Module Description

Advanced Topics in Control

Courses:

Module Responsibility:

Prof. Herbert Werner

Admission Requirements:

None

Recommended Previous Knowledge:

H-infinity optimal control, mixed-sensitivity design, linear matrix inequalities

Educational Objectives:

Professional Competence

Theoretical Knowledge

• Students can explain the advantages and shortcomings of the classical gain scheduling approach
• They can explain the representation of nonlinear systems in the form of quasi-LPV systems
• They can explain how stability and performance conditions for LPV systems can be formulated as LMI conditions
• They can explain how gridding techniques can be used to solve analysis and synthesis problems for LPV systems
• They are familiar with polytopic and LFT representations of LPV systems and some of the basic synthesis techniques associated with each of these model structures

• Students can explain how graph theoretic concepts are used to represent the communication topology of multiagent systems
• They can explain the convergence properties of  first order consensus protocols
• They can explain analysis and synthesis conditions for formation control loops involving either LTI or LPV agent models

• Students can explain the state space representation of spatially invariant distributed systems that are discretized according to an actuator/sensor array
• They can explain (in outline) the extension of the bounded real lemma to such distributed systems and the associated synthesis conditions for distributed controllers

Capabilities

• Students are capable of constructing LPV models of nonlinear plants and carry out a mixed-sensitivity design of gain-scheduled controllers; they can do this using polytopic, LFT or general LPV models 
• They are able to use standard software tools (Matlab robust control toolbox) for these tasks

• Students are able to design distributed formation controllers for groups of agents with either LTI or LPV dynamics, using Matlab tools provided

• Students are able to design distributed controllers for spatially interconnected systems, using the Matlab MD-toolbox

Personal Competence

Social Competence

Students can work in small groups and arrive at joint results.

Autonomy

Students are able to find required information in sources provided (lecture notes, literature, software documentation) and use it to solve given problems. 

ECTS-Credit Points Module:

6 ECTS

Examination:

Oral exam

Workload in Hours:

Independent Study Time: 124, Study Time in Lecture: 56

Course: Advanced Topics in Control

Lecturer:

Herbert Werner

Language:

English

Period:

Winter Semester

Content:

• Linear Parameter-Varying (LPV) Gain Scheduling
  - Linearizing gain scheduling, hidden coupling
  - Jacobian linearization vs. quasi-LPV models
  - Stability and induced L2 norm of LPV systems
  - Synthesis of LPV controllers based on the two-sided projection lemma
  - Simplifications: controller synthesis for polytopic and LFT models
  - Experimental identification of LPV models
  - Controller synthesis based on input/output models
  - Applications: LPV torque vectoring for electric vehicles, LPV control of a robotic manipulator

• Control of Multi-Agent Systems
  - Communication graphs
  - Spectral properties of the graph Laplacian
  - First and second order consensus protocols
  - Formation control, stability and performance
  - LPV models for agents subject to nonholonomic constraints
  - Application: formation control for a team of quadrotor helicopters

• Control of Spatially Interconnected Systems
  - Multidimensional signals, l2 and L2 signal norm
  - Multidimensional systems in Roesser state space form
  - Extension of real-bounded lemma to spatially interconnected systems
  - LMI-based synthesis of distributed controllers
  - Spatial LPV control of spatially varying systems
  - Applications: control of temperature profiles, vibration damping for an actuated beam

Literature:

• Werner, H., Lecture Notes "Advanced Topics in Control"
• Selection of relevant research papers made available as pdf documents via StudIP

Examination:

Oral exam

ECTS-Credit Points Course:

6 ECTS