AUTOMATIC CONTROL A - L
Academic Year 2025/2026 - Teacher: MATTIA FRASCAExpected Learning Outcomes
Knowledge and Understanding
Knowledge of the main methods of analysis and control of a linear time-invariant system.
Applied Knowledge and Understanding
Ability to represent a dynamical system through a mathematical model. Ability to design an automatic control system.
Autonomy of Judgment
Ability to choose the type of control system to be used in regulation.
Communication Skills
Knowledge and proper use of technical terminology related to linear systems and automatic control systems. Ability to present the main issues concerning such systems in research and professional contexts.
Learning Skills
Ability to apply basic knowledge of control systems in order to carry out in-depth study of topics related to them but not explicitly covered in the course.
Course Structure
Required Prerequisites
Attendance of Lessons
Detailed Course Content
Textbook Information
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Fundamental definitions and general concepts. Classification of systems. Representation of finite-order discrete-time and continuous-time linear systems by means of constant-coefficient difference/differential equations. (Planned lecture time: 7 hours) | 3 |
| 2 | Input–output representation and behavior. Natural and forced response. Laplace transform. Main properties and applications. Convolution integral. Impulse response. Inverse transform. Notion of transfer function. Poles and zeros. (Planned lecture time: 7 hours) | 3 |
| 3 | First- and second-order systems. Time constants. Theoretical and experimental examples. Canonical step response. Rise time, overshoot, settling time. Dominant poles. (Planned lecture time: 5 hours) | 3 |
| 4 | Block diagram algebra. Rules and manipulations. (Planned lecture time: 5 hours) | 3 |
| 5 | Mathematical models in state-space form. State transition matrix and solution. Controllability and observability. Relationship between state-space models and transfer function. (Planned lecture time: 8 hours) | 3 |
| 6 | Stability of linear systems. Routh stability criterion. (Planned lecture time: 8 hours) | 3 |
| 7 | Feedback systems. Specifications. Stability of feedback systems. Response speed. Accuracy. Effect of feedback on disturbances. (Planned lecture time: 5 hours) | 3 |
| 8 | Frequency response. Analysis of feedback systems. Harmonic function. Bode diagrams. Bode theorem. Minimum-phase systems. Bode stability criterion. Stability margins. Bandwidth. (Planned lecture time: 10 hours) | 3 |
| 9 | Nyquist diagrams. Nyquist stability criterion. Relative stability indices. (Planned lecture time: 12 hours) | 3 |
| 10 | Definition of the controller design. Trial-and-error synthesis. Compensator networks: lead and lag. Saddle network. Standard controllers: PID regulators. (Planned lecture time: 12 hours) | 3 |
| 11 | Basic notions on the use of MATLAB. MATLAB exercises on system analysis and controller design. (Planned lecture time: 8 hours) | 3 |
Learning Assessment
Learning Assessment Procedures
Examples of frequently asked questions and / or exercises
State equations; transfer function; closed-loop systems; stability; controllability; observability; linear regulator.
Exercises: determine the impulse response of a system; compute a compensator for a linear time-invariant system; compute the frequency response of a linear time-invariant system.