Pavel Trnka

Structured Model Order Reduction of Parallel Models in Feedback

Parallel working units in closed-loop operation are frequently encountered in industrial applications of advanced process control (boilers, turbines, chemical reactors, etc.). Control strategies typically require different low-order models for each configuration of parallel units. These different models are usually obtained by heuristics applied to the parallel models. To replace these heuristics, this paper proposes a systematic solution based on structured model order reduction. Two methods are considered, the first has general applicability to stable closed-loop systems, but gives no a priori error bounds; the second linear matrix inequality (LMI)-based method comes with an explicit error bounds, but cannot be applied to general models. However, it is shown that for models composed of cascades of stable subsystems and negative feedbacks of strictly positive real subsystems, the LMIs are always feasible. Both methods are demonstrated on a practical example of a cogeneration power plant with multiple boilers. It is proved that the second LMI-based method can always be applied to general problems with structures similar to the boiler-header systems considered in this paper.

Plant Energy Management

In the IMC-AESOP project, a plant energy management use case was developed to highlight advantages of service orientation, event-driven processing and information models for increased performance, easier configuration, dynamic synchronisation and long-term maintenance of complicated multi-layer solutions, which are deployed nowadays in the continuous process plants. From the application perspective, three scenarios were implemented including advanced control and real-time optimisation of an industrial utility plant, enterprise energy management enabling interactions with the external electricity market, and advanced alarm management utilizing the Complex Event Processing technology.

Structured Model Order Reduction of Boiler-Header Models

Abstract This paper presents a model reduction of a boiler-header system. Since it is desirable that the reduced model retains the structure of the full model where the boilers are interconnected with the header, a structured model reduction technique is applied, which takes the entire system into account. This method requires the solution of two linear matrix inequalities to obtain the structured Gramians of the system, but in general it is not possible to guarantee feasibility of these linear matrix inequalities. However for stable systems that are connected in series with a negative feedback-loop with strictly positive real subsystems, we prove that solutions always exist. By showing that the boiler-header system belongs to this class of systems it follows that the structured model reduction method can be applied regardless of the system parameters.

Application of Distributed MPC to Barcelona Water Distribution Network

Abstract The paper presents application of Distributed Model Predictive Control (DMPC) schemes to complex system of Barcelona water distribution network. The dual decomposition of convex optimization problems is well known and has been already adopted to DMPC. However, the application of dual based DMPC to truly large scale systems requires efficient algorithms for consensus iterations. The paper treats DMPC with and without centralized coordinator. The non-centralized coordination is based on Nesterov accelerated gradient method and centralized coordination is based on limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method.

Subspace identification method incorporating prior information

Subspace identification methods proved to be a powerful tool, which can further benefit from the incorporation of prior information. In the industrial environment, there is often strong prior information about the identified system, that can be used to improve the model quality and its compliance with physical reality. Such prior information can be the known static gains, the dominant time constants, the impulse response smoothness, etc. An idea comes from the possibility to consider the subspace identification as an optimization problem of finding a model with the optimal multi-step predictions on the experimental data. Further, the problem is reformulated to the Bayesian framework allowing to combine available prior information with the information contained in the experimental data by covariance matrix shaping. The paper is completed with an application to experimental data from an oil firing steam boiler with the rated effective power of 100 MW.

OPC-UA information model for large-scale process control applications

The distributed and networked control of large-scale systems is typically designed as multi-layer control architecture. This brings advantage of a simplified design for complex control strategies; however, it complicates the information consistency between individual layers (PID controllers, advanced process controllers, real time optimizers) under changes in controlled plant topology and other events. Individual control layers require different representation of knowledge; however, the information solution has to guarantee the cross-layer integration, consistency and uniform representation of on-line and off-line process data, topology information and dynamics/performance models. The paper presents solution based on OPC Unified Architecture (OPC-UA) model and two levels control architecture. The solution unifies representation of data and topology in Service Oriented Architecture (SOA) and adopts Cloud Computing paradigm.

Distributed MPC with parametric coordination

The paper presents an effective coordination scheme for a distributed optimization based on dual decomposition. The targeted class of optimization problems are strictly convex quadratic functions with linear constraints, where the dual function with coupling equality constraints in Lagrangian is continuous piecewise quadratic. The coordination is based on multi-parametric programming - the subproblem solvers return their solution on a polyhedron around a given Lagrange multiplier value. Centralized coordinator constructs the gradient and Hessian of a dual function and reaches exact consensus in a finite number of iterations, while only some subproblems are queried for a new solution in each iteration. The algorithm is applied to the distributed model predictive control. The efficiency, in terms of optimization time and the number of iterations, is demonstrated on the distributed model predictive control of the Barcelona water distribution network.

Biofuel co-firing with inferential sensor

Abstract Renewable energy sources are playing an increasingly important role in reducing the emission of greenhouse gases, with biomass providing the largest carbon dioxide reduction potential when it replaces coal as the dominant fuel in large scale heat and electricity production. However, the volatility of biomass properties may become a limiting factor to the proportion of biomass used. The paper presents a model based control strategy for multiple fuel co-firing, which enables direct compensation of the variability of fuel properties and stabilizes the heat power using an inferential sensing approach. Kalman filter with significantly increased robustness with respect to model uncertainty is required to make the inferential sensing practically applicable.

Overlapping models merging and interconnection for large-scale model management

The application of advanced control methods to large-scale systems in variable industrial environment requires modeling and identification platform capable of keeping global model with description of its uncertainties, building global model from sub-systems, retrieval of sub-models with mutual consistency, model actualization from new sub-models or new data, etc. This article treats the problem of assembling global model for large-scale system from interconnected and possibly overlapping sub-models, i.e. there can be duplicity in the models. The quality of sub-models can also be different and is taken into account. The article presents two new results: merging of multiple models for the same system by using equivalent data and consistent combination of arbitrary connected models with parametric uncertainty into single model by using statistics of random vectors convolution.

Integrating Prior Information into Subspace Identification Methods

Integrating prior information into subspace identification methods improves their usability for industrial data, where experimental data by them self are in many cases not good enough to give a proper model. The identification experiments in the industrial environment are limited by the economical and safety reasons. However, in practical applications, there is often strong prior information about the identified system, which can be exploited in the identification. The presented algorithm formulates subspace identification as a multi-step predictor optimization. Reformulation to the Bayesian framework allows to incorporate prior information. The paper is completed with the application to the experimental data from the oil burning steam boiler with the rated power of 100 MW.