35245 - Automatic Control Systems

Learning outcomes

At the end of the course the student handles Linear Time-Invariant (LTI) systems and their representation through state-space methods, Laplace transform and its inverse, and transfer functions. Students understands the basic principles of linear-system stability and the response modes (1st and 2nd order elementary systems and their composition to implemented higher-order systems). Students know how to use Bode diagrams and root locus to design controllers for linear systems, which include lead and lag networks, PID controllers and cascade controllers. The student will be exposed to the control of nonlinear system via linearization-based methods.

Course contents

1. Introduction to Control Systems. Examples of control systems. Definition of system: control and disturbance inputs, outputs, state variables. Principles of control systems design.
2. Mathematical Models of Systems. Differential equation models of physical systems; Linear approximations of nonlinear models. Modeling principles: Electric systems; Mechanical systems; Flow systems.
3. State Variable Models. State-space models. Realization from differential equation models: Canonical forms. Solution of the state equation.
4. Input-Output Models. Laplace transform. Transfer functions. Forced and free response. Computation of the response via partial fraction expansion. Block diagrams. Signal-flow graphs. Relation with state-space models. 
   
5. Stability of Systems. Definitions. Stability of state-space models: Internal stability and external stability. Transient and steady-state response. External stability (BIBO stability). Routh-Hurwitz criterion.
6. Feedback Systems. Introduction. Error-signal Analysis. Sensitivity Analysis. Test input signals. Time-response of first- and second-order systems. Higher-order models. Transient response. Performance specification in time-domain and relation with pole location. Steady-state error of feedback control systems. Design examples.
   
7. Root Locus. Definition and procedure. Parameter design via the root locus method. Introduction to PID controllers. Design examples. Design using computer software.
8. Frequency Response Methods. Frequency response. Polar plots and Bode plots. Performance specifications in the frequency domain. Design Examples.
9. Feedback Control Systems Design. Cascade compensators. Phase-lead compensator networks: Frequency domain and root-locus design methods. Phase-lag design: Frequency domain and root-locus design methods. Lead-lag controllers. Pre-filters. Design examples.

Readings/Bibliography

Course Textbook: 

P. Bolzern, R. Scattolini, N. Schiavoni, "Fondamenti di controlli Automatici'', McGraw-Hill.

Supplementary Textbooks:

G. Marro, "Controlli Automatici", Zanichelli, Bologna, 2004.

H. Khalil, "Control Systems: An Introduction",  Michigan Publishing, 2023. Note: this textbook is freely available in electronic form at https://control.eecs.umich.edu

Copies of the slides used in the lectures will be made available to the students. These are by no means to be considered exhaustive to achieve proficiency in the subject matter of the course.

Teaching methods

In-class lectures only. In extenuating circumstances, occasional remote lectures may be delivered in both synchronous and asynchronous mode for make-ups.

Assessment methods

Comprehensive oral exam. Exams may include written questionnaires and/or design problems.

Teaching tools

• Worked-outxamples and recitation sessions.
• Computer-aided design tools (MATLAB®/Simulink®)

Office hours

See the website of Andrea Serrani

See the website of Ivano Notarnicola