Advanced Control

1. State space models of linear time-invariant (LTI) dynamical systems
- Mathematical modeling of lumped dynamical systems from physical laws
- Control tasks and controller structures
- Equilibria and stability
- Linearization
- Stability criteria for linear systems

2. Design of linear state feedback controllers in a two-degrees-of-freedom structure
- Eigenvalue placement
- Controllability and controller canonical form
- Ackermann's formula and parametric state feedback
- LQR optimal control

3. Design of linear state observers
- Observability and observer canonical form
- Duality between controller and observer design
- Separation principle
- Decoupling control and effect of zeros

4. Methods for disturbance rejection
- Disturbance model and disturbance observer
- Constant disturbance feedback
- Disturbance decoupling
- Effect of integral action

5. Extended controller structures
- Extensions of the 2 DOF controller structure, e.g. by dynamic feedforward control

6. Input-output linearization for SISO systems
- Relative degree
- Lie derivative
- Internal dynamics and stability

Upon successful completion of the module the students are able to
- represent real-world dynamical systems in state space form, determine their equilibria and to obtain linear state space models by linearization,
- compute the solutions of linear state differential equations and analyze the dynamical system for stability, observability and controllability.
- understand the purpose and advantage of a two-degrees-of-freedom controller structure,
- design feedforward controllers that guarantee zero output error in nominal steady state,
- design state-feedback controllers using the pole placement method and as a Linear Quadratic Regulator (LQR),
- design a Luenberger state-observer to reconstruct non-measurable states of the system,
- further modify the closed loop system by adding measures to cope with different disturbances,
- have a basic knowledge about the prerequisites and the application of nonlinear control by input-output linearization.

We require the students to have basic background in the field of automatic control and the necessary mathematical tools. The prerequisites are in general taught in
- undergraduate courses in higher mathematics dealing with basic linear algebra (matrix computations, eigenvalues, determinants,...) and complex numbers' theory.
- an undergraduate course in automatic control comprising the analysis of dynamical systems in time and frequency domain (Laplace transform, transfer functions, impulse responses, poles and zeros, stability, ), and the design of basic controllers (PID) in single-loop control systems.

The teaching follows a classical scheme of weekly lecture (90 min.) + exercise (45 min.), complemented by additional offers, which help the student to catch up quickly with the syllabus in the case of difficulties.
To achieve the study goals, the students are expected to prepare the lectures by a first reading of the announced sections in the lecture notes. They are supposed to try themselves to solve the problems posed in the exercises, before the solutions are presented in class and are made available online.
A set of additional problems is offered for homework. The solutions are also made available online and are presented in the weekly tutorial. This optional offer gives the opportunity to discuss problems and open questions related to the exercises.
The optional revision courses are additional opportunities to clarify open questions concerning the content of the lecture. Moreover, they allow to discuss topics and advanced questions that go beyond the scope of the course.
At the begin of the module, two recapitulation lessons are offered to review the required preliminaries on linear systems' theory.

The lectures and exercises will be written on the blackboard and supplemented with slides and handouts.
Typeset lecture notes, exercises, homework and solutions, as well as additional material, are available for download (moodle).

The lecture is self-contained. However, the following textbooks are recommended for the interested reader:

Very complete book about linear systems theory with a focus on fundamental properties and results:
[1] Antsaklis, P. J., Michel, A. N.: Linear Systems. Birkhäuser, 2006. – ISBN 9780817644352 In der TUM Bibliothek auch als E-Book vorhanden unter https://doi.org/10.1007/0-8176-4435-0
Classical textbook for linear systems analysis and controller/observer design in state space:

[2] Kailath, T.: Linear Systems, Prentice Hall, 1980. – XXI, 682 S. ISBN 0135369614.
In der TU Bibliothek vorhanden
Three textbooks that cover very broadly the topics of linear system modeling, analysis and control design, mainly in the frequency domain. Chapters about state space modeling, state feedback control and observer design. Many examples, problems and Matlab exercises:

[3] Dorf, R. C., Bishop, R. H.: Modern Control Systems. 13´th ed. – Harlow, England: Pearson, 2017. – 1025 S. ISBN 9781292152974.
In der TU Bibliothek vorhanden

[4] Franklin, G. F., Powell, J. D., Emami-Naeini, A.: Feedback Control of Dynamic Systems. 8. Ed. – New York: Pearson, 2020. In der TU Bibliothek auch als E-Book vorhanden unter https://ebookcentral.proquest.com/lib/munchentech/detail.action?docID=5834413

[5] Ogata, K.: Modern Control Engineering. – 5. Ed.- Boston (u.a.) : Pearson, 2010. ISBN 9780137133376
In der TU Bibliothek vorhanden

In a calculation part of the 90 min. written exam, which is oriented at the exercise problems and makes up about 2/3 of the achievable points, the students demonstrate their ability to
- model and linearize dynamical systems,
- analyze the properties which are important for control design and
- compute the different components of the controller structures for the control tasks considered in the course.

In a more theoretical part (approx. 1/3 of the achievable points), the students have to show their knowledge about
- the application of the mathematical tools that are used in the context of the course,
- the system theoretic properties of linear time invariant systems,
- the general setting of the presented state space control structures (goals, prerequisites, properties, realizations),
- the applicability of control methods in terms of system properties and
- short proofs of important facts about the analysis of LTI systems and the presented control design framework.

Some of these theoretical questions are formulated as multiple choice questions, in accordance with the examination rules.

Allowed material for the exam:
- One handwritten (DIN A4, double-sided) sheet of paper (“cheat sheet”)
- No calculators, computers and other electronic devices

Note: The contents and the learning outcomes to be examined of the modules MW1420 "Advanced Control" and MW0538 " Moderne Methoden der Regelungstechnik 1" are equivalent. “Advanced Control” is preferably offered for English speaking students. If both modules are integrated in degree programs, only one of the two modules can be completed for the degree. It is not possible to take the modules twice in order to improve grades (see APSO §24, paragraph 4, sentence 2).