Control of ball mill grinding circuit using model predictive control scheme

Ball mill grinding circuits are essentially multivariable systems with high interaction among process variables. Traditionally grinding circuits are controlled by detuned multi-loop PI controllers that minimize the effect of interaction among the control loops. Detuned controllers generally become sluggish and a close control of the circuit is not possible. Model Predictive Controllers (MPC) can handle such highly interacting multivariable systems efficiently due to its coordinated approach. Moreover, MPC schemes can handle input and output constraints more explicitly and operation of the circuits close to their optimum operating conditions is possible. Control studies on a laboratory ball mill grinding circuit are carried out by simulation with detuned multi-loop PI controllers, unconstrained and constrained model predictive controllers and their performances are compared.     

Model Predictive Control of water resources systems: A review and research agenda

Model Predictive Control (MPC) has recently gained increasing interest in the adaptive management of water resources systems due to its capability of incorporating disturbance forecasts into real-time optimal control problems. Yet, related literature is scattered with heterogeneous applications, case-specific problem settings, and results that are hardly generalized and transferable across systems. Here, we systematically review 149 peer-reviewed journal articles published over the last 25 years on MPC applied to water reservoirs, open channels, and urban water networks to identify common trends and open challenges in research and practice. The three water systems we consider are inter-connected, multi-purpose and multi-scale dynamical systems affected by multiple hydro-climatic uncertainties and evolving socioeconomic factors. Our review first identifies four main challenges currently limiting most MPC applications in the water domain: (i) lack of systematic benchmarking of MPC with respect to other control methods; (ii) lack of assessment of the impact of uncertainties on the model-based control; (iii) limited analysis of the impact of diverse forecast types, resolutions, and prediction horizons; (iv) under-consideration of the multi-objective nature of most water resources systems. We then argue that future MPC applications in water resources systems should focus on addressing these four challenges as key priorities for future developments.     

Model Predictive Control Coupled with Artificial Intelligence for Eddy Current Dynamometers

The recent studies on Artificial Intelligence (AI) accompanied by enhanced computing capabilities supports increasing attention into traditional control methods coupled with AI learning methods in an attempt to bringing adaptiveness and fast responding features. The Model Predictive Control (MPC) technique is a widely used, safe and reliable control method based on constraints. On the other hand, the Eddy Current dynamometers are highly nonlinear braking systems whose performance parameters are related to many processes related variables. This study is based on an adaptive model predictive control that utilizes selected AI methods. The presented approach presents an updated the mathematical model of an Eddy Current Dynamometer based on experimentally obtained system operational data. Finally, the comparison of AI methods and related learning performances based on the assessment technique of mean absolute percentage error (MAPE) issues are discussed. The results indicate that Single Hidden Layer Neural Network (SHLNN), General Regression Neural Network (GRNN), Radial Basis Network (RBNN), Neuro Fuzzy Network (ANFIS) coupled MPC have quite satisfying performances. The presented results indicate that, amongst them, GRNN appears to provide the best performance.     

MPC: Current practice and challenges

Linear Model Predictive Control (MPC) continues to be the technology of choice for constrained, multivariable control applications in the process industry. Successful deployment of MPC requires “getting right” multiple aspects of the control problem. This includes the design of the underlying regulatory controls, design of the MPC(s), test design for model identification, model development, and dealing with nonlinearities. Approaches and techniques that are successfully applied in practice are described, including the challenges involved in ensuring a successful MPC application. Academic contributions are highlighted and suggestions provided for improving MPC.     

High-order Volterra Model Predictive Control and its application to a nonlinear polymerisation process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.     

Nonlinear Model Predictive Control of Electrical Submersible Pumps based on Echo State Networks

Employed for artificial lifting in oil well production, Electrical Submersible Pumps (ESP) can be operated with Model Predictive Control (MPC) to drive an optimal production, while ensuring a safe operation and respecting system constraints. Due to the nonlinear dynamics of ESPs, Echo State Networks (ESNs), a recurrent neural network with fast training, are employed for efficient system identification of unknown dynamic systems. Besides the synthesis of highly accurate prediction models, this work contributes by designing two Nonlinear MPC (NMPC) strategies for the control of an ESP-lifted oil well: a standard Single-Shooting NMPC that embeds the ESN model completely, and the Practical Nonlinear Model Predictive Controller (PNMPC) that approximates the NMPC through fast trajectory-linearization of the ESN model. Another contribution is the implementation of an error correction filter to reject disturbances and counter modeling errors in both NMPC strategies. Finally, in computational experiments, both ESN-based NMPC strategies performed well in controlling simulated ESP-lifted oil wells when the model of the plant is unknown. However, PNMPC was more efficient and induced a similar performance to standard NMPC.     

Linear offset-free Model Predictive Control

This work addresses the problem of offset-free Model Predictive Control (MPC) when tracking an asymptotically constant reference. In the first part, compact and intuitive conditions for offset-free MPC control are introduced by using the arguments of the internal model principle. In the second part, we study the case where the number of measured variables is larger than the number of tracked variables. The plant model is augmented only by as many states as there are tracked variables, and an algorithm which guarantees offset-free tracking is presented. In the last part, offset-free tracking properties for special implementations of MPC schemes are briefly discussed.     

Robust constrained receding-horizon predictive control via bounded data uncertainties

The main objective of this work consists of obtaining a new robust and stable Model Predictive Control (MPC). One widely used technique for improving robustness in MPC consists of the Min–Max optimization, where an analogy can be established with the Bounded Data Uncertainties (BDU) method. The BDU is a regularization technique for least-squares problems by taking into account the uncertainty bounds. So BDU both improves robustness in MPC and offers a guided way of tuning the empirically tuned penalization parameter for the control effort in MPC due to the duality that the parameter coincides with the regularization one in BDU. On the other hand, the stability objective is achieved by the use of terminal constraints, in particular the Constrained Receding-Horizon Predictive Control (CRHPC) algorithm, so the original CRHPC–BDU controller is stated, which presents a better performance from the point of view of robustness and stability than a standard MPC.     

Improving performance and stability of MPC relevant identification methods

Model Predictive Control (MPC) Relevant Identification (MRI) methods are a good option for identification, if there is model structure mismatch. Herein a new MRI method, named Enhanced Multistep Prediction Error Method (EMPEM), is proposed. EMPEM combines the best characteristics of others MRI methods in a single algorithm. It was developed to identify either closed-loop or open-loop systems; its convergence and stability make it perform better than the other presented methods. To show the advantages of EMPEM, a comparison is made against two other methods (one MRI and one PEM). The statistical analysis indicates that in the cases studied, the performance and the robustness of the new method is equal or better than the other ones.     

Model Predictive Control in Pulsed Electrochemical Machining

In this work a Model Predictive Control (MPC) approach is used for controlling a Pulsed Electrochemical Machining (PECM) process. The MPC problem is formulated in order to optimally reach a desired state while satisfying various restrictions. PECM is modeled as a constrained nonlinear system. In the first approach the system is input-output linearized and a linear MPC scheme is applied to control it. In comparison a second approach uses the linearization around the current working point resulting in a Linear Time Variant system. This linear system is controlled using Linear Time Variant MPC (LTV-MPC). The simulation results are compared and the most promising controller is implemented on a real time platform controlling a PECM plant. The experimental results with online parameter estimation are shown and discussed.     

Reference trajectory tuning of model predictive control

An approach to minimize tuning effort of nominal Model Predictive Control algorithms is proposed. The algorithm dynamically calculates output set points to accommodate user-defined output importance, which is more intuitive than selecting values for the MPC weighing matrices. Instead of tuning the weights on the outputs deviations from their set points, weights on the input values and input increments, which are the usual tuning parameters of MPC, the desired output control performance of the MPC can be specified by performance factors. The proposed method extends the existing methods that consider a reference trajectory for the output tracking to the case of zone control and input targets. The proposed method also assumes that, as in most commercial MPC packages, the controller has two layers: a static layer and an extended dynamic layer. The method is illustrated by three case studies, contemplating both SISO and MIMO systems. It is observed that: the output set point tracking performance can be changed without modifying the MPC tuning weights, the approach is capable of achieving similar performance to conventional MPC tuned by multiobjective optimization techniques from the literature, with a fraction of computer effort, and it can be integrated with Real Time Optimization algorithms to control complex systems, always respecting output constraints.     

Regulator configuration design by means of model predictive control

This paper presents new concepts and methods for regulator configuration design for stable and unstable multivariable systems. Nowadays the self-definitions of dynamic relative gain rarely consider the interaction influences of closed-loop controllers, and the interaction measurement can be also showed from the effects from controlled variables to manipulated variables through closed-loop controllers. Model Predictive Control (MPC) is an important multivariable centralized control strategy; by means of SFPC (State Feedback Predictive Control) and MGPC (Multivariable Generalized Predictive Control), two closed-loop interaction analysis methods are first put forward. Based on the control rate optimized, two inverse normalized gain arrays are obtained from SFPC and MGPC which show the dynamic effects of controlled variables on manipulated variables. With the inverse normalized gain arrays, the regulator configuration design of unstable systems can be carried out due to the effect of multivariable centralized control. Finally the advantages and effectiveness of proposed interaction analysis approaches are highlighted via several examples.     

Model predictive control springer,Berlin, 1999, ISBN 3540762418, 280 pages

This volume is a recent addition to the Camacho and Bordons' book ‘Model Predictive Control in the Process Industry’, edited by Springer Verlag. The book presents a complete review of the theory and applications of Model Predictive Control MPC, from the simple unconstrained SISO case to the more complex constrained MIMO situations. Special attention is given to the Generalized Predictive Controller that is one of the most known and cited MPC strategies. In all the chapters the results are illustrated with simulation examples and also with some experimental results that validated the controllers and tuning rules analyzed in the book. Copyright © 2003 John Wiley & Sons, Ltd.     

Application of Model Predictive Control suitable for closed-loop re-identification to a polymerization reactor

Recently, a linear Model Predictive Control (MPC) suitable for closed-loop re-identification was proposed, which solves the potential conflict between the persistent excitation of the system (necessary to perform a suitable identification) and the control, and guarantees recursive feasibility and attractivity of an invariant region of the closed-loop. This approach, however, needs to be extended to account for a proper robustness to moderate-to-severe model mismatches, given that re-identifications are necessary when the system is not close to the operating point where the current linear model was identified. In this work, new results on robustness are presented, and an exhaustive application of the new MPC suitable for closed-loop re-identification to a nonlinear polymerization reactor simulator is made to explore the difficulties arising from a real life identification. Furthermore, several closed-loop re-identification are performed in order to clearly show that the proposed controller provides uncorrelated input–output data sets, which together with the guaranteed stability, constitute the main controller benefit.     

Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance

This work presents an alternative way to formulate the stable Model Predictive Control (MPC) optimization problem that allows the enlargement of the domain of attraction, while preserving the controller performance. Based on the dual MPC that uses the null local controller, it proposed the inclusion of an appropriate set of slacked terminal constraints into the control problem. As a result, the domain of attraction is unlimited for the stable modes of the system, and the largest possible for the non-stable modes. Although this controller does not achieve local optimality, simulations show that the input and output performances may be comparable to the ones obtained with the dual MPC that uses the LQR as a local controller.     

Convergence properties of constrained linear system under MPC control law using affine disturbance feedback

This paper shows new convergence properties of constrained linear discrete time system with bounded disturbances under Model Predictive Control (MPC) law. The MPC control law is obtained using an affine disturbance feedback parametrization with an additional linear state feedback term. This parametrization has the same representative ability as some recent disturbance feedback parametrization, but its choice together with an appropriate cost function results in a different closed-loop convergence property. More exactly, the state of the closed-loop system converges to a minimal invariant set with probability one. Deterministic convergence to the same minimal invariant set is also possible if a less intuitive cost function is used. Numerical experiments are provided that validate the results.     

A tool to analyze robust stability for model predictive controllers

A strategy based on Nonlinear Programming (NLP) sensitivity is developed to establish stability bounds on the plant/model mismatch for a class of optimization-based Model Predictive Control (MPC) algorithms. By extending well-known nominal stability properties for these controllers, we derive a sufficient condition for robust stability of these controllers. This condition can also be used to assess the extent of model mismatch that can be tolerated to guarantee robust stability. In this derivation we deal with MPC controllers with final time constraints or infinite time horizons. Also for this initial study we concentrate only on discrete time systems and unconstrained state feedback control laws with all of the states measured. To illustrate this approach we give two examples: a linear first-order dynamic system and a nonlinear SISO system involving a first order reaction. ©     

On the solution of the tracking problem for non-linear systems with MPC

This paper presents a Model Predictive Control (MPC) algorithm for non-linear systems which solves the tracking problem for asymptotically constant references. Closed-loop stability of the equilibrium and asymptotic zero-error regulation are guaranteed. The performance of the method is discussed with the classical Continuous Stirred Tank Reactor (CSTR) control application.     

Model Predictive Control oriented experiment design for system identification: A graph theoretical approach

We present a new approach to Model Predictive Control (MPC) oriented experiment design for the identification of systems operating in closed-loop. The method considers the design of an experiment by minimizing the experimental cost, subject to probabilistic bounds on the input and output signals due to physical limitations of actuators, and quality constraints on the identified model. The excitation is done by intentionally adding a disturbance to the loop. We then design the external excitation to achieve the minimum experimental effort while we are also taking care of the tracking performance of MPC. The stability of the closed-loop system is guaranteed by employing robust MPC during the experiment. The problem is then defined as an optimization problem. However, the aforementioned constraints result in a non-convex optimization which is relaxed by using results from graph theory. The proposed technique is evaluated through a numerical example showing that it is an attractive alternative for closed-loop experiment design.     

Generalized terminal state constraint for model predictive control

A terminal state equality constraint for Model Predictive Control (MPC) laws is investigated, where the terminal state/input pair is not fixed a priori but it is a free variable in the optimization. The approach, named “generalized” terminal state constraint, can be used for both tracking MPC (i.e. when the objective is to track a given steady state) and economic MPC (i.e. when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state). It is shown that the proposed technique provides, in general, a larger feasibility set with respect to the existing approaches, given the same prediction horizon. Moreover, a new receding horizon strategy is introduced, exploiting the generalized terminal state constraint. Under mild assumptions, the new strategy is guaranteed to converge in finite time, with arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal state constraint, while still enjoying a larger feasibility set. The features of the new technique are illustrated by an inverted pendulum example in both the tracking and the economic contexts.