ELE-3606 Control Engineering - 10 stp

Dynamic models:

• Mathematical modelling of linear dynamic systems
• Transfer functions and state space representations

Dynamic response for LTI systems:

• Superposition and time invariance
• Poles and zeros, and relation to stability and response
• Routh’s stability criterion with applications for trivial controller design

Feedback control for LTI systems:

• Open and closed loops
• System types and the effect of integral and derivative action
• PID and feedforward control

State space design:

• Canonical forms (CCF, MCF, OCF) and linear transformations
• Controllability and observability
• State feedback control for state space systems
• State estimators for state space systems
• The separation principle

Nonlinear system principles:

• Mathematical models for nonlinear systems
• Piecewise continuity and Lipschitz properties
• Nonlinear state transformations and diffeomorphisms
• Equilibrium points

Two-dimensional systems:

• Phase portraits
• Classification of equilibrium points using linearization

Stability of equilibrium points:

• Definitions of equilibrium point stability (stability, instability, asymptotic and exponential stability) and region of attraction
• Lyapunov functions
• Positive/negative (semi)definite and radially unbounded time-invariant functions
• Lyapunov indirect and direct methods for stability analysis
• The invariance principle
• Converse theorems

Time-varying and perturbed system:

• Comparison functions
• Positive/negative (semi)definite, radially unbounded and decrescent time-varying functions
• Definitions of equilibrium point stability (uniform stability)
• Lyapunov methods for analysing time-varying nonlinear systems
• Stability of perturbed systems
• Brief overview of boundedness, ultimate boundedness and input-to-state stability

State feedback stabilization:

• Definitions of stabilization (local, regional, global, semi-global, practical)
• Controller design for nonlinear systems (linearization, feedback linearization, integrator backstepping)
• Passivity and zero-state observability
• Passivity-based control

Robust state feedback design:

• Model dependency and robustness
• Robust controller design (sliding mode control)

A relevant undergraduate Bachelor degree in Engineering program in power electronics and electrical machines. Basic knowledge in power systems is also an advantage.

In addition, the following requirements must be met:

- minimum 25 credits in mathematics (equivalent to Mathematical Methods 1, 2 og 3), 5 credits in statistics and 7,5 ects i physics on a higher level is required.

Application code: 9371

After completing the course, the candidates will have the following learning outcome:

Knowledge

The candidate has knowledge of:

• general system configurations and control loops for LTI systems
• basic LTI modelling principles for selected system types, including transfer functions and state space representations
• basic LTI system principles, and the relation between pole placement and stability
• basic system configurations, system types and PID control for LTI systems
• state space models and canonical forms, controllability and observability, state feedback control and estimation, and the separation principle
• mathematical models for nonlinear systems and basic properties (piecewise continuity and Lipschitz, equilibrium points, diffeomorphisms)
• basic principles and classification of equilibrium points for 2D systems, and the notion of stability of equilibrium points
• stability properties for time-invariant nonlinear systems and the stability hierarchy
• stability properties for time-varying nonlinear systems and comparison functions
• stability and stabilization (local, regional, global, semiglobal and practical) and controller design methodologies
• robustness in controller design

Skills

The candidate can:

• model physical systems and derive transfer functions and state space models
• determine stability and final value outputs for LTI systems, and perform trivial control design using Routh’s stability criterion
• derive and transform between state space models, canonical forms and transfer functions
• determine controllability and observability for LTI systems
• design state feedback controllers and state estimators for LTI systems
• determine equilibrium points for nonlinear systems
• determine equilibrium point stability properties for nonlinear systems using linearization
• determine equilibrium point stability properties for time-invariant nonlinear systems using Lyapunov methods
• determine equilibrium point stability properties for time-varying nonlinear systems and perturbed systems using Lyapunov methods
• design controllers using linearization, feedback linearization, integrator backstepping and passivity
• design robust controller design using sliding mode

General competence

The candidate has a general competence on:

• application of control engineering
• choosing suitable model representations for different systems
• stability analysis with definitions and theorems
• choosing suitable methods for stability analysis for different systems
• choosing suitable controller structures and design methods for different systems
• Use of simulation tools (Matlab/Simulink) for analysis and simulation of linear and nonlinear systems (general for all modules)