All programmes > Optimization of Mechatronic Systems

Optimization of Mechatronic Systems (B-KUL-H04U1C)

6 ECTSEnglish50 First termCannot be taken as part of an examination contract
Decré Wilm (coordinator) |  Patrinos Panos |  N. |  Decré Wilm (substitute)
POC Werktuigkunde

Aims

The course gives insight into the mathematical formulation of optimization problems and deals with advanced methods and algorithms to solve these problems. The knowledge of the possibilities and shortcomings of these algorithms should lead to a beter understanding of their applicability in solving concrete engineering problems. An emphasis will be placed on mechatronic systems: the student learns to select the appropriate solving methods and software for a wide range of optimization problems from the field of mechatronics, and learns to correctly interpret the results.

The following knowledge and skills will be acquired during this course:

  • The student will be able to formulate a mathematical optimization problem starting from a concrete engineering problem.
  • The student will be able to classify optimization problems into appropriate categories (e.g., convex vs. non-convex problems).
  • The student will be familiar with different optimization strategies and their properties, and will hence be able to decide which strategy to use for a given optimization problem.
  • The student will be able to formulate the optimality conditions for a given optimization problem.
  • The student will have a profound understanding of a wide variety of optimization algorithms and their properties, and will be able to apply the appropriate algorithms for a given optimization problem.
  • The student will be familiar with state-of-the-art optimization software packages, and will be able to use these in an efficient manner.
  • The student is able to independently define and solve practical optimization problems for mechatronic systems (e.g. trajectory optimization, motion control, vibration reduction). To this end he is able to formulate a mathematical model of the mechatronic system, the objective function and the constraints (e.g. in terms of position/velocity/acceleration, actuation limits, technological limits). While doing this he is able to make simplifying assumptions, and to make these assumptions explicit.
  • Based on the mathematical formulation the student is able to recognize the nature of the optimization problem, select an appropriate numerical solution technique and apply this solution technique using existing software packages.
  • The student is able to verify the validity of the obtained results, and is able to critically evaluate and interpret the results (e.g. obtained accuracy, required calculation time) based on physical insight in light of the assumptions made.

Previous knowledge

Skills: the student should be able to analyze, synthesize and interpret.

Knowledge:

  • Basic knowledge of analysis, numerical mathematics, and numerical linear algebra.
  • Basic knowledge of systems and control, kinematics and dynamics of machinery, mechanical vibrations and electrical machines, as introduced in the subjects H01N0A, H01L8A and H01F7A or equivalent.

Is included in these courses of study

Activities

4 ects. Optimization: Lecture (B-KUL-H03E3a)

4 ECTSEnglishFormat: Lecture30 First term
Patrinos Panos
POC Wiskundige ingenieurstechnieken

Content

1. Introduction
- a number of motivating examples (control, fitting, planning)
- mathematical modelling of optimization problems
- the importance of convexity
- classification of optimization problems
2. Algorithms for continuous optimization without constraints
- the two basic strategies: line search or trust region techniques
- gradient-based techniques: the steepest gradient and the added gradient method
- Newton and quasi-Newton techniques
- special methods for non-linea least square problems
3. Algorithms for continuous optimization with constraints
- the KKT-optimization conditions
- algorithms for linear problems: simplex-method and primal-dual interior point method
- algorithms for quadratic problems: active-set technique and interior point method
- convex optimization: formulation, the concept duality, algorithms
- general non-linear optimization (penalizing and barrier techniques, connection to interior point algorithms)

4. Introduction to global optimization methods
- deterministic methods (branch and bound, ...)
- stochastic and heuristic methods (Monte Carlo methods, simulated annealing, evolutionary algorithms, swarm-based algorithms,...)

5. Software
- discussion of the possibilities of the most current optimization software-packages
- sources on the internet: the Network Enabled Optimization Server

Course material

Study cost: 1-10 euros (The information about the study costs as stated here gives an indication and only represents the costs for purchasing new materials. There might be some electronic or second-hand copies available as well. You can use LIMO to check whether the textbook is available in the library. Any potential printing costs and optional course material are not included in this price.)

- Numerical Optimization, J. Nocedal and S. Wright, Springer, New York, 1999.
- Optimization Software Guide, J. Moré and S. Wright, SIAM, Philadelphia, 1993.

Is also included in other courses

2 ects. Optimization of Mechatronic Systems: Exercises and Laboratory Sessions (B-KUL-H04U1a)

2 ECTSEnglishFormat: Practical20 First term
N. |  Decré Wilm (substitute)
POC Werktuigkunde

Content

1) guided exercise sessions on:

  • appropriate formulations of problems as (convex) optimization problems
  • working out and applying numerical optimization techniques such as Gauss-Newton methods, sequential quadratic programming, interior point algorithms...
  • optimal control and algorithmic differentiation

2) independent project work: formulate and solve a mechatronic optimization problem (individually or in a group of two students)

Course material

- Numerical Optimization, J. Nocedal and S. Wright, Springer, New York, 1999.
- Optimization Software Guide, J. Moré and S. Wright, SIAM, Philadelphia, 1993.

Evaluation

Evaluation: Optimization of Mechatronic Systems (B-KUL-H24U1c)

Type : Exam during the examination period
Description of evaluation : Oral, Written
Type of questions : Open questions
Learning material : List of formulas, Calculator

Explanation


Evaluation method:

  • Evaluation of the OLA “Optimization: lecture”: written exam.
  • Evaluation of the OLA “Optimization of mechatronic systems: exercises and laboratory sessions": oral exam based on independent project work.

Grading:

The OPO grade is calculated as a weighted sum of the OLA grades, using the number of ECTS credits for each OLA as a weighting factor.