At the end of the course Advanced Control Engineering (ACE) the student will be able to
- Derive a control-relevant state-space model from (non-linear) 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 loop-gain 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, pole-zero cancellation, Youla parametrization, transfer function interpolation) especially for simple systems.
- Quantify performance in terms of system norms (H-inf and H-two) and synthesize controllers for nominal performance based on weighted sensitivity minimization.
- Analyze robust stability via small-gain 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 state-space system
- Develop (optimal) state-feedback 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. Multiple-input multiple-output 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)
- State-space based analysis and control design by state feedback and observers (optimal control, pole-placement, 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 multi-ports, non-linear 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 self-chosen case. These assignments are supported by tutorials. Final knowledge is assessed by an individual written exam.
Assumed previous knowledge
|Mandatory 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 materials|
|Feedback Systems, K.J. Åström and R.M. Murray (freely available online)
|A Mathematical Introduction to Robotic Manipulation, R.M. Murray, Z. Li, S. Shankar Sastry (freely available online)
|Feedback Control Theory, J.C. Doyle, B.A. Francis, A.R. Tannenbaum (freely available online)
|Multivariable Feedback Control – Analysis and Design, S. Skogestad, I. Postlethwaite (Chapters 1, 2, 3 available online)
|Modern Control Engineering, K. Ogata
|Self study without assistance|
|Written examination and Assignment(s)|
RemarkWeekly assignment in groups and individual written exam