Control Systems
(9 credits)

Prof. Leonardo Lanari

schedule 2017-2018 academic year, Fall 2017: 25 Sep - 21 Dec 2017 - course will start on October 2nd
classes Mon 14:00-16:00 (room 1), Wed 8:00-11:00 (room 1), Fri 8:00-11:00 (room 1)
office hours Tue 12:00-13:00 (temporary), office A212, DIAG, Via Ariosto 25 (only during the first semester)
extra office hours below
course website

This 9-credit module is
primarily offered to students of the Laurea Magistrale in Ingegneria Meccanica (MMER) of the FacoltÓ di Ingegneria Civile e Industriale of Sapienza University of Rome.


This course provides some basic tools for the analysis and control of linear systems.


Analysis of linear systems:
Linear dynamical systems. Free evolution (Zero Input response). Asymptotic stability and Routh criterion. Forced evolution (Zero State response). Steady-state and frequency response. Bode diagrams. Interconnected systems. Stability of feedback systems: Nyquist criterion.

Structure and requirements in the design of control systems
Compensation and feedback in automatic control examples, structure and fundamental properties. Precision. Steady-state error. Disturbance rejection and attenuation. Transient response. Performance analysis and sensitivity functions.

Frequency domain design techniques:
Elementary compensators and their realization. Design of compensators based on Bode diagrams. Loop shaping.

Root locus design techniques:
Root locus and its sketching. Stabilization of minimum-phase systems. Design of minimum-dimension controllers.

Direct design techniques:
Design by pole assignment.

State space design techniques:
Structural properties: reachability and observability. Structural decompositions. Eigenvalue assignment. Stabilization via state feedback. Asymptotic observer. Separation principle. Detectability  and stabilization via output feedback.

Stability of nonlinear systems:
Stability definitions according to Lyapunov. The direct method of Lyapunov. Invariant set theorems. The indirect method of Lyapunov.

Examples of application. Design and simulation of control systems via MATLAB/Control System Toolbox and Simulink.

Reference material

Supplemental material

Some interesting links


Special office hours:

- Tuesday 30/01/2018, 11:30-13:00
- Thursday 01/02/2018, 11:30-13:00

    To see what we do at the DIAG Robotics Lab visit the YouTube channel RoboticsLabSapienza
    Seminar (2015): "Controllo di un elicottero quadrirotore" Ing. Marco Cognetti - DIAG
Seminar (2015): "Controllo del robot Pendubot" Ing. Massimo Cefalo - DIAG
    Seminar (2015): "Controllo piattaforma CyberWalk" Prof. Alessandro De Luca - DIAG

   Future exams
   (due to the large number of students, it is essential to know in advance how many students will attend the exam, this requires that the reservations close some days before the actual exam)

   Next exam: 05/02/2018 (morning)
   exam: be in Aula 33 (Via Eudossiana) at 8:45
Last minute variations are possible, please always check the webpage
   No calculators will be allowed

   Recall that nothing will be provided so please bring your own paper, lead/lag functions and semilog paper.

   Important: Last reservation day is 29/01/18 (midnight Italy time) - no requests for exam reservation will be accepted afterwards.
  Important: For those students who are not able to enroll due to delays in the approval of their exam plan, try until midnight of the 29/01 (sometimes the situation unblocks at the last minute). Otherwise send me an email on the 30th of January (no delays, late requests will not be accepted).
   Do not sed me email days before.

   Other dates:
   05/02/2018 (this date has changed)
(this exam is reserved to particular situations - see here)

   Exam 05/02/2018: results

    The corrected exams can be viewed:
  # 20/02/2018 from 14:00 to 15:00 (I will not be available after 15:00) in Aula 6 - Via Ariosto 25
  # 21/02/2018 from 14:00 to 15:00 (I will not be available after 15:00) in Aula 7 - Via Ariosto 25
   I need a decision (acceptance or not) of the grade within February 21 (midnight).
   No answer not only means no acceptance of the grade but also that I will write "Bocciato" (Failed) on the official report (verbale)

   You can directly send me an email if you accept the proposed grade (there is no need of signing any document).