Sensitivity-based NMPC with Delayed Optimization

Victor M. Zavala and Lorenz T. Biegler
Chemical Engineering Department
Carnegie Mellon University
Pittsburgh, PA USA 15213
{vzavala, lb01}@andrew.cmu.edu

Recently developed strategies for fast Nonlinear Model Predictive Control (NMPC) are discussed and refined. Based on the concept of nonlinear programming (NLP) sensitivity, the approach solves the moving horizon NLP problem in background and updates the solution through a perturbed problem that incorporates the most recent state estimate. This approach shares many advantages with the real-time iteration approach of Diehl and coworkers. However, here it is applied to a simultaneous, collocation-based approach with a full space NLP solver. In particular, the controller is easily updated using straightforward sensitivity calculations from the full-space KKT system at the NLP solution. This study considers three variants of this NMPC approach (shifted, nonshifted and delayed) and provides nominal and robust stability properties through a well-known Lyapunov-type analysis.  The approach is demonstrated on several process examples; on-line calculations are reduced by over two orders of magnitude without significant losses in controller performance.
 

Lorenz T. (Larry) Biegler is currently the Bayer Professor of Chemical Engineering at Carnegie Mellon University, which he joined after receiving his PhD from the University of Wisconsin in 1981. His research interests are in the areas of computer aided process analysis and design and include flowsheet optimization, optimization of systems of differential and algebraic equations, reactor network synthesis and algorithms for constrained, nonlinear process control.  Prof. Biegler has been a visiting scholar at Northwestern University, a scientist-in-residence at Argonne National Lab, a Distinguished Faculty Visitor at the University of Alberta, a Gambrinus Fellow at the University of Dortmund and a Fulbright Fellow at the University of Heidelberg.  He has authored or co-authored over 200 archival publications, authored or edited seven books and presented numerous conference papers.

 

Nonlinear Model Predictive Control  over Networks With Guaranteed Stability
 

Rolf Findeisen

IST, University of Stuttgart, Germany

 

Significant advances in the area information technology have lead by to a widespread use of non-deterministic data networks for control purposes over the recent years. While the use of such networks is often very cost efficient and does lead to an increased flexibility, it also holds a series of control challenges such as loss of information due to package losses in the communication channel, or variable delays. Delays and package losses often degrade the performance of the control loop significantly or might lead to instability. In the frame of this talk we outline some of the appearing challenges and show how one can guarantee closed loop stability of nonlinear model predictive control subject to variable delays and package losses.

 

 

Rolf Findeisen is Habilitand (equivalent to assistant professor) and lecturer at the Institute for Systems Theory in Engineering at the University of Stuttgart. His main research areas are: nonlinear model predictive control, output feedback control, optimization based control and state estimation, differential algebraic systems, nonlinear control, system theoretical methods in biomedical engineering and biological systems; and the application of these methods in  chemical, biological and mechanical systems.

 

 

 

 

Why is it worth thinking about "robust" in "robust predictive control"?
 

Eric Kerrigan

Imperial College London, U.K.

The main benefit from implementing a feedback control scheme is to minimize the effect of model uncertainty and disturbances on a controlled system. Though model predictive control is a feedback control method, the effect of model uncertainty and disturbances is not explicitly incorporated into most commercially available schemes. This has important consequences for closed-loop operation, especially for plants that are difficult to control, such as unstable and non-minimum phase plants or plants where the nonlinearity is significant. This talk will look at a couple of examples that illustrate why standard predictive controllers may be highly sensitive to model mismatch and disturbances, thereby complicating the design and implementation. We will show how a simple modification to the original formulation can robustify the predictive controller, such that the closed-loop performance is guaranteed to degrade gracefully in the presence of model mismatch or disturbances. The resulting optimization problem is only slightly more complicated than the original, non-robust formulation, but this small increase in computational cost is outweighed by the resulting improvement in closed-loop performance.

 

 

Eric Kerrigan is a Lecturer and Royal Academy of Engineering Research Fellow at Imperial College London, where he has a joint appointment in the Department of Aeronautics and the Department of Electrical and Electronic Engineering. He received a BSc(Eng) in Electrical Engineering from the University of Cape Town in 1996, and a PhD in Control Engineering from the University of Cambridge in 2001. During 1997 he was with the Council for Scientific and Industrial Research (CSIR), South Africa and from 2001 to 2005 he was a Research Fellow at the Department of Engineering, University of Cambridge. His research interests include optimal and robust control of dynamic systems with constraints, predictive control, dynamic optimization and applications of control in fluid mechanics and aerodynamics.

 

 

 

Industrial applications of predictive functional control


J. Richalet1, H. Luft2  

1Founder of ADERSA; 2Degussa, Germany

The PFC principles were established in 1968, and the first commissioned industrial applications took place in 1973. (distillation / reactors / furnaces). The monovariable PFC control strategy was voluntarily designed to be accessible to classical PID users. Based on First Principles or Black Box models, PFC is able to take into account constraints on the manipulated variables (MV) and state variables. The future MV is selected in a Functional Basis (most of the time polynomial expansion), so that there is no lag error on polynomial set points. The computation of the MV does not use matrix calculus neither quadratic minimisation. Its field of application is beyond what PID cannot achieve and concerns, either slow processes in production industries, or fast processes like in mechanical or defence systems. If the interest of Predictive control was strong in the Petroleum industry at the beginning of the 70s, there is now a growing interest in heat exchange based industries: like chemical, pharmaceutical, furnaces, food, drying, air conditioning etc.. The batch reactor in Chemical Industry is a typical example. Many reactors, in different countries are now under PFC control, either by acting on the temperature, the flow or the enthalpy of the jacket fluid. On line dynamic estimators of the exothermic reaction by an inverse PFC have a significant interest. Several examples of varied industrial applications will be presented, with their technical / economic results, and with their short pay-out times.

 

 

 

Jaques Richalet was born in Versailles, France, in 1936. He studied aeronautical engineering at ENSAE in Paris and graduated in 1960. He then went to Berkeley, USA, where he obtained his MSc degree under the guidance of Prof. Zadeh. Back in Paris he worked in the field of applied mathematics and received his PhD in 1965. his interest in model based predictive control started as early as 1968. In the same year he founded the process engineering consulting company ADERSA with a major breakthrough being the first commissioned application of model based predictive control to a binary distillation column in 1973. Since then he has been active in the areas of process identification, modelling and diagnosis methods such as predictive maintenance. Applications range from petro-chemical and food industry to faster systems as encountered in the automotive and defense sector. He was a manager of ADERSA till 2001 and is still working as a consultant for modelling and predictive control. In his academic career he published more than fifty articles as well as three books on identification and predictive control. He has been president of the National Committee of Automatic Control and chairman of EEC Interest Group "CIDIC". For his achievements he was awarded the status as Chevalier de l'Ordre National du Merite and many researchers would probably agree to call him the "grandfather of predicted control". Biography of J Richalet

 

 

 

Applications of NMPC to industrial batch processes

 

Tor Steinar Schei

Cybernetica AS, Norway 

 

 

 

Tor Steinar Schei was born in Norway in 1959. He received the Siv. Ing. degree (MSc) in electrical engineering from The Norwegian University of Science and Technology (NTNU) in Trondheim in 1983. He received the Dr. Ing. degree (PhD) in Engineering Cybernetics from the same institution in 1992. From 1983 to 1984 he served as a scientific assistant at NTNU and as a teacher in the Norwegian Navy. He worked at Statoil Research Centre in Trondheim from 1984 to 1985. From 1985 to 2000 he was employed as Research Scientist, Senior Scientist and Chief Scientist at SINTEF in Trondheim. His work at SINTEF included industrial process control in general and particularly the application of nonlinear model predictive control, estimation and tuning techniques to the process industry. In 2000 he co-founded the company Cybernetica AS together with colleagues from SINTEF and NTNU. Cybernetica provides systems for model based control, supervision and optimization of industrial processes. The company is in particular focusing on the development and implementation of model predictive control solutions based on first-principles models. Tor Steinar Schei is Technical Director and Chairman of the Board at Cybernetica.