CONTROLLI AUTOMATICI

Lessons will be mainly frontal; sometimes personal computer will be used to maximise learning objectives. It will also be used to make numerical exercises and simulations.

During exercitations some students will be asked to actively participate together wiith the professor, at the aim to stimulte attention and to perform a "sample check" of the real state of the learning status

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Students have not to attend the lessons mandatorily.  Regular attendance at lectures and exercises is however strongly recommended for
achievement of the expected training objectives on schedule.

Module 1: Dynamic systems and state-space representation. Concept of dynamic systems – MIMO, SISO, MISO, and SIMO systems; state variables; block diagram algebra; state-space models. (Teaching hours: 6)

Module 2: Review of the Laplace transform and transfer function. Laplace transform; transform of canonical signals; theorems regarding frequency shifting, time delay, differentiation and integration, and initial and final values. Inverse Laplace transform – poles and zeros – partial fraction expansion – concept of transfer function (TF); invariance of the TF. (Teaching hours: 11)

Module 3: Time-domain analysis and stability. Lagrange's formula for linear continuous-time systems; state transition matrix: properties, definition, and calculation; minimal form; poles and eigenvalues. Stability of linear systems. Routh's criterion. (Teaching hours: 7)

Module 4: First- and second-order systems – harmonic response function; Bode plots. Time-domain response performance of first- and second-order linear systems: time constants, rise time, settling time. Dependence of response characteristics on system pole locations in the s-plane. Frequency response characteristics of first- and second-order systems: crossover frequency, bandwidth, resonant peak. Non-minimum phase systems. (Teaching hours: 18)

Module 5 – Characteristics of feedback systems and stability analysis. Open-loop and closed-loop control. Effect of feedback on sensitivity to parameter variations, on disturbances in the forward and feedback paths, and on the bandwidth of a linear system. Steady-state accuracy of a feedback system for step, ramp, and parabolic inputs; classification of feedback control systems by type. Polar plots. Stability analysis of linear feedback systems using the Nyquist criterion. Stability margins. (Teaching hours: 15)

Module 6. Control system specifications and controller synthesis. Static and dynamic specifications. Conversion of time-domain specifications into frequency-response specifications. Nichols chart. Synthesis by trial and error. Elementary compensating networks: lead networks and lag (attenuator) networks. Synthesis by trial and error for frequency-response compensation. (Teaching hours: 18)

Module 7. Standard PID controllers. Standard regulators: empirical tuning methods, analytical tuning methods. (Teaching hours: 5)

Module 8. Exercises using MATLAB code. (Teaching hours: 7)

Example exercises

1. Given a system, determine state-space equations and/or a transfer function; analyze its stability.

2. Given a system represented by a transfer function, design a feedback controller that meets specific static and dynamic requirements, using trial-and-error synthesis in the frequency domain.

3. Given a system represented by a transfer function, determine its closed-loop stability using the Nyquist criterion.

Example questions

1. How is the stability of a feedback system analyzed?

2. Nyquist criterion: statement and proof.

3. What are the specifications for a control system?

4. How are control system specifications transformed from the time domain to the frequency domain?

5. How is synthesis in the frequency domain performed?

6. How is a standard PID controller designed?