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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

Comes after

  • Introduction to control

Opens up

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=[BAB⋯An−1B]\mathcal{C} = \begin{bmatrix} B & AB & \cdots & A^{n-1}B \end{bmatrix}

  • Observability matrix

    O=[CCA⋮CAn−1]\mathcal{O} = \begin{bmatrix} C \\ CA \\ \vdots \\ CA^{n-1} \end{bmatrix}

  • Algebraic Riccati equation, LQR

    ATP+PA−PBR−1BTP+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

Quick answers

When is Dynamics and control of systems taught?

Dynamics and control of systems (0542-4622) is taught in Semester B (spring), 4 weekly hours. It counts toward “Core: systems” in the Tel Aviv University Mechanical Engineering elective requirements.

What do I need before 0542-4622?

Before Dynamics and control of systems you need: Introduction to control.

What software is used in Dynamics and control of systems?

Dynamics and control of systems is normally taught with MATLAB Control System Toolbox, Simulink, Python control.

Which jobs does Dynamics and control of systems prepare you for?

Dynamics and control of systems is part of the preparation for these roles: Robotics engineer, Control and GNC engineer, Mechatronics and embedded systems engineer, Algorithm engineer, from mechanical engineering, Space systems engineer.

Which interest areas include Dynamics and control of systems?

Dynamics and control of systems sits in these interest areas: Mechatronics and robotics, Aeronautics and space.

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The topic outlines are not official syllabi. The university publishes a catalogue blurb per course, not lecture-by-lecture material, so each outline describes what a course of that name, at those hours, with those prerequisites teaches at engineering schools generally, cross-checked against the standard textbook for the subject. Treat it as an informed map, not as a transcript of the lectures.