoni , Fondamenti di controlli automatici 3/ed. McGraw-Hill, 2008

Type of exam

Written and oral

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