# Regeltechniek onderwerpen

## Feedback Control Systems

• Mathematical Modeling
• Transfer Function and Block Diagram Models
• Transient and Steady-State Response Analyses
• Root-Locus Method and Design
• Frequency Response Method
• Control Systems Analysis in State Space
• Differential Equations of Physical Systems
• Signal-Flow Graph Models, State Variable Models
• Laplace, Fourier, and Z-Transform
• Stability, Nyquist plot, Bode plot

• Modeling of Physical Systems
• Bond Graphs
• Lagrangian
• Euler-Lagrange Equations
• Hamiltonian

• Convex optimization and linear matrix inequalities
• LQ optimal control and dissipativity
• Controller design and the H/H2 norm
• Behavioral system theory
• Alternative proofs and algorithms related to well-known results and theorems in system theory

## Modern Control Theory (State-Space Control)

• State-space description of multivariable linear dynamic systems, interconnections, block diagrams
• Linearization, equilibria, stability, Lyapunov functions and the Lyapunov equation
• Dynamic response, relation to modes, the matrix exponential and the variation-of-constants formula
• Realization of transfer matrix models by state space descriptions, coordinate changes, normal forms
• Controllability, stabilizability, uncontrollable modes and pole-placement by state-feedback
• LQ regulator, robustness properties, algebraic Riccati equations
• Observability, detectability, unobservable modes, state-estimation observer design
• Output feedback synthesis (one- and two-degrees of freedom) and separation principle
• Disturbance and reference signal modeling, the internal model principle

## Digital Control

• Discrete-time systems: Sampling of continuous-time signals, The sampling theorem, Aliasing
• The z-transform
• Selection of sampling-rate
• Analysis of discrete-time systems: Stability, Controllability, Reachability and Observability
• Disturbance: Disturbance models, Reduction of effects of disturbances, Stochastic models
• Discrete Design methods
• Discrete approximations of continuous systems
• Digital PID-controller
• State-space systems in discrete-time
• State-space design methods: Observers, Poleplacement, Optimal design methods, Linear Quadratic control, Prediction, LQG-control
• Implementation aspects of digital controllers

## System Identification

• Subspace Identification
• Parametric Identification

## Mechatronic System Design

• Dynamics of motion systems in the time and frequency domain, including analytical frequency transfer functions that are
represented in Bode and Nyquist plots.
• Electromechanical actuators, mainly based on the electromagnetic Lorentz principle. Reluctance force and piezoelectric
actuators will be shortly presented to complete the overview.
• Motion control in the frequency domain with PID and advanced fractional order PID-feedback and model-based feedforward
control-principles that effectively deal with the mechanical dynamic anomalies (resonances and eigenmodes) of the plant.
• Vibration control and active damping for mechatronics application.

## Nonlinear Control and Systems Theory

• Dynamical System Modeling: State-Space Models, Linearization of Nonlinear Models, Nonlinear Phenomena, Equilibrium Point, Differential-Algebraic Model Equations, From Rn to Manifolds
• Stability and Stabilization: Autonomous Systems, Stability and Instability, Asymptotic and Exponential Stability, Lyapunov’s Linearization Method, Local Versus Global Stability, Lyapunov’s Direct Method, Properties of Lyapunov Functions, Lyapunov Theorem for Local Stability, Lyapunov Theorem for Global Stability, Local and Global Invariant Set Theorem, Stabilization Based on Linearization, Stabilization using Lyapunov’s direct method
• Dissipative and Passive Systems: Introduction to  Dissipative and Passive Systems, Passivity and Stability, Hill-Moylan Conditions, Stability of Interconnected Passive Systems, Strict Output Passivation of Passive Systems
• Controllability and Observability of Nonlinear Systems: Lie Derivatives, Lie Brackets, Distributions, Integrability of Distributions, Controllability, Observability
• Feedback Linearization: Conditions for Feedback Linearization, Input-State Linearization, Input-Output Linearization

## Robust and Multivariable Control Design

• Multivariable system control: Nyquist, interaction, decoupling
• Directionality in multiloop control, gain and interaction measure
• Stabilizing controllers and the concept of the generalized plant
• Parametric uncertainty descriptions, approximations
• The general framework of robust control
• Robust stability analysis
• Nominal and robust performance analysis
• The H-infinity control problem
• The structured singular value: Definition of mu
• Mu synthesis, DK-iteration, role of uncertainty structure.
• Design of robust controllers, choice of performance criterion and weights