Predictive control (MPC) is by now a well-established methodology whereby one bases the design of the control law on the optimisation of system predictions. This allows both constraint handling, interaction and performance to be included systematically and thus has proved hugely successful in industry, but mostly on large scale problems where small improvements in performance result in significant gains in profit. The most significant barriers to wider application are the cost and complexity and thus MPC application in many lower cost applications where clear benefits could accrue is still somewhat limited. This statement is even more pertinent for non-linear systems where the computational complexity of implementing MPC can be substantial. There are a number of different avenues that could be pursued which would simplify a predictive control algorithm, making it simpler to understand and implement, but two gaps of core interest to researchers in Sheffield are simplicity of concept and simplicity of implementation: the first requires that the control law is easy to understand and tune for operators and the second, that it is easy to code and maintain, once installed.
The core concepts in predictive control are how the performance objective and how the degrees of freedom in the control design are defined. Changing these definitions can make the algorithm very high performance but computationally demanding and expensive, or conversely, much simpler but with slightly less optimal performance. In a similar way, changing the parameterisation of the degrees of freedom can have a significant impact on computational loading and complexity, for an algorithm with the same expected performance. There are multiple possible aims that students interested in this area could pursue and all are of interest to the workers in Sheffield. A few are listed next, but the list is not exclusive:
1. A focus on applications and demonstrating code that works effectively in practical scenarios (current students are looking at applications to additive manufacturing and previous students looked at embedding on low cost computational hardware).
2. A focus on theoretical developments (current students have focussed on non-linear MPC, modernising the PFC algorithm and tailoring the approach for wave energy applications).
3. Computational efficiency (a recent student focussed on how to exploit different parameterisations to vastly simplify and speed up non-linear MPC).
4. Modifications and extensions to deal with uncertainty in a conceptually and computationally simple way (the current project on additive manufacturing is considering one means of doing this).
These projects are self-funded which means students can negotiate with the supervisor over the detailed aims and objectives to be pursued to meet their own career development ambitions. It is also worth noting that it is common place within the department, but not mandatory, for the projects to have a second supervisor who brings additional and specific application expertise into a project (such as additive manufacturing).
We accept any students with a strong engineering background into the group, although some prior knowledge of control and a strong aptitude for mathematics and programming are an advantage.
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