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0542-4622

Dynamics and control of systems

Also listed as: דינמיקה ובקרה של מערכות

Classical control rebuilt in state space, then observers, optimal control and the digital implementation. The course behind every guidance, navigation and motion-control job.

Semester
Semester B
Weekly hours
4h
Counts as
Core: systems
Interest areas
Mechatronics and robotics · Aeronautics and space

What it covers

State-space modelling

  • Review of transfer functions, root locus, Bode and Nyquist
  • State equations, linearisation, the matrix exponential and the transition matrix
  • Similarity transforms and canonical forms
  • Stability: eigenvalues, Lyapunov direct and indirect methods, BIBO against internal

Controllability, feedback and estimation

  • Controllability and observability, Kalman rank tests, PBH, Gramians
  • Minimal realisations and pole-zero cancellation
  • State feedback and pole placement, Ackermann, integral action
  • Full and reduced-order observers, Luenberger, the separation principle

Optimal, digital and nonlinear

  • Linear quadratic regulator and the Riccati equation
  • Introduction to LQG and the Kalman filter
  • MIMO systems
  • Discrete-time control: sampling, the z-transform, discretisation
  • Introduction to nonlinear analysis: describing functions, phase plane

Results worth carrying out

  • State space

    x˙=Ax+Bu,y=Cx+Du\dot{x} = Ax + Bu, \qquad y = Cx + Du
  • Controllability matrix

    C=[BABAn1B]\mathcal{C} = \begin{bmatrix} B & AB & \cdots & A^{n-1}B \end{bmatrix}
  • Observability matrix

    O=[CCACAn1]\mathcal{O} = \begin{bmatrix} C \\ CA \\ \vdots \\ CA^{n-1} \end{bmatrix}
  • Algebraic Riccati equation, LQR

    ATP+PAPBR1BTP+Q=0A^{\mathsf{T}}P + PA - PBR^{-1}B^{\mathsf{T}}P + Q = 0

Figures worth knowing

  • Block diagrams
  • Root locus, Bode and Nyquist plots
  • Phase-plane portraits
  • Pole maps in the s- and z-planes
  • Step-response comparisons

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