MMH626810-22-B Model Predictive Control Assignment

Structure of the CW:

Structure your CW as follows:

1. Title:

• Choose a descriptive and accurate title that clearly reflects the content of your work.
• Avoid using technical jargon or abbreviations that might not be familiar to your audience.
• Make your title engaging and attention-grabbing by using active language and focusing on the most interesting aspect of your research.

2. Abstract:

• Keep your abstract concise, typically between 150-250 words.
• Clearly and succinctly summarize the main objectives, methods, and results of your research.
• Use clear and simple language that is easy to understand for a general audience.

3. Introduction:

• Begin with a brief background of the topic and explain why it is important and relevant.
• Clearly state the research question or hypothesis that you aim to answer.
• Provide an overview of existing literature and how your research builds upon it.
• Explain the scope and limitations of your study, as well as the methodology and techniques used.
• End the introduction with a clear and concise thesis statement that summarizes the main argument or contribution of your work.

4. Problem Definition:

• Clearly define the control problem and explain why it is important.
• Provide a formal definition of the dynamical system you are studying and the variables and parameters involved.
• Define any constraints, requirements, or objectives that must be satisfied by the system.
• Use clear and consistent notation throughout your work and provide units for all variables and parameters.

5. Main Body:

• Organize your main body into logical sections and subsections that address different aspects of the problem.
• Clearly state the purpose and main ideas of each section in the opening paragraph.
• Provide clear and detailed explanations of the methods and techniques used to solve the problem.
• Use appropriate visual aids such as diagrams, charts, and graphs to enhance your explanations and clarify your results.
• Use clear and concise language that is easy to understand, avoiding unnecessary jargon or technical terms.
• Make sure that each section builds on the previous one and logically leads to the next.

6. Conclusion:

• Summarize the main findings and conclusions of your research in a clear and concise manner.
• Restate your thesis statement and explain how your work has contributed to solving the problem.
• Highlight any limitations or weaknesses of your study and suggest future research directions.
• End with a strong and memorable concluding statement that leaves a lasting impression on the reader.

7. Appendix:

• Include any supplementary materials or data that are relevant to your research but not essential to the main body.
• Label each appendix clearly and refer to it in the main body when necessary.
• Make sure that all data and information presented in the appendix are accurate and relevant to your research.

Coursework Assignment

Dig into the literature carefully and find a linear/nonlinear system which has at least 1 disturbance input, w, 1 control input u, 3 states, x and 1 output, y, which can be represented as
x? = Ax + Bu + Hw
y = Cx + Du + Ew
after the linearisation.

Once you have decided on a system, please share that information with me by explicitly providing me with a reference to the source. This needs to be done ASAP before you start working on your CW

1. Considering the system matrices, comment on the open-loop stability, stabilisability and detectability of the system. Choose a reasonable sampling time, Ts, prediction horizon N for the system and create a discretised state-space model of the sampled system. (10 points)
2. Assuming all control, state and output constraints are in place, design a full state feedback MPC for the system which minimises the effects of disturbances on the controlled outputs. Compare the performance of the controller with the uncontrolled system if the open-loop system is stable. (15 points/ 10 points if MPC toolbox is used)
3. Assuming all control, state and output constraints are in place, design an observer based MPC for the system which minimizes the effects of disturbances on the controlled outputs. Compare the performance of the controller with the uncontrolled system if the open-loop system is stable. You might use either Luenberger Observer or a Kalman observer. (15 points/ 10 points if MPC toolbox is used)
4. Assuming that there are no constraints on control, state and outputs, design a full state feedback MPC for the system which minimizes the effects of disturbances on the controlled outputs. Compare the performance of the controller with the uncontrolled system if the open-loop system is stable. (15 points/ 10 points if MPC toolbox is used)
5. Assuming that there are no constraints on control, state and outputs, design an observer based MPC for the system which minimizes the effects of disturbances on the controlled outputs. Compare the performance of the controller with the uncontrolled system if the open-loop system is stable. You might use either Luenberger or a Kalman observer. (15 points/ 10 points if MPC toolbox is used)
6. Choose a suitable control method (e.g. PID, LQR, LQG, adaptive control, etc.) that would fit your system’s structure and compare its performance to that of MPC you obtained in Q3. (15 points/ 10 points if MPC toolbox is used)
7. 15 points are reserved for the general structure, organisation and quality of communication of technical knowledge.

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