A framework for hybrid model predictive control in mineral processing

doi:10.1016/j.conengprac.2015.02.006

Control Engineering Practice

Volume 40, July 2015, Pages 1-12

https://doi.org/10.1016/j.conengprac.2015.02.006 Get rights and content

Highlights

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A framework for hybrid model predictive control, which includes a hybrid state estimator, was developed.
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A crushing plant and a rougher flotation line were modeled.
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Hybrid controllers were implemented in both processes using the framework.
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Hybrid controllers outperform conventional controllers in simulation tests.

Abstract

Model Predictive Control (MPC) is an advanced technique for process control that has seen a significant and widespread increase in its use in the process industry since its introduction. In mineral processing, in particular, several applications of conventional MPC can be found for the individual processes of crushing, grinding, flotation, thickening, agglomeration, and smelting with varying degrees of success depending on the variables involved and the control objectives. Given the complexity of the processes normally found in mineral processing, there is also great interest in the design and development of advanced control techniques which aim to deal with situations that conventional controllers are unable to do. In this aspect, Hybrid MPC enables the representation of systems, incorporating logical variables, rules, and continuous dynamics. This paper firstly presents a framework for modeling and representation of hybrid systems, and the design and development of hybrid predictive controllers. Additionally, two application examples in mineral processing are presented. Results through simulation show that the control schemes developed under this framework exhibit a better performance when compared with conventional expert or MPC controllers, while providing a highly systematized methodology for the analysis, design, and development of hybrid MPC controllers.

Introduction

Model predictive control (MPC) refers to a class of computer algorithms for process control that rely on the use of dynamic models to make predictions of the evolution of the process. Using this predictions, a MPC algorithm performs an optimization of predefined control objectives to compute the control sequence needed to drive the process to the optimal operating point. Only the first action in the control sequence is sent into the plant, and the optimization is repeated on the next control interval with the most recent state information (García, Prett, & Morari, 1989).

Predictive control is being increasingly applied in the process industry, mainly due to its ability to handle multi-variable plants naturally and incorporate constraints on operating variables (Maciejowski, 2002). Additionally, the tuning of the controller parameters is relatively easy and intuitive, making it particularly attractive to staff with limited knowledge of control theory (Camacho & Bordons, 2002).

In the mineral processing industry, several applications of MPC can be found for the individual processes. For instance, Ramasamy, Narayanan, and Rao (2005) performed a comparative analysis between a MPC strategy and a multi-loop PI control scheme applied to a mineral grinding plant. A similar comparison was performed by Chen, Zhai, Li, and Li (2007). In Suichies, Leroux, Dechert, and Trusiak (2000), a single-input/single-output (SISO) MPC algorithm and a AutoRegressive eXogeneous (ARX) model identification routine were implemented in several sulfide flotation circuits. In Gatzke and Doyle (2001), two control methods based on predictive control, soft output constraints, and prioritized control objectives were tested on a simulated granulation process.

The organization of this paper is as follows. Section 2 presents a review of conventional MPC applications in mineral processing. Section 3 describes the hybrid modeling of dynamic systems. The design and implementation of Hybrid Model Predictive Control (HMPC) is detailed in Section 4. In Section 5, the proposed HMPC framework is described. Section 6 presents two new applications of HMPC in mineral processing. Finally, conclusions are presented in Section 7.

Section snippets

Conventional MPC applications

Even though PID controllers are the most usual approach to feedback control found in mineral processing plants (Hodouin, 2011), several implementations of model-based controllers, tested through simulation and in real plants, can be found in the literature.

In Muller and Vaal (2000), a model predictive controller for a milling circuit was developed. Additionally, an optimizing algorithm was used to automatically tune the controller parameters. The controller was implemented and tested on a

Hybrid modeling of dynamic systems

Hybrid dynamic models are used to describe the evolution of dynamic systems that present both continuous and logical components. Several subclasses of hybrid systems are found in the literature: Linear Complementarity (LC) systems, Mixed Logical Dynamical (MLD) systems, PieceWise Affine (PWA) systems, among others.

PWA systems are a composition on linear time-invariant dynamic models that can approximate non-linear dynamics with arbitrary accuracy by increasing the number of linearization at

Predictive control of hybrid systems

The next section describes the implementation of the predictive controller for hybrid systems based on the MLD representation (2a), (2b), (2c). Additionally, a hybrid state estimator is presented. This estimator is based on the PWA representation (1) and simultaneously estimates the value of the continuous state of the system and the current active subsystem.

Hybrid model predictive control has been successfully implemented in several areas. In Nandola and Rivera (2013), an improved model

HMPC framework

Several alternatives for hybrid model predictive control are available. One of such alternatives is the Multi-Parametric Toolbox 3.0 (Herceg, Kvasnica, Jones, & Morari, 2013), which offers multiple functionalities for implementing model-based predictive controllers, such as the ability to generate explicit MPC solutions, replacing on-line optimization and greatly reducing computation time. Nonetheless, the HMPC framework presented in this study was designed and developed from the ground up so

HMPC applications in mineral processing

In this section, two implementations of the hybrid control framework in mineral processing are presented. All the applications were designed and tested through simulation.

Conclusion

This paper presents a framework for hybrid model predictive control applied to mineral processing. The hybrid modeling of dynamic systems using the MLD representation, and the hybrid predictive control of these systems through mixed-integer quadratic programming are detailed, and two applications in crushing and flotation are presented.

The proposed framework of hybrid systems adopted in this paper offers a highly systematized methodology for the analysis, modeling and development of hybrid

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^☆: This study was funded by the Fondecyt project 1120047, “Distributed Hybrid Model Predictive Control for Mineral Processing”.

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A framework for hybrid model predictive control in mineral processing☆

Highlights

Abstract

Introduction

Section snippets

Conventional MPC applications

Hybrid modeling of dynamic systems

Predictive control of hybrid systems

HMPC framework

HMPC applications in mineral processing

Conclusion

Minerals Engineering

Automatica

Energy and Buildings

Minerals Engineering

Automatica

Powder Technology

Automatica

Journal of Process Control

Powder Technology

Minerals Engineering

Journal of Process Control

Minerals Engineering

Control Engineering Practice

Control Engineering Practice