Jakob Kjøbsted Huusom

Finite horizon MPC for systems in innovation form

System identification and model predictive control have largely developed as two separate disciplines. Nevertheless, the major part of industrial MPC commissioning is generation of data and identification of models. In this contribution we attempt to bridge this gap by contributing some of the missing links. Input-output models (FIR, ARX, ARMAX, Box-Jenkins) as well as subspace models can be represented as state space models in innovation form. These models have correlated process and measurement noise. The correct LQG control law for systems with correlated process and measurement noise is not well known. We provide the correct finite-horizon LQG controller for this system and use this to develop a state space representation of the closed-loop system. This representation is used for closed-loop frequency and covariance analysis. These measures are used in tuning of the unconstrained and constrained MPC. We demonstrate our results on a simulated industrial furnace.

Tuning of methods for offset free MPC based on ARX model representations

In this paper we investigate model predictive control (MPC) based on ARX models. ARX models can be identified from data using convex optimization technologies and is linear in the system parameters. Compared to other model parameterizations this feature is an advantage in embedded applications for robust and automatic system identification. Standard MPC is not able to reject a sustained, unmeasured, non zero mean disturbance and will therefore not provide offset free tracking. Offset free tracking can be guaranteed for this type of disturbances if Δ variables are used or if the state space is extended with a disturbance model state. The relation between the base case and the two extended methods are illustrated which provides good understanding and a platform for discussing tuning for good closed loop performance.

Brief paper: A design algorithm using external perturbation to improve Iterative Feedback Tuning convergence

Iterative Feedback Tuning constitutes an attractive control loop tuning method for processes in the absence of process insight. It is a purely data driven approach for optimization of the loop performance. The standard formulation ensures an unbiased estimate of the loop performance cost function gradient, which is used in a search algorithm for minimizing the performance cost. A slow rate of convergence of the tuning method is often experienced when tuning for disturbance rejection. This is due to a poor signal to noise ratio in the process data. A method is proposed for increasing the data information content by introducing an optimal perturbation signal in the tuning algorithm. The theoretical analysis is supported by a simulation example where the proposed method is compared to an existing method for acceleration of the convergence by use of optimal prefilters.

Mechanistic modeling of biodiesel production using a liquid lipase formulation

In this article, a kinetic model for the enzymatic transesterification of rapeseed oil with methanol using Callera™ Trans L (a liquid formulation of a modified Thermomyces lanuginosus lipase) was developed from first principles. We base the model formulation on a Ping‐Pong Bi‐Bi mechanism. Methanol inhibition, along with the interfacial and bulk concentrations of the enzyme was also modeled. The model was developed to describe the effect of different oil compositions, as well as different water, enzyme, and methanol concentrations, which are relevant conditions needed for process evaluation, with respect to the industrial production of biodiesel. The developed kinetic model, coupled with a mass balance of the system, was fitted to and validated on experimental results for the fed‐batch transesterification of rapeseed oil. The confidence intervals of the parameter estimates, along with the identifiability of the model parameters were presented. The predictive capability of the model was tested for a case using 0.5% (wt. Enzyme/wt. Oil), 0.5% (wt. Water /wt. Oil) and feeding 1.5 times the stoichiometric amount of methanol in total over 24 h. For this case, an optimized methanol feeding profile that constrains the amount of methanol in the reactor was computed and the predictions experimentally validated. Monte‐Carlo simulations were then used to characterize the effect of the parameter uncertainty on the model outputs, giving a biodiesel yield, based on the mass of oil, of 90.8 ± 0.55 mass %.

Iterative feedback tuning of uncertain state space systems

Iterative Feedback Tuning is a purely data driven tuning algorithm for optimizing control parameters based on closed loop data. The algorithm is designed to produce an unbiased estimate of the performance cost function gradient for iteratively improving the control parameters to achieve optimal loop performance. This tuning method has been developed for systems based on a transfer function representation. This paper presents a state feedback control system with a state observer and its transfer function equivalent in terms of input output dynamics. It is shown how the parameters in the closed loop state space system can be tuned by Iterative Feedback Tuning utilizing this equivalent representation. A simulation example illustrates that the tuning converges to the known analytical solution for the feedback control gain and to the Kalman gain in the state observer. In case of parametric uncertainty, different choices of tuning parameters are investigated. It is shown that the data driven tuning method produces optimal performance for convex problems when it is the model parameter estimates in the observer that are tuned.

Challenges and opportunities in integration of design and control

Abstract Process synthesis and design of plant operation are related topics but current industrial practice solves these problems sequentially. The implication of this sequential strategy may result in design of processing systems which are very hard to control. This paper presents a discussion on drivers for an integrated approach and outlines the challenges in formulation of such a multi-objective synthesis problem. This discussion is viewed in relation to some of the changing trends in the industry. Significant results have been published which in different ways seek to handle the integrated problem. Further, advancements in control algorithms and software have widened the range of feasible operation and control for strongly interconnected production systems. In light of these advances in different areas of the field, recommendations for further research and initiatives for development of an integrated approach are given with focus on how new results on the short term can improve industrial practice.

Noise Modelling and MPC Tuning for Systems with Infrequent Step Disturbances

Abstract In this paper, an offset-free SISO MPC implementation based on an ARX model of the system dynamics is investigated. Special emphasis is directed to achieving good closed loop performance for systems which may be step wised perturbed by a sustained, unmeasured disturbance. Hence a noise model which expresses the behaviour of this non-stationary noise process is sought. Tuning of the ARX-based MPC implementation is discussed and illustrated in a simulation example. Guidelines for tuning of the free parameters are presented.

ARX-Model based Model Predictive Control with Offset-Free Tracking

ARX models, is a suitable model class for linear control implementations. The parameter estimation problem is convex and easily handed for both SISO and MIMO system in contrast to ARMAX or State Space model. Model predictive control implementations insuring offset-free tracking are discussed and related. Special attention is given to an adaptive disturbance estimation method with time-varying forgetting which is shown to be less sensitive to the nature of the disturbance.

Data Driven Tuning of State Space Control loops with unknown state information and model uncertainty.

Abstract As an alternative to model reestimation and subsequent control design for state space systems in case unsatisfactory loop performance, direct tuning is investigated. Direct tuning is shown able to optimize loop performance when the control design and state observer are based on an uncertain model estimate.

Optimal operation and stabilising control of the concentric heat-integrated distillation column (HIDiC)

Abstract This paper presents the application of a systematic control configuration design procedure on the HIDiC with a reboiler. The application is illustrated through two case studies of industrial relevance, namely the separation of benzene/toluene and a multicomponent mixture of aromatic compounds. Results of static optimisations and dynamic simulations are presented based on a realistic column model, which accounts for dynamic pressure drops and liquid holdups, dynamic energy balances and more. Using a decentralised control scheme, good stabilising and economic performance are achieved by controlling both column section pressures and the temperature profile in one of the sections, while the economic variables are controlled by cascade control loops. Guidelines for the design of both the regulatory control layer and the supervisory control layer are provided.