Mathematical Models. State space representations. Linear models. Nonlinear models and its linearization around equilibrium points and solutions.

Time domain
analysis. Output and state free response. Natural modes and modal
decomposition. State and output forced response. Impulsive and step
response. Rise time, settling time and maximal overshooting and
undershooting.

Frequancy domain analysis. Fundamental properties of Laplace transform and most used transforms. Transfer functions. Input-output models.

Stability of linear systems: main notions and criteria. Routh criterion.

Bode plots. Armonic response. Steady state and transient response with sinusoidal and polynomial inputs.

Controllability and observability. Controllability and observability grammians and matrices. Hautus tests for controllability and observability. Point-to-point control problems. State reconstruction problems.

Time domain design. Eigenvalue assignment and state estimation and reconstruction. Steady state performances.

Interconnected systems: series, parallel and feedback interconnections. General properties of feedback interconnections. Zero-pole cancellations.

Stability of linear feedback systems. Polar plots and Nyquist criterion. Frequency domain design. Proportional, derivative and integral control actions.

Steady state performance: tracking and disturbance compensation. Transient performances: phase margin and cross-over frequency versus cut-off frequency and resonce peak. Zero-pole control actions for phase margin and cross-over frequency modification.

Root-locus. Stabilization and pole assignment with root-locus methods.

Frequancy domain analysis. Fundamental properties of Laplace transform and most used transforms. Transfer functions. Input-output models.

Stability of linear systems: main notions and criteria. Routh criterion.

Bode plots. Armonic response. Steady state and transient response with sinusoidal and polynomial inputs.

Controllability and observability. Controllability and observability grammians and matrices. Hautus tests for controllability and observability. Point-to-point control problems. State reconstruction problems.

Time domain design. Eigenvalue assignment and state estimation and reconstruction. Steady state performances.

Interconnected systems: series, parallel and feedback interconnections. General properties of feedback interconnections. Zero-pole cancellations.

Stability of linear feedback systems. Polar plots and Nyquist criterion. Frequency domain design. Proportional, derivative and integral control actions.

Steady state performance: tracking and disturbance compensation. Transient performances: phase margin and cross-over frequency versus cut-off frequency and resonce peak. Zero-pole control actions for phase margin and cross-over frequency modification.

Root-locus. Stabilization and pole assignment with root-locus methods.

Module I
```
Mathematical
Models. State space representations. Linear models. Nonlinear
models and its linearization around equilibrium points and
solutions.
```

Module II Time domain analysis. Output and state free response. Natural modes and modal decomposition. State and output forced response. Impulsive and step response. Rise time, settling time and maximal overshooting and undershooting.

Module III Frequency domain analysis. Fundamental properties of Laplace transform and most used transforms. Transfer functions. Input-output models.

Module IV Stability of linear systems: main notions and criteria. Routh criterion.

Module V Steady state and transient response with sinusoidal and polynomial inputs.

Module VI Bode plots. Armonic response. Steady state and transient response with sinusoidal and polynomial inputs.

Module VII Controllability and observability. Controllability and observability grammians and matrices. Hautus tests for controllability and observability. Point-to-point control problems. State reconstruction problems. Time domain design. Eigenvalue assignment and stabilization via state feedback. Asympotic state estimation and reconstruction. Eigenvalue assignment and stabilization via output feedback: the separation principle.Module VIII Interconnected systems: series, parallel and feedback interconnections. General properties of feedback interconnections. Zero-pole cancellations.

Module IX Stability of linear feedback systems. Polar plots and Nyquist criterion. Frequency domain design. Proportional, derivative and integral control actions.

Module X Root locus. Stabilization and pole placement for minimum phase system. Non minimum phase systems and direct pole assignment.

Module XI Steady-state performances in frequency domain. Tracking and disturbance compensation.

Module
XII Transient
response design in frequency domain.
Crossover frequency and phase margin design via anticipative/attenuative
control actions.

Errata corrige

S. Battilotti, Notes on Linear Control Systems, Esculapio, 2016, II ed.

G. Marro, Controlli Automatici, V ed., Zanichelli.

A. Isidori, Sistemi di controllo, Siderea, 1979.

S. Monaco, Sistemi Lineari: Elementi di analisi, Progetto Leonardo ed., Bologna, 2000.

R. C. Dorf, R. H. Bishop, Controlli Automatici, Pearson, Prentice Hall, 2010.

O. M. Grasselli, L. Menini, S. Galeani, Sistemi Dinamici, Hoepli, IV ed., Milano, 2012.

C. Gori Giorgi, S. Monaco, S. Battilotti, S. Di Gennaro, Teoria dei Sistemi: complementi ed esercizi, EuRoma.

L. Lanari, G. Oriolo, Controlli automatici: esercizi di sintesi, EuRoma.

Starting
a.a. 2020-2021, the exam will consist exclusively of a written
test. The grade of the written test will be directly
registered on the records.

The written test consists of three exercises focused on the topics covered during the course. The allotted time for the test is 2.5 hours . Below find a collection of past exams, partly with solutions.

### Exam
Papers

2.2.2018(b) (text) 7.4.2018 (text) 14.9.2018 (text) 27.10.2018 (text) 8.1.2019(b) (text) 5.2.2019(b) (text) 4.6.2019(b) (text) 16.9.2019 (text) 26.10.2019--(text) 7.1.2020(a) (text) 7.1.2020(b)--(text) 4.2.2020(a) (text) 4.2.2020(b) (text) 6.5.2020 (text) 4.6.2020 (text) 30.6.2020--(text) 1.9.2020 (text) 30.10.2020 (text) 11.1.2021 (text) 2.2.2021 (text) 20.3.2021 (text) 1.6.2021 (text) 6.7.2021 (text) 9.9.2021 (text) 29.10.2021 (text) 24.01.2022 (text) 18.02.2022 (text) 17.6.2022 (text) 22.7.2022 (text) 23.9.2022 (text) 3.11.2022 (text) 9.1.2023(A) (text) 9.1.2023(B) (text) 3.2.2023(A) (text) 3.2.2023(B) (text) 24.3.2023 (text) 5.6.2023 (text) 4.9.2023 (text) 3.11.2023 (text) 8.1.2024(a) (text) 8.1.2024(b) (text) 2.2.2024(a) (text) 2.2.2024(b) (text) 22.3.2024 (text)
### Exam
Papers (with solutions)

9.1.2018(a) ((text), (solution)) 2.2.2018(a) ((text), (solution)) 5.6.2018 ((text), (solution)) 3.7.2018 ((text), (solution)) 14.9.2018 ((text), (solution)) 27.10.2018 ((text), (solution)) 8.1.2019(a) ((text), (solution)) 5.2.2019(a) ((text), (solution)) 23.3.2019 ((text), (solution)) 4.6.2019(a) ((text), (solution)) 2.7.2019(a) ((text), (solution)) 16.9.2019 ((text), (solution)) 26.10.2019 ((text),

The written test consists of three exercises focused on the topics covered during the course. The allotted time for the test is 2.5 hours . Below find a collection of past exams, partly with solutions.

2.2.2018(b) (text) 7.4.2018 (text) 14.9.2018 (text) 27.10.2018 (text) 8.1.2019(b) (text) 5.2.2019(b) (text) 4.6.2019(b) (text) 16.9.2019 (text) 26.10.2019--(text) 7.1.2020(a) (text) 7.1.2020(b)--(text) 4.2.2020(a) (text) 4.2.2020(b) (text) 6.5.2020 (text) 4.6.2020 (text) 30.6.2020--(text) 1.9.2020 (text) 30.10.2020 (text) 11.1.2021 (text) 2.2.2021 (text) 20.3.2021 (text) 1.6.2021 (text) 6.7.2021 (text) 9.9.2021 (text) 29.10.2021 (text) 24.01.2022 (text) 18.02.2022 (text) 17.6.2022 (text) 22.7.2022 (text) 23.9.2022 (text) 3.11.2022 (text) 9.1.2023(A) (text) 9.1.2023(B) (text) 3.2.2023(A) (text) 3.2.2023(B) (text) 24.3.2023 (text) 5.6.2023 (text) 4.9.2023 (text) 3.11.2023 (text) 8.1.2024(a) (text) 8.1.2024(b) (text) 2.2.2024(a) (text) 2.2.2024(b) (text) 22.3.2024 (text)

9.1.2018(a) ((text), (solution)) 2.2.2018(a) ((text), (solution)) 5.6.2018 ((text), (solution)) 3.7.2018 ((text), (solution)) 14.9.2018 ((text), (solution)) 27.10.2018 ((text), (solution)) 8.1.2019(a) ((text), (solution)) 5.2.2019(a) ((text), (solution)) 23.3.2019 ((text), (solution)) 4.6.2019(a) ((text), (solution)) 2.7.2019(a) ((text), (solution)) 16.9.2019 ((text), (solution)) 26.10.2019 ((text),

Semilogarithmic Charts (for Bode Plots): required

Compensating functions chart (anticipative/attenuative functions): required

Nichols chart (for Nichols Plots): not required