Optimal Control

11M1270

Master

German, English

5.0

only summer term

1 semester

Classic control engineering methods were developed for linear systems. In addition to being partly heuristic, these methods have the disadvantage that they cannot explicitly take into account control variable constraints, which always exist in practice. Optimisation approaches were therefore developed as early as the 1960s to address these issues. However, the practical implementation of these methods has only been possible since the 1990s. In addition to fast computers, new fast algorithms were particularly crucial for this. Today, optimisation methods are an indispensable part of process control. Optimal identification methods are already used in data-based modelling. The control and disturbance behaviour of the control loop can be addressed using methods to achieve optimal control quality or by considering worst-case scenarios. Finally, model predictive control makes it possible to take control variable constraints into account through optimisation over moving time horizons in a way that can also be transferred to real-world process control applications. The lecture aims to provide an overview of the fundamentals of optimisation and the corresponding algorithms, as well as their application in exemplary process control problems.

1. Mathematical foundations of constrained and unconstrained optimisation
2. Numerical foundations of optimisation
3. Special algorithms (in particular SQP)
4. Applications: identification, optimal estimation methods (Kalman filter), optimal control and regulation (time optimality, optimal control quality), model predictive control

The total workload for the module is 150 hours (see also "ECTS credit points and grading").

• Written examination or
• oral exam or
• Project Report, written

• Field work / Experimental work

by choice of lecturer

Graded examination performance:

• Written examination: see applicable study regulations
• Oral examination: see general section of the examination regulations
• Project report (written): 5-minute presentation, paper: 10–20 pages

Ungraded examination performance:

• Experimental work: Experiment: approx. 6 experiments in total

Fundamentals of mathematics as typically taught in the first two semesters of a science or engineering degree programme.

Fundamentals of control engineering as typically taught in an engineering degree programme.

Graduates are familiar with the key issues involved in optimisation and are able to apply exact and numerical solution methods. They are familiar with the main applications in process control and are able to develop appropriate solution methods.

Graduates are able to select process optimisation methods tailored to specific problems and can use appropriate software tools to solve problems.

Graduates are able to classify current scientific literature on process control and apply it to new technical applications.

• Rehm, Ansgar

• Rehm, Ansgar