Nonlinear Robust Model Predictive Control
Lead Research Organisation:
Imperial College London
Department Name: Electrical and Electronic Engineering
Abstract
Relevance: Model Predictive Control (MPC) is a generic controller design methodology, involving on-line optimisation. MPC has already achieved a greater impact on industrial practice than any other modern control approach, because of its versatility and constraint handling capability. We can expect in the future to see increasingly sophisticated applications of MPC, as computer technology advances extends the scope for intensive on-line computations. This project will broaden the applicability of the MPC methodology, by providing new control algorithms to take better account of plant nonlinearities and modelling errors. Background: In many control engineering applications domains, chemical processing for example, the underlying plant dynamics are typically highly complex and the models used for controller design provide at best good approximations to the system response for a limited range of inputs and initial conditions. This is why robustness (the requirement that performance is not significantly degraded by model mismatch and the presence of unknown input signals or 'disturbances') is such a major issue in control systems design. Traditional MPC methodologies do not aim explicitly to achieve robustness. An important development in MPC design is the emergence of robust MPC algorithms. Prominent among the proposed approaches to robust MPC design are tube-based methods, developed for plants with linear models. Here, additional linear feedback (a 'robustifying inner feedback loop') is introduced to counter the effects of uncertainty and to confine the state trajectory within a narrow tube about the 'stable' trajectory that would be followed under a traditional MPC strategy alone, if there were no uncertainty. Proposed Research: The aim of this project is to design robust MPC algorithms based on fully non-linear plant models. The main idea behind the proposed design methodology is the introduction of an additional optimization stage into each controller update step, to replace the robustifying inner feedback loop of the linear tube-based method. A key advantage of this approach is that the on-line computational burden of implementing the new robust MPC algorithms is of the same order of magnitude as that required for traditional 'non-robust' MPC algorithms. (The solution to two similar optimization problems needs to be computed at each step, not one). There is therefore the potential to apply the algorithms to high dimensional plants (involving 20 or more state variables, say).The new algorithms will be provided with an analytical foundation, which will yield precise conditions for closed loop stability, and also assist in systematic selection of algorithm parameters governing tightness of tracking, transients and other aspects of closed loop response.A case study involving the control of a solar collector plant will be undertaken. This will permit the assessment, through simulations, of the new control design techniques in challenging, high-dimensional scenarios, where approximation of the plant model by a linear model, or a family of linear models ('gain scheduling'), is inadequate, and where it hard constraints of state and control variables need to be observed.
Organisations
Publications
Longo S
(2011)
A parallel formulation for predictive control with nonuniform hold constraints
in Annual Reviews in Control
Goodwin G
(2010)
An introduction to the control of switching electronic systems
in Annual Reviews in Control
Longo S
(2014)
Constrained LQR for low-precision data representation
in Automatica
Falugi P
(2014)
Getting Robustness Against Unstructured Uncertainty: A Tube-Based MPC Approach
in IEEE Transactions on Automatic Control
Spjøtvold J
(2008)
Inf-sup control of discontinuous piecewise affine systems
in International Journal of Robust and Nonlinear Control
Mayne D
(2011)
Jason L. Speyer and David H. Jacobson: Primer on Optimal Control Theory SIAM, 2010
in Journal of Optimization Theory and Applications
Rawlings James Blake
(2009)
Model Predictive Control: Theory and Design
Pannocchia G
(2010)
On Computing Solutions to the Continuous Time Constrained Linear Quadratic Regulator $ $
in IEEE Transactions on Automatic Control
Goodwin G
(2008)
Optimization opportunities in mining, metal and mineral processing
in Annual Reviews in Control
Title | None |
Description | Nominal entry |
Type Of Art | Artefact (including digital) |
Year Produced | 2010 |
Impact | Nominal entry |
Description | Model Predictive Control (MPC) is an approach to controller design, in which the updated control action is obtained by the solution, in real time, of an optimization problem, which incorporates the plant model and constraints on variables while penalising deviations from the desired trajectory to be tracked. It has had greater impact on industrial practice than any other modern control methodology. Early versions of MPC algorithms were found often to be unreliable when the plant model in the design only approximately captures the true plant behaviour. The principle aim of the project was to propose new, computationally efficient 'robust' MPC algorithms whose performance is less affected by modeling errors. The main achievement was to devise new robust MPC algorithms, within an analytic framework identifying the situations in which it would achieve important control objectives (closed loop plant stability, acceptable transient response, etc.), which reduce the computation time (compared with earlier 'iteration over policy space' algorithms) by an order of magnitude. The algorithms are 'generic' in the sense that do not depend heavily of the special features of the plant to be controlled, and therefore have the potential for widespread application. They were successfully demonstrated on a high dimensional simulation of a solar power extraction plant. The proposed algorithm, which was the culmination of many years of work by one of the investigators, Prof. David Mayne FRS, has had a large following in subsequent papers and conference presentations. Professor Mayne obtained two highly prestigious awards during the time he was working on the project: the 2009 IFAC High Impact Paper Award, and the IEEE Control Systems Award (Field Award), for his work on robust MPC. This grant terminated on 14/09/11. There are no further outputs to report. |
Exploitation Route | Robust MPC has the potential to improve the performance of controllers and achieve energy efficiency, in a multitude of areas, including aeronautical control, active suspension design, engine management and chemical processing Communication of research findings to other research groups, with a track record implementing MPC controllers for applications in the aeronautics, process control, mechanical control and other areas. Open access to a MATLAB toolbox, and supporting documentation, to provide easy access to the algorithms. The outputs have fed into a major EPSRC programme grant, in which MPC is a significant element |
Sectors | Aerospace, Defence and Marine,Energy,Transport |
URL | http://divf.eng.cam.ac.uk/cfes/Main/CfesResearch |
Description | ideas in numerous journal papers produced been taken up and further developed, for example, in the programme grant 'Control for Energy and Sustainability 'http://divf.eng.cam.ac.uk/cfes/Main/CfesResearch |
First Year Of Impact | 2009 |
Sector | Education |
Impact Types | Cultural |
Description | None |
Geographic Reach | Local/Municipal/Regional |
Policy Influence Type | Citation in systematic reviews |
Impact | This is a 'null entry'. The object of the grant was not to influence policy |
Description | EPSRC |
Amount | £5,490,976 (GBP) |
Funding ID | EP/G066477/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 09/2009 |
End | 03/2015 |
Description | European Union EU Brussels |
Amount | £591,000 (GBP) |
Funding ID | PITN-GA-2010-264735 |
Organisation | European Commission |
Sector | Public |
Country | European Union (EU) |
Start | 01/2009 |
End | 09/2014 |
Title | None |
Description | Nominal entry |
Type Of Material | Improvements to research infrastructure |
Provided To Others? | No |
Impact | Nominal entry |
Title | None |
Description | Nominal entry |
Type Of Material | Computer model/algorithm |
Provided To Others? | No |
Impact | Nominal entry |
Title | None |
Description | Nominal entry |
IP Reference | |
Protection | Copyrighted (e.g. software) |
Year Protection Granted | |
Licensed | No |
Impact | Nominal entry. The main outcomes of this research were ideas, publications etc., |
Title | None |
Description | Nominal entry |
Type | Therapeutic Intervention - Medical Devices |
Current Stage Of Development | Initial development |
Year Development Stage Completed | 2010 |
Development Status | Closed |
Impact | Nominal entry |
Title | Imperial College London Optimal Control Software (ICLOCS) |
Description | The code allows users to define and solve optimal control problems with general path and boundary constraints and free or fixed final time. It is also possible to include constant design parameters as unknowns. ICLOCS is implemented in MATLAB. It includes the ability of using the nonlinear optimization code Ipopt and the SUNDIALS ODE solver CVODES for sensitivity analysis. |
Type Of Technology | Software |
Year Produced | 2010 |
Open Source License? | Yes |
Impact | Used by universities in the UK and abroad to compute optimal controls |
URL | http://www.ee.ic.ac.uk/ICLOCS/ |
Description | 50 years of Nonlinear Control and Optimization |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Participants in your research and patient groups |
Results and Impact | Workshop at Royal Society to celebrate and promote the research of Professor D Q Mayne, an investigator on the grant Stimulus to further research in model predictive control |
Year(s) Of Engagement Activity | 2011 |
Description | Constrained control |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Participants in your research and patient groups |
Results and Impact | Invited seminar in "Symposium on Systems and Control Theory" in honour of Jozsef Bokor on his 60th birthday. Stimulus to further research in control engineering |
Year(s) Of Engagement Activity | 2009 |
Description | Model Predictive Control: Achievements and Challenges |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Participants in your research and patient groups |
Results and Impact | The Wittenmark Symposium on Control (in honour of Bjorn Wittenmark on his 65th birthday), Lund University, Lund, Sweden. Eventy to mark retirement of major figure in control engineering research in Sweden Stimulated interest in David Mayne's research |
Year(s) Of Engagement Activity | 2008 |
Description | Robust Model Predictive Control |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Participants in your research and patient groups |
Results and Impact | Invited seminar at the Department of Computing, Imperial College London. Stimulated interest in Professor Mayne's recent research |
Year(s) Of Engagement Activity | 2010 |
Description | The role of model predictive control |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Participants in your research and patient groups |
Results and Impact | Invited Seminar in "Second Monterey Workshop: Computational Issues in Nonlinear Control", Naval Postgraduate School, Monterey, CA, USA. publicised Professor Mayne's research in roust model predictive control |
Year(s) Of Engagement Activity | 2011 |
Description | Tube-based robust nonlinear model predictive control |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Participants in your research and patient groups |
Results and Impact | Invited talk at Institut fuer Systemtheorie und Regelungstechnik, Universitaet Stuttgart. This invited talk in a leading Germain university working in control stimulated interest in Professor Mayne's recent research |
Year(s) Of Engagement Activity | 2009 |
Description | Tube-based robust nonlinear model predictive control |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Participants in your research and patient groups |
Results and Impact | Dr Falugi gave a talk about her work on the grant the "BELS control meeting" in London. Regular day of talk for UK control research community to share ideas. Much interest on part of delegates Raised level of interest in the research presented |
Year(s) Of Engagement Activity | 2011 |