Clinical Engineering

Design in the Laplace Domain The root locus. Stabilization of minimum phase systems via the Root Locus. Stabilization of non-minimum phase systems. Direct synthesis for pole assignment. Structural Properties of LTI systems Reachability (controllability) and observability: definitions, criteria and the corresponding state decompositions. The Kalman decomposition and the internal structure of dynamical LTI systems. The relation with the excitability and observability of natural modes. Design in the Time Domain The eigenvalue assignment problem by state feedback. The reconstructor problem and the asymptotic state observer. The separation principle. Criteria for the choice of closed-loop eigenvalues. Inclusion of the reference signal in state feedback schemes. Nonlinear Systems and Lyapunov Stability Stability of equilibria. The Lyapunov Theorem and the invariance principle. Stability via the linear approximation and the describing function method. Examples Applicative control problems from distinct engineering and science domains to illustrate the analysis and design methodologies.

Analisi Matematica II e Geometria Basics on mathematics: real and complex n-valued functions; graphical representation; basics on integral and differential calculus. Basics on linear algebra and geometry: linear operators; vector spaces. Basics con physics.

G.F. Franklin, D.Powell, A.E.Naeni, "Feedback control of dynamic system", Prentice- Hall, 2002

Attendance of lessons not necessary but recommended

Written exam and , if necessary, a supplementary oral exam

Teaching in classroom

Oriented dynamic systems and state representations: from phenomenon to model to abstract system. Concept of causal dynamic system and their representations: linear, stationary, finite-dimensional systems; implicit and explicit representation; decomposition of the response into free and forced; transition matrix and impulse response matrix and their properties. Time domain analysis Natural modes in the free evolution of the state for regular representations; laws of motion and trajectories of natural modes; natural modes in the forced response in state and output and their properties (excitability and observability). Complex variable domain analysis The Laplace transform for the analysis of continuous-time systems; The transfer function and its representations. The forced response as a system model: the step response and the gain. Basics on stability theory Introduction to the stability of equilibrium points of dynamic systems. Definition of stability for linear systems; conditions and criteria. Internal stability: the Routh criterion for continuous-time systems. Frequency domain analysis Steady state and transient state; steady-state response to canonical inputs. Graphical representations of the harmonic response. The harmonic response. Representation of the transfer function. Bode and Polar plots. Significant parameters of the magnitude of the harmonic response and the step response; connection between time and frequency behavior. Input-output models and state representations The realization problem and the calculation of state-space representations from input-output models. Reachable canonical form realizations and observable canonical form realizations. Control systems: structure and design specifications Specifications in the design of a control system. Feedback, compensation, and mixed control schemes. Response precision. Limitations on steady-state error. Disturbance rejection and attenuation. Transient response specifications and links with the open-loop harmonic response. Design in the frequency domain Elementary compensating functions. Synthesis of compensating functions based on Bode or Nyquist plots. Design in the Laplace Domain The root locus. Stabilization of minimum phase systems via the Root Locus. Stabilization of non-minimum phase systems. Direct synthesis for pole assignment. Structural Properties of LTI systems Reachability (controllability) and observability: definitions, criteria and the corresponding state decompositions. The Kalman decomposition and the internal structure of dynamical LTI systems. The relation with the excitability and observability of natural modes. Design in the Time Domain The eigenvalue assignment problem by state feedback. The reconstructor problem and the asymptotic state observer. The separation principle. Criteria for the choice of closed-loop eigenvalues. Inclusion of the reference signal in state feedback schemes. Nonlinear Systems and Lyapunov Stability Stability of equilibria. The Lyapunov Theorem and the invariance principle. Stability via the linear approximation and the describing function method. Examples Applicative control problems from distinct engineering and science domains to illustrate the analysis and design methodologies.

Formal Prerequisites: Geometria, Analisi Matematica II. Basics on mathematics: real and complex n-valued functions; graphical representations; basics on integral and differential calculus. Basics on linear algebra and geometry: linear operators, vectorial spaces. Basics on physics.

[1] S. Palani (2022). Automatic Control Systems. Springer Cham. [2] Franklin, G. F., Powell, J. D., & Emami-Naeini, A. (2010). Feedback control of dynamic systems (Vol. 10). Upper Saddle River, NJ: Pearson.

Classic lectures for theoretical aspects and tutoring sessions for the practical part

Attendance is not mandatory but highly recommended.

Written exam and, if necessary, a supplementary oral exam. In the latter case, the written exam will count as 75% of the final mark.

Classic lectures for theoretical aspects and tutoring sessions for the practical part