Examination arrangement

Course content

The course will cover mathematical designs of robust and nonlinear model-based control laws and observer algorithms applicable to automatic control of ships, underwater vehicles, marine structures, machinery and propulsion systems, and other marine applications. The overall course will be based on lectures, theory and simulation assignments, and a project of practical marine problems - the Dynamic Positioning Lab (DP-Lab) in MC-Lab (if resources are sufficient).

The course consists of lectures on nonlinear systems theory and nonlinear robust control and observer designs, such as:

1. Stability theory for nonlinear systems.
2. Observer and estimation theory, persistency of excitation, observability, etc.
3. Observer designs (linear and nonlinear observers, separation principle).
4. Robust nonlinear control methods (backstepping methods, nonlinear PID and integral control, ISS designs, etc.).
5. Dynamic Positioning (DP) control system algorithms for thrust allocation, positioning control, and DP observer designs.
6. Maneuvering control theory and path-following control designs for marine vessels (path parameterization, path generation, guidance theories, and feedback control laws).

Learning outcome

At the end of the course, the student shall be able to:

• Draw the typical topology of a feedback control system and translate each component and the interconnections to a set of ordinary differential equations (ODEs).
• Describe properties of solutions of time-invariant and time-varying ordinary differential equations.
• Characterize local, global, uniform, and asymptotic stability properties of nonlinear systems in the sense of Lyapunov and related theorems.
• Discuss the most common types of control objectives, define the concept of a Control Lyapunov Function (CLF), and apply a CLF-based methodology to design a control law according to a defined problem statement.
• Relate bounded perturbations to input-to-state stability (ISS) of a nonlinear system and convert this into equivalent bounds for the Lyapunov function.
• Discuss safety objectives in the state space, define the concept of a Control Barrier Function (CBF), and apply a CBF to synthesize safeguarding controls.
• Explain the difference between minimum phase and non-minimum phase systems, what zero dynamics is, and calculate the relative degree of nonlinear systems.
• Explain the concept of uniform complete observability, demonstrate how to design a Luenberger observer for a linear system, and explain the separation principle.
• Demonstrate how to design state observers to fuse and filter measurements and reconstruct unmeasured states, e.g. the velocity state of a marine vehicle.
• Demonstrate how to design control laws based on feedback linearization, backstepping, and robust nonlinear control laws with integral action.
• Apply Control Barrier Functions (CBFs) to design safeguarding control laws that ensure the state of the nonlinear control system never leaves specified safe subsets of the state space.
• Formulate a control objective as a maneuvering problem and design a corresponding maneuvering control law.
• Explain concepts related to autonomous ships navigating in marine traffic.
• Use nonlinear control theory, relevant control design method(s), and observer design method(s) to design, implement, and test a Dynamic Positioning control system for a model ship, including thrust allocation, joystick control, DP state observer, DP control law, and a guidance system functionality.
• To carry out project work in teams; deduce theoretical solutions to practical marine control problems, implement algorithms in a real control system, perform simulations and laboratory testing, and write up the results in a report with a clear and concise exposition of control problem, control design, and resulting (closed-loop) performance.
• Maintain personal integrity by conducting academic studies and written works in an honest and ethical manner, without any sort of plagiarism or misconduct in work assignments, projects, and examinations.

Learning methods and activities

Lectures, exercises, and a project to put the control theories into practice. The course will include exercises and, if resources are sufficient, a laboratory activity on Dynamic Positioning, as a control system case study, in the Marine Cybernetics Lab (MC-Lab) using a free-floating model ship - we call it the DP-Lab. The students will then work on these lab setups to gain hands-on experience with practical implementation of control/observer algorithms using ROS with nodes coded in Python. The alternative, if lab resources are insufficient or facilities are not available, is a simulation-based project. The project work shall result in a project report and presentation that will count as a part in the final grade in addition to the exam.

Compulsory assignments

• Laboratory work

Further on evaluation

The basis for the grade in the course includes project work with a report and group presentation, and final written (possibly digital) exam. The result for each part is given a letter grade A-F, which is combined into an overall letter grade. Each partial assessment must be passed to pass the course. Postponed/repeated exams are typically also written, but may be oral.

Recommended previous knowledge

It is recommended to study this course in series with TMR4240 Marine Control Systems I.

Required previous knowledge

Required prerequisites:

• TTK4105 Control Engineering (or equivalent).

Course materials

Textbooks:

• Khalil, H. K. (2015). Nonlinear Control, Global edition, Pearson Education Ltd, England.
• Alternatively the more extensive "Nonlinear Systems" by H.K. Khalil, 3rd ed. Prentice Hall, 2002.

Other: Lecture notes, digital lecture videos, and selected articles, reports, and theses.