Portale di Ateneo - En.Unibs.it

Introduction to the control problem

Caontrol systems. Controlled and control variables. Disturbances. Regulation and servo control. Open-loop and closed-loop control. Sensors and actuators. Application examples.

Linear dynamic systems. Transfer functions.

Classification of dynamic systems. Continuous-time linear dynamic systems. Laplace transform. Transfer function. Poles, zeros, time constants, gains, naturla frequency and damping coefficients. Inverse Laplace transform. System modes. Stability of a system. Block schemes. Series, parallel and feedback systems transfer function. Routh-Hurwitz stability criterion. Step response of first and second-order systems. Dominant poles.

Linear dynamic systems. Frequency response.

Frequency response function. Filtering properties of a dynamic system. Bode diagrams. Minimum-phase systems. Bode's integral formula. Bode’s gain phase relationship. Dead times. Nyquist diagrams. Nichols diagrams. Approximated models of dynamic systems.

Design of control systems.

Feedback control systems. Analysis of feedback control systems. Nyquist and Bode criterion. Performance of a control system. Sensitivity, complementary sensitivity and control sensitivity
transfer functions. Steady-state error. Bandwidth and settling time. Overshoots. Design of the controller in the frequency domain. Analytical design. Constant M and N loci. Controller implementation.

State-space modelling.

State variables. State-space modelling of a system. State and output trajectory and portrait. Equilibrium states and outputs. Stability of a trajectory and of an equilibrium point.

Structural properties of linear systems

Linearization of nonlinear systems. Equivalent models. Diagonalization of a system. Lagrange formula. Eigenvalues and modes. Stability. Controllability. Observability. Canonical decomposition. State space models and input-output models.

State-feedback control

Feedback state-space control design. Observer. Separation principle.