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# Marine Control Systems II

Language

English

Course format On-site
Date 2021-01-11 - 2021-05-07

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 period with practical marine laboratory exercises.

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).

## Prerequisites

TTK4105 Control Engineering and TMR4240 Marine Control Systems I (or similar) are required prerequisites.

##### Recommended previous knowledge

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

## Learning outcomes

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

• Describe conditions for existence, uniqueness, and completeness of solutions of time-invariant (autonomous) and time-varying (nonautonomous) 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 the nonlinear system and convert this into equivalent conditions for the Lyapunov equations.
• 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 (nonlinear) 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.
• Explain the difference between direct adaptive control and indirect adaptive control and understand the equivalence between observability and persistency of excitation in order to achieve convergence of adaptive parameter estimates. Demonstrate how to design an adaptive control law based on backstepping.
• Formulate a control objective as a maneuvering problem and design a corresponding maneuvering control law.
• Use basic nonlinear control theory and relevant control design and observer design method(s) to design, implement, and test a Dynamic Positioning control system for a model ship, including a DP observer, thrust allocation, DP control law, and a guidance functionality.
• To carry out laboratory work in teams, solve practical marine control problems, and to write up the results in a report with a clear and concise exposition of results, critical analysis, and conclusions.
• Maintain personal integrity by conducting academic studies and written works in an honest and ethical manner, without any sort of plagiarism and misconduct in work assignments and projects.

## ISCED Categories

Scientific modelling
Machinery and operators