# 376.060 Control systems 2 This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_20",{id:"j_id_20",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_22",{id:"j_id_22",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2022S 2021S 2020S 2019S 2018S 2017S 2016S 2015S 2014S

2021S, VO, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VO Lecture
• Format: Distance Learning

## Learning outcomes

After successful completion of the course, students are able to

• understand and apply the mathematical principles and methods to describe and analyze nonlinear systems.
• apply Lyapunov theory to analyze stability and devise nonlinear control strategies such as integrator backstepping, PD control and computed torque.
• utilize singular perturbation methods to reduced-order models systematically.
• develop nonlinear control schemes based on differential-geometric and differential-algebraic methods such as differential flatness or exact input-state linearization.

## Subject of course

introduction to nonlinear system theory, examples of nonlinear systems (mechanical, electrical, hydraulic), stick-slip effect, basics of dynamical systems, existence and uniqueness of solutions, sensitivity equations, Lyapunov stability, invariance principle of Krasowskii-LaSalle, direct and indirect method of Lyapunov, Lyapunov equation, stability of non-autonomous systems, Lemma of Barbalat, singular perturbation theory, fast and slow manifold, boundary layer model, Theorem of Tikhonov, Lyapunov-based controller design (simple PD-law, computed torque, integrator backstepping, generalized backstepping, recursive backstepping), affine-input systems, exact input-output and input-state linearization of SISO- and MIMO-systems, relative degree, zero dynamics, trajectory tracking, flatness, basics of differential geometry (manifold, tangent and cotangent space, Lie derivatives, Theorem of Frobenius), observer design for linear time-variant systems

## Teaching methods

lecture, presentation of examples during the lecture

## Mode of examination

Oral

A preliminary discussion is given in the first lecture.

## Course dates

DayTimeDateLocationDescription
Tue08:00 - 10:0002.03.2021 - 29.06.2021 Zoom meeting via TUWEL (LIVE)online lecture
Wed08:00 - 10:0003.03.2021 - 30.06.2021 Zoom meeting via TUWEL (LIVE)online lecture
Control systems 2 - Single appointments
DayDateTimeLocationDescription
Tue02.03.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Wed03.03.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Tue09.03.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Wed10.03.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Tue16.03.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Wed17.03.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Tue23.03.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Wed24.03.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Tue13.04.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Wed14.04.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Tue20.04.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Wed21.04.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Tue27.04.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Wed28.04.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Tue04.05.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Wed05.05.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Tue11.05.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Wed12.05.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Tue18.05.202108:00 - 10:00 Zoom meeting via TUWELonline lecture
Wed19.05.202108:00 - 10:00 Zoom meeting via TUWELonline lecture

oral exam

Not necessary

## Literature

Lecture notes are available here.

German