
At the end of the course Advanced Control Engineering (ACE) the student will be able to
 Derive a controlrelevant statespace model from (nonlinear) differential equations and linearize if needed.
 Analyze frequency response, poles, zeroes, and the initial and final step response for a linear MIMO system.
 Analyze stability of a MIMO system from its loop gain and analyze stability margins and performance of a SISO system from its loopgain and sensitivity functions and apply loop shaping to obtain the desired properties.
 Compute the relative gain array of a MIMO system and decouple the dynamics of a MIMO mechanical system.
 Perform analysis and synthesis via algebraic methods (polynomial factorization, polezero cancellation, Youla parametrization, transfer function interpolation) especially for simple systems.
 Quantify performance in terms of system norms (Hinf and Htwo) and synthesize controllers for nominal performance based on weighted sensitivity minimization.
 Analyze robust stability via smallgain theorem and synthesize controllers that ensure robust stability as well as robust performance based on mixed sensitivity minimization.
 Formulate synthesis problems in generalized plant framework and perform single as well as multiple objective syntheses.
 Explain fundamental limitations in controller synthesis for a linear feedback loop (interpolation constraints, waterbed effect, achievable bandwidth) and perform/adjust syntheses in view of them.
 Analyze and prove the reachability and observability of a MIMO statespace system
 Develop (optimal) statefeedback and output feedback controllers and (optimal) state estimators
 Analyze and prove the passivity and stability of controlled interacting systems
 Analyze the stability of a nonlinear system using Lyapunov stability and Lasalles’ Invariance Principle
 Design a controller for a nonlinear MIMO system in joint space using inverse dynamics compensation or feedback linearization



Production machines, robot arms, aircraft, drones, Segways, robotic prosthetics and exoskeletons are all mechanical systems with controlled motion. Control of mechanical systems will even become more important with current trends in automation and robotization. Advanced Control Engineering treats various advanced control theoretic concepts and controller design methods.
The application focus is on motion control. Multipleinput multipleoutput systems are considered. Mostly tools for linear systems are discussed, but also control of nonlinear systems is addressed. The course extends the basic (Bachelor) knowledge of control theory and prepares for courses on more specific control methods. Extensive treatment of various algorithms to obtain the controllers is not part of the course. The course covers the following topics:
 Frequency domain analysis and control design by loop shaping (frequency response, decoupling, characteristic loci, generalized Nyquist, gain and phase margins, Bode sensitivity integral)
 Statespace based analysis and control design by state feedback and observers (optimal control, poleplacement, reachability, observability, Luenberg Observers, Kalman Filter, Optimal control, LQR, LQG)
 Robust stability and performance analysis; robust controller synthesis (signal and system norms, uncertainty representation, small gain theorem, mixed sensitivity minimization, generalized plant framework)
 Stability of interacting systems through Passivity analysis (general passivity proofs, positive real condition, passive multiports, nonlinear passivity)
 Nonlinear dynamic analysis and control by dynamics compensation or feedback linearization (equilibria, Lyapunov stability and Lasalles’ Invariance Principle, passivity, computed torque control, joint space)
The theory is introduced through lectures. The theory is practiced through weekly assignments, which are partly on a selfchosen case. These assignments are supported by tutorials. Final knowledge is assessed by an individual written exam.




 Assumed previous knowledgeMandatory basic knowledge on differential equations, classical dynamical mechanical modelling, linear systems, Laplace and Fourier transforms, PID control. This knowledge can be obtained through the following UT Bachelor Modules: • ME module Mechatronics (201700128) • EE module Systems and Control (201700145) • Minor Biorobotics (201800178) 
Master Mechanical Engineering 
Master Biomedical Engineering 
  Required materialsBookFeedback Systems, K.J. Åström and R.M. Murray (freely available online)
ISBN:9781400828739 
 BookA Mathematical Introduction to Robotic Manipulation, R.M. Murray, Z. Li, S. Shankar Sastry (freely available online)
ISBN:9780849379819 

 Recommended materialsBookFeedback Control Theory, J.C. Doyle, B.A. Francis, A.R. Tannenbaum (freely available online)
ISBN:9780486469331 
 BookMultivariable Feedback Control – Analysis and Design, S. Skogestad, I. Postlethwaite (Chapters 1, 2, 3 available online)
ISBN: 9788126552672 
 BookModern Control Engineering, K. Ogata
ISBN: 9780136156734 

 Instructional modesAssessmentPresence duty   Yes 
 AssignmentPresence duty   Yes 
 Lecture
 Self study without assistance
 Tutorial

 TestsWritten examination and Assignment(s) RemarkWeekly assignment in groups and individual written exam


 