Model-Based Control: A Practical Approach

This part of the workshop focuses on concepts rather than mathematical detail; a good graduate who understands the concepts properly will find the mathematics and effective design choices are largely self-evident.
This talk starts by looking at examples where a simple classical feedback approach fails and these form the motivation for more advanced strategies. Human approaches are dissected to gain an understanding of the core components and these insights are used to frame what is now commonly known as model predictive control. These insights are also used to outline some ‘best practice’ guidance in the implementation of predictive control.

Having set up the core concepts underlying MPC, the next talk focuses on the mathematical and programming aspects, that is, how we implement this thinking in practice. Nevertheless, the talk aims to focus on core assumptions and principles rather than going through the fine details of the algebra. Having defined the basic algorithm, the talk then moves to what appears a contradictory statement which is a warning to naïve users: why does an off-the-shelf MPC algorithm often fail to perform well? This is supplemented with numerous MATLAB illustrations.

The previous talk finished by emphasising that one can easily tune MPC poorly and users need to follow good guidance and understand the repercussions of different choices. This section begins by giving a large number of illustrations which demonstrate the conceptual thinking behind different choices and hence why some choices are good and others are bad. This section finishes with some outline guidance for systematic but simple tuning.

A core reason for using MPC is the ability to incorporate constraint handling into the controller design systematically rather than using ad hoc post-design rules. This brief segment reiterates why that is important and introduces concisely the algebra required to do this for a GPC type of law. Constraint handling for dual-mode and other laws requires some modifications which will be largely self-evident but is not covered explicitly here.

The talk on tuning may have raised many questions about whether we can avoid issues link to poor choices by a better initial design. The answer is provided here as dual-mode MPC approaches are introduced. However, it is also noted that while these have much better analytical properties, they are often ignored by industry due to the increased complexity and potential feasibility issues.

All real systems are non-linear and yet most control strategies are based on linear modelling assumptions, largely because many systems work in a relatively tight operating range for which a linear approximation is accurate enough. However, what if that is not the case? A good property of MPC is that the extension to the non-linear case is straightforward and systematic, but of course at the price of increased mathematical and computing complexity. This brief segment introduces the basic concepts of how a nonlinear MPC algorithm can be defined. Code is not provided as good code for NL MPC requires significant expertise to develop and is largely in the realm of a few specialists; you only go this route if the performance benefits are significant.

Workshop 1 – MPC design for a flotation plant.
Workshop 2 – Build a simulator of the flotation system (software provided – bring a laptop).

The modelling updates will cover nonlinear elements, such as piece-wise linear, nonlinear steady-state and even nonlinear economic objective functions, which capture the flotation performance.

Attendees might like to know that MATLAB online is now free to use for those without a license and this also allows some memory space where personal files can be stored.
https://uk.mathworks.com/products/matlab-online.html

The workshop files are in a zip file and largely users can simply run and edit the script files directly as will be demonstrated during the workshop. The variables are defined within the script files in what we hope is an intuitive manner. However, these files are deliberately simple and transparent for illustrative/educational purposes; hence they are not written to be robust against poor user choices and other possible errors such as infeasibility. A wider range of MATLAB files associated to the author’s book (A First Course in Predictive Control, 2018, Taylor and Francis) are also included in the zip file in a separate subfolder on the same webpage. Explanation of these is within the book but largely the ‘example’ files illustrate how to run and use the more complicated files.

https://sites.google.com/sheffield.ac.uk/controleducation/mainindex
(See chapter 8, end of page)

TBC