Advanced and Multivariable Control– 10 cfu

Master of Science (“Laurea magistrale”) in Automation and Control Engineering

School of Industrial and Information Engineering – Leonardo Campus

Aims and learning outcomes

The objective of this course is to present advanced methods for the analysis of dynamical systems and for the synthesis of multi-input, multi-output controllers. First, the Lyapunov stability theory will be introduced and applied to nonlinear system analysis. Then, the structural properties of linear dynamical systems (poles, invariant zeros, principal gains) will be described together with performance and robustness indices. Pole placement, Linear Quadratic and predictive control synthesis methods will be introduced and applied to a number of application examples. Further topics will concern state estimators based on pole assignment and Kalman filtering, LQG control, gain scheduling regulators and synthesis techniques relying on the robust control synthesis approach.

Syllabus

1. Nonlinear systems: equilibria, stability, Lyapunov theorems. Synthesis of the control law with control Lyapunov functions and the backstepping procedure.
2. Norms and gain of dynamical systems. Small gain theorem.
3. Structural properties of linear systems: reachability, observability, poles, and invariant zeros.
4. Nominal and robust stability of multivariable feedback systems. Static and dynamics performances. Schemes with integral action.
5. Pole placement control of single-input, single-output and multivariable systems. State observers and dynamic output feedback. Disturbance estimation with state observers.
6. Optimal control. Linear quadratic control: definitions, properties, examples of application. Kalman filtering and LQG control. H₂ and H_∞ control, model order reduction.
7. Model predictive control: formulations in the state space and with input-output models. Stabilizing properties of MPC.
8. Control design examples: control of a chemical reactor, a distillation column, an inverted pendulum, an aircraft.

Bibliography

L. Magni, R. Scattolini: “Analysis and design of multivariable feedback systems”, Pitagora Editrice, 2014 (in preparation).

Lectures notes

H. K. Khalil: “Nonlinear Systems”, Prentice Hall, 1996.

J.M. Maciejowski: “Multivariable Feedback Design”, Addison-Wesley, 1989.

S. Skogestad, I. Postlethwaite: “Multivariable Feedback Control”, Wiley, 1996.

T. Glad, L. Ljung: “Control Theory”, Taylor & Francis, London, 2000.

The final assessment will be a written exam consisting of exercises and theoretical questions.