Multi-parametric Model Predictive Control Research Articles

Two Case Studies of Robust Multi-parametric Model Predictive Control Algorithm

This paper presents case studies of robust algorithm of multi-parametric model predictive control (mpMPC). For discrete-time linear parameter-varying (LPV) systems, the robust algorithm is investigated based on the solution of the mpMPC problem for discrete-time linear time-invariant (LTI) systems. The algorithm provides a controller design method, adaptable to parameter changes of a LPV system. By this controller the performance of the controller LPV system is improved in terms of robustness particularly for slowly varying parameters in the system. Thus the design method is applicable to systems suffering from slow parameter variations due, for example, to aging or degradation. The paper illustrates two control problems, one of which is disturbance rejection problem while the other is reference tracking problem. Each control problem is studied by computer simulation. Particularly for the reference tracking problem the robust mpMPC technique not only reduces the tracking error but renders a system stable while the nominal mpMPC could not.

Robust multi-parametric model predictive control for LPV systems with application to anaesthesia

We present a multi-parametric model predictive controller (mpMPC) for discrete-time linear parameter-varying (LPV) systems based on the solution of the mpMPC problem for discrete-time linear time-invariant (LTI) systems. The control method yields a controller that adapts to parameter changes of the LPV system. This is accomplished by an add-on unit to the implementation of the mpMPC for LTI systems. No modification of the optimal mpMPC solution for LTI systems is needed. The mpMPC for LPV systems is entirely based on simple computational steps performed on-line. This control design method could improve the performance and robustness of a mpMPC for LPV systems with slowly varying parameters. We apply this method to process systems which suffer from slow variation of system parameters due, for example, to aging or degradation. As an illustrative example the reference tracking control problem of the hypnotic depth during intravenous anaesthesia is presented: the time varying system matrix mimics an external disturbance on the hypnotic depth. In this example the presented mpMPC for LPV systems shows a reduction of approximately 60% of the reference tracking error compared to the mpMPC for LTI systems.

Multi-parametric model predictive control-based regulation of blood glucose in type 1 diabetics under unmeasured meal disturbances: a simulation study

Closed-loop control of Blood Glucose Concentration (BGC) is performed using a model differencing-based multi-parametric model predictive controller. An empirical model derived from a virtual nominal patient is used in the design of the controller. A time varying hard constraint is imposed on the control action based on insulin onboard criterion. By varying the model parameters used in the Sorensen’s patient model, 25 virtual patients are created. Varying meal disturbances over a period of five days, the Mean Square Error (MSE) of BGC’s deviation from reference (100 mg/dL) is used to tune the controller. In-silico trials with simulated sensor noise (± 20 mg/dL range) show that the multi-parametric model predictive controller performs well under model uncertainties and also regulates the BGC within the safe limits (above 60 mg/dL) during multiple meal disturbances.

Distributed multiparametric model predictive control design for a quadruple tank process

Distributed control for plant wide control has received attention lately. In this paper, multiparametric quadratic programming based controllers have been developed for a benchmark quadruple tank problem. A centralized control strategy is developed by partitioning its six dimensional vector space based on constraint satisfaction, stability and optimality. Control design is simplified using its decentralized version after a relative gain array analysis of the benchmark. A cooperative game theory based distributed model predictive controller and decentralized proportional integral (PI) controller are also designed for the same system. A decoupling based cooperative distributed multiparametric model predictive controller (mpMPC) is proposed. The controllers are subjected to reference tracking and disturbance rejection and the performance measures are compared. Also, the robustness of cooperative mpMPC to parameter uncertainties is discussed. Distributed design approach is a natural fit for the vector space partitioning based mpMPC design. Simulations results are analyzed and the performance of the five controllers is discussed.

Clinical Evaluation of a Personalized Artificial Pancreas

OBJECTIVEAn artificial pancreas (AP) that automatically regulates blood glucose would greatly improve the lives of individuals with diabetes. Such a device would prevent hypo- and hyperglycemia along with associated long- and short-term complications as well as ease some of the day-to-day burden of frequent blood glucose measurements and insulin administration.RESEARCH DESIGN AND METHODSWe conducted a pilot clinical trial evaluating an individualized, fully automated AP using commercial devices. Two trials (n = 22, nsubjects = 17) were conducted using a multiparametric formulation of model predictive control and an insulin-on-board algorithm such that the control algorithm, or “brain,” can be embedded on a chip as part of a future mobile device. The protocol evaluated the control algorithm for three main challenges: 1) normalizing glycemia from various initial glucose levels, 2) maintaining euglycemia, and 3) overcoming an unannounced meal of 30 ± 5 g carbohydrates.RESULTSInitial glucose values ranged from 84–251 mg/dL. Blood glucose was kept in the near-normal range (80–180 mg/dL) for an average of 70% of the trial time. The low and high blood glucose indices were 0.34 and 5.1, respectively.CONCLUSIONSThese encouraging short-term results reveal the ability of a control algorithm tailored to an individual’s glucose characteristics to successfully regulate glycemia, even when faced with unannounced meals or initial hyperglycemia. To our knowledge, this represents the first truly fully automated multiparametric model predictive control algorithm with insulin-on-board that does not rely on user intervention to regulate blood glucose in individuals with type 1 diabetes.

Blood glucose concentration regulation in Type 1 diabetics using multi model multi parametric model predictive control: An empirical approach

A Glucose- Insulin steady state static map is obtained from the Hovorka's 8th order virtual patient model. Three First Order Plus Time Delay (FOPTD) models are derived for the three piecewise linear regions in it. Through polyhedral vector space partitioning based on constraint violation, critical regions in state vector space are identified. A state feedback gain based controller is designed for each critical region. The controller design prevents constraint violations and ensures convexity while regulating the state vector to origin. The solution is also globally minimal. The state vector space of each empirical model is subjected to such analysis, resulting in three different set of critical regions and corresponding controllers. Gain Scheduling (GS) based on the Blood Glucose Concentration (BGC) measurement ensured proper profile selection. Through delay time compensation techniques, the multi model multi-parametric Model Predictive Control (mp-MPC) is designed for pure dynamics of each linear region. It is observed that the gain scheduled controller regulates the BGC within the acceptable range (80mg/dL to 160 mg/dL) during multiple meal disturbances. The explicit state feedback gain nature of the controller implies ease of deployment on memory constrained embedded devices.

Combined model approximation techniques and multiparametric programming for explicit nonlinear model predictive control

This work presents a methodology to derive explicit multiparametric controllers for nonlinear systems, combining model approximation techniques and multiparametric model predictive control (mp-MPC) algorithms. Particular emphasis is given to an approach that applies a nonlinear model reduction technique, based on balancing of empirical gramians, which generates a reduced order model suitable for nonlinear mp-MPC algorithms. This approach is compared with a recently proposed method that uses a meta-modelling based model approximation technique which can be directly combined with standard multiparametric programming algorithms. The methodology is illustrated for two nonlinear models, of a distillation column and a train of CSTRs, respectively.

Tuning of a tracking multi-parametric predictive controller using local linear analysis

Multi-parametric model predictive control (mp-MPC) makes possible the application of MPC controllers with a low on-line computational demand and rapid sampling. It is appealing for low-level control applications, where the disturbance-rejection properties are very important. This study explores two important issues in the transition from mp-MPC theory to the implementation of an industrial controller: offset-free output-feedback tracking, and controller tuning based on local linear analysis of the closed-loop system. An experimental case study on a two-input single-output system for pressure control in the vacuum chamber of a wire annealer is presented.

Off-line model reduction for on-line linear MPC of nonlinear large-scale distributed systems

Model predictive control (MPC) is an efficient method for the controller design of a large number of processes. However, linear MPC is often inappropriate for controlling nonlinear large-scale systems, while non-linear MPC can be computationally costly. The resulting optimization-based procedure can lead to local minima due to the, non-convexities that non-linear systems can exhibit. To overcome the excessive computational cost of MPC application for large-scale nonlinear systems, model reduction methodology in conjunction with efficient system linearizations have been exploited to enable the efficient application of linear MPC for nonlinear distributed parameter systems (DPS). An off-line model reduction technique, the proper orthogonal decomposition (POD) method, combined with a finite element Galerkin projection is first used to extract accurate non-linear low-order models from the large-scale ones. Trajectory Piecewise-Linear (TPWL) methodologies are subsequently developed to construct a piecewise linear representation of the reduced nonlinear model, both in a static and in a dynamic fashion. Linear MPC, based on quadratic programming, can then be efficiently performed on the resulting low-order, piece-wise affine system. Our combined methodology is readily applicable in combination with advanced MPC methodologies such as multi-parametric MPC (MP-MPC) ( Pistikopoulos, 2009). The stabilisation of the oscillatory behaviour of a tubular reactor with recycle is used as an illustrative example to demonstrate our methodology.

Development of a multi-parametric model predictive control algorithm for insulin delivery in type 1 diabetes mellitus using clinical parameters

Abstract A multi-parametric model predictive control (mpMPC) algorithm for subcutaneous insulin delivery for individuals with type 1 diabetes mellitus (T1DM) that is computationally efficient, robust to variations in insulin sensitivity, and involves minimal burden for the user is proposed. System identification was achieved through impulse response tests feasible for ambulatory conditions on the UVa/Padova simulator adult subjects with T1DM. An alternative means of system identification using readily available clinical parameters was also investigated. A safety constraint was included explicitly in the algorithm formulation using clinical parameters typical of those available to an attending physician. Closed-loop simulations were carried out with daily consumption of 200 g carbohydrate. Controller robustness was assessed by subject/model mismatch scenarios addressing daily, simultaneous variation in insulin sensitivity and meal size with the addition of Gaussian white noise with a standard deviation of 10%. A second-order-plus-time-delay transfer function model fit the validation data with a mean (coefficient of variation) root-mean-square-error (RMSE) of 26 mg/dL (19%) for a 3 h prediction horizon. The resulting control law maintained a low risk Low Blood Glucose Index without any information about carbohydrate consumption for 90% of the subjects. Low-order linear models with clinically meaningful parameters thus provided sufficient information for a model predictive control algorithm to control glycemia. The use of clinical knowledge as a safety constraint can reduce hypoglycemic events, and this same knowledge can further improve glycemic control when used explicitly as the controller model. The resulting mpMPC algorithm was sufficiently compact to be implemented on a simple electronic device.

A Novel mp-NLP Algorithm for Explicit/Multi-parametric NMPC

In this work we present a novel multi-parametric nonlinear programming (mp-NLP) algorithm for explicit multi-parametric nonlinear model predictive control (mp-NMPC). The algorithm is based on (i) local sensitivity analysis of nonlinear programs (NLP), and (ii) an exploration procedure which makes use of successive linearizations of the dynamic system and the nonlinear constraints. The algorithm is illustrated with an example problem drawn from the open literature.

Hybrid explicit model predictive control of a nonlinear process approximated with a piecewise affine model

The recently developed methods of explicit (multi-parametric) model predictive control (e-MPC) for hybrid systems provide an interesting opportunity for solving a class of nonlinear control problems. With this approach, the nonlinear process is approximated by a piecewise affine (PWA) hybrid model containing a set of local linear dynamics. Compared to linear-model-based MPC, a performance improvement is expected with the reduction of the plant-to-model mismatch; however at a cost of controller computation complexity. In order to reduce the computational load, so that desired horizon lengths may be used, we present an efficient sub-optimal solution. The feasibility of the approach for the application was evaluated in an experimental case study, where an output feedback, offset-free-tracking hybrid e-MPC controller was considered as a replacement for a PID-controller-based scheme for the control of the pressure in a wire-annealing machine.