Real time optimization (RTO) with model predictive control (MPC)

Efficiency-Oriented Model Predictive Control: A Novel MPC Strategy to Optimize the Global Process Performance

Existing control strategies, such as Real-time Optimization (RTO), Dynamic Real-time Optimization (DRTO), and Economic Model Predictive Control (EMPC) cannot enable optimal operation and control behavior in an optimal fashion. This work proposes a novel control strategy, named the efficiency-oriented model predictive control (MPC), which can fully realize the potential of the optimization margin to improve the global process performance of the whole system. The ideas of optimization margin and optimization efficiency are first proposed to measure the superiority of the control strategy. Our new efficiency-oriented MPC innovatively uses a nested optimization structure to optimize the optimization margin directly online. To realize the computation, a Periodic Approximation technique is proposed, and an Efficiency-Oriented MPC Type I is constructed based on the Periodic Approximation. In order to alleviate the strict constraint of Efficiency-Oriented MPC Type I, the zone-control-based optimization concept is used to construct an Efficiency-Oriented MPC Type II. These two well-designed efficiency-oriented controllers were compared with other control strategies over a Continuous Stirred Tank Reactor (CSTR) application. The simulation results show that the proposed control strategy can generate superior closed-loop process performance, for example, and the Efficiency-Oriented MPC Type I can obtain 7.11% higher profits than those of other control strategies; the effectiveness of the efficiency-oriented MPC was, thereby, demonstrated.

Beyond the quadratic norm: Computationally efficient constrained nonlinear MPC using a custom cost function

A new approach to nonlinear Model Predictive Control (MPC) is discussed in this work. A custom user-defined cost function is used in place of the typically considered quadratic norm. An approximator of the cost function is applied to obtain a computationally simple procedure and linearization of two trajectories is carried out online. The predicted output trajectory of the approximator and the predicted trajectory of the manipulated variable, both over the prediction horizon, are repeatedly linearized online. It yields a simple quadratic programming task. The algorithm is implemented for a simulated neutralization benchmark modeled by a neural Wiener model. The resulting control quality is excellent, identical to that observed in the MPC scheme with nonlinear optimization. Validity of the described MPC algorithms is demonstrated when only simple box constraints are considered on the process input variable and in a more demanding case when additional soft limitations are put on the predicted output. Two structures of the approximator are compared: polynomial and neural; the advantages of the latter one are shown and stressed.

Multi-objective predictive control based on the cutting tobacco outlet moisture priority

In this paper, we propose a new priority multi-objective optimization strategy of system output variables in cutting tobacco process. The proposed strategy focuses on the cutting tobacco moisture-controlled output variables optimization in feasible regions with two levels according to the priority. This study aims to provide a novel technical support for the chemical industry contained drying process. In order to alleviate the lack of degree of freedom of the system, strict set-point control is given, meanwhile, other output variables adopt zone control. Firstly, the system control output variables are optimized in ascending order of priority. Secondly, the specific lower-level target constraints are first relaxed. Finally, the relaxation of other high-priority target constraints is stopped when the optimization is feasible. Thus, the system control output variables move along the optimal target trajectory. From the perspective of practical application of engineering, under the condition of disturbance existing in the cutting tobacco drying process, the simulation shows that the proposed approach has good robustness when there is disturbance, and the previous method cannot meet the control requirement. The proposed strategy meanwhile has better tracking effect through single and multiple output variables simulation, which compared with traditional predictive control in real cutting tobacco drying process.

Batch-to-Batch Adaptive Iterative Learning Control-Explicit Model Predictive Control Two-Tier Framework for the Control of Batch Transesterification Process

To harness energy security and reduce carbon emissions, humankind is trying to switch toward renewable energy resources. To this extent, fatty acid methyl esters, also known as biodiesel, are popularly used as a green fuel. Fatty acid methyl esters can be produced by a batch transesterification reaction between vegetable oil and alcohol. Being a batch process, fatty acid methyl esters production is beset with issues such as uncertainties and unsteady state behavior, and therefore, adequate process control measures are necessitated. In this study, we have proposed a novel two-tier framework for the control of the fatty acid methyl esters production process. The proposed approach combines the constrained batch-to-batch iterative learning control technique and explicit model predictive control to obtain the desired concentration of the fatty acid methyl esters. In particular, the batch-to-batch iterative learning control technique is used to generate reactor temperature set-points, which is further utilized to obtain an optimal coolant flow rate by solving a quadratic objective cost function, with the help of explicit model predictive control. Our simulation results indicate that the fatty acid methyl esters concentration trajectory converges to the desired batch trajectory within four batches for uncertainty in activation energy and six batches for uncertainty in both inlet concentration of triglyceride and in activation energy even in the presence of process disturbances. The proposed approach was compared to the heuristic-based approach and constraint iterative learning control approach to showcase its efficacy.

Efficiency-Oriented MPC: Using Nested Structure to Realize Optimal Operation and Control

Optimal operation and control, which can result in the global optimal operation performance of industrial processes, has been a hot topic in recent control strategy designs. However, existing control strategies, such as real-time optimization (RTO), dynamic real-time optimization (DRTO), and economic model predictive control (EMPC), have their own limitations, and they can only generate sub-optimal operation performance. In order to further improve online global operation performance, a new kind of control strategy named efficiency-oriented model predictive control (EfiMPC) is proposed in this paper. The aim of the EfiMPC is discussed first, and then, the ideal EfiMPC strategy with a nested structure is proposed, where the inner layer is the offline construction of an efficiency-oriented terminal region, and the outer layer is the direct optimization of the transient operation performance. This efficiency-oriented terminal region can guarantee a dynamic operation performance in the closed-loop perspective, and a better global operation performance can thus be obtained. A practical EfiMPC strategy, which replaces the offline construction of the efficiency-oriented terminal region with the online optimization of the average dynamic operation performance in the inner layer, is also proposed, and the recursive feasibility as well as the closed-loop stability of practical EfiMPC are discussed. Finally, a CSTR application was used to test the superiority of the proposed EfiMPC strategy, and the simulation results show that EfiMPC can obtain the best global operation performance compared with the other three control strategies; thus, the effectiveness of EfiMPC is demonstrated.

Multi-Objective-Based Tuning of Economic Model Predictive Control of Drinking Water Transport Networks

In this paper, the tuning of economic model predictive control (EMPC) applied to drinking water transport networks (DWTNs) is addressed using multi-objective optimization approaches. The tuning strategies are based on Pareto front calculations of the underlying multi-objective problem. This feature represents an improvement with respect to the standard EMPC approach for weight tuning based on trial and error. Different multi-objective optimization methods with corresponding normalization approaches of the controller objectives are first studied to explore the dynamic nature of the Pareto fronts. An automated decision-making strategy is proposed to select the preferred controller parameters as a function of different disturbance values. The tuning requires an offline training phase and an online application phase. During the offline phase, the controller parameters are selected for different disturbances using the decision-making strategy. During the online phase, two approaches are evaluated: (i) exploiting the controller parameters with the highest frequency in the resulting histogram or (ii) using a regression model between the controller parameters and the disturbances. The proposed tuning strategies are applied to a real-life simulation case study based on the Barcelona DWTN. The simulation results show that the proposed tuning strategies outperform the baseline results by exploiting the periodicity of the water demands profile.

Multi Set-Point Explicit Model Predictive Control for Nonlinear Process Systems

In this article, we introduce a novel framework for the design of multi set-point nonlinear explicit controllers for process systems engineering problems where the set-points are treated as uncertain parameters simultaneously with the initial state of the dynamical system at each sampling instance. To this end, an algorithm for a special class of multi-parametric nonlinear programming problems with uncertain parameters on the right-hand side of the constraints and the cost coefficients of the objective function is presented. The algorithm is based on computed algebra methods for symbolic manipulation that enable an analytical solution of the optimality conditions of the underlying multi-parametric nonlinear program. A notable property of the presented algorithm is the computation of exact, in general nonconvex, critical regions that results in potentially great computational savings through a reduction in the number of convex approximate critical regions.

Model-Free Extremum Seeking Control of Bioprocesses: A Review with a Worked Example

Uncertainty is a common feature of biological systems, and model-free extremum-seeking control has proved a relevant approach to avoid the typical problems related to model-based optimization, e.g., time- and resource-consuming derivation and identification of dynamic models, and lack of robustness of optimal control. In this article, a review of the past and current trends in model-free extremum seeking is proposed with an emphasis on finding optimal operating conditions of bioprocesses. This review is illustrated with a simple simulation case study which allows a comparative evaluation of a few selected methods. Finally, some experimental case studies are discussed. As usual, practice lags behind theory, but recent developments confirm the applicability of the approach at the laboratory scale and are encouraging a transfer to industrial scale.

An Optimal Feedback Control Strategy for Nonlinear, Distributed-Parameter Processes

In this work, an optimal state feedback control strategy is proposed for non-linear, distributed-parameter processes. For different values of a given parameter susceptible to upsets, the strategy involves off-line computation of a repository of optimal open-loop states and gains needed for the feedback adjustment of control. A gain is determined by minimizing the perturbation of the objective functional about the new optimal state and control corresponding to a process upset. When an upset is encountered in a running process, the repository is utilized to obtain the control adjustment required to steer the process to the new optimal state. The strategy is successfully applied to a highly non-linear, gas-based heavy oil recovery process controlled by the gas temperature with the state depending non-linearly on time and two spatial directions inside a moving boundary, and subject to pressure upsets. The results demonstrate that when the process has a pressure upset, the proposed strategy is able to determine control adjustments with negligible time delays and to navigate the process to the new optimal state.

GEKKO Optimization Suite

This paper introduces GEKKO as an optimization suite for Python. GEKKO specializes in dynamic optimization problems for mixed-integer, nonlinear, and differential algebraic equations (DAE) problems. By blending the approaches of typical algebraic modeling languages (AML) and optimal control packages, GEKKO greatly facilitates the development and application of tools such as nonlinear model predicative control (NMPC), real-time optimization (RTO), moving horizon estimation (MHE), and dynamic simulation. GEKKO is an object-oriented Python library that offers model construction, analysis tools, and visualization of simulation and optimization. In a single package, GEKKO provides model reduction, an object-oriented library for data reconciliation/model predictive control, and integrated problem construction/solution/visualization. This paper introduces the GEKKO Optimization Suite, presents GEKKO’s approach and unique place among AMLs and optimal control packages, and cites several examples of problems that are enabled by the GEKKO library.