Constrained multivariable control of a distillation column using a simplified model predictive control algorithm

Distillation columns are important process units in petroleum refining and need to be maintained close to optimum operating conditions because of economic incentives. Model predictive control has been used for control of these units. However, the constrained optimization problem involved in the control has generally been solved in practice in a piece-meal fashion. To solve the problem without decomposition, the use of a linear programming (LP) formulation using a simplified model predictive control algorithm has been suggested in the literature. In this paper, the LP approach is applied for control of an industrial distillation column. The approach involved a very small size optimization problem and required very modest computational resources. The control algorithm eliminated the large cycling in the product composition that was present using SISO controllers. This resulted in a 2.5% increase in production rate, a 0.5% increase in product recovery, and a significant increase in profit.     

Experimental evaluation of model predictive control with excitation (MPC-X) on an industrial depropanizer

It is commonly observed that over the lifetime of most model predictive controllers, the achieved performance degrades over time. This effect can often be attributed to the fact that the dynamics of the controlled plant change as the plant ages, due to wear and tear, refurbishment and design changes of the plant, to name a few factors. These changes mean that re-identification is necessary to restore the desired performance of the controller. An extension of existing predictive controllers, capable of producing signals suitable for closed loop re-identification, is presented in this article. The main contribution is an extensive experimental evaluation of the proposed controller for closed loop re-identification on an industrial depropanizer distillation column in simulations and in real experiments. The plant experiments are conducted on the depropanizer during normal plant operations. In the simulations, as well as in the experiments, the updated models from closed loop re-identification result in improvement of the performance. The algorithm used combines regular model predictive control with ideas from applications oriented input design and linear matrix inequality based convex relaxation techniques. Even though the experiments show promising result, some implementation problems arise and are discussed.     

Steady-state target optimization designs for integrating real-time optimization and model predictive control

In industrial practice, the optimal steady-state operation of continuous-time processes is typically addressed by a control hierarchy involving various layers. Therein, the real-time optimization (RTO) layer computes the optimal operating point based on a nonlinear steady-state model of the plant. The optimal point is implemented by means of the model predictive control (MPC) layer, which typically uses a linear dynamical model of the plant. The MPC layer usually includes two stages: a steady-state target optimization (SSTO) followed by the MPC dynamic regulator. In this work, we consider the integration of RTO with MPC in the presence of plant-model mismatch and constraints, by focusing on the design of the SSTO problem. Three different quadratic program (QP) designs are considered: (i) the standard design that finds steady-state targets that are as close as possible to the RTO setpoints; (ii) a novel optimizing control design that tracks the active constraints and the optimal inputs for the remaining degrees of freedom; and (iii) an improved QP approximation design were the SSTO problem approximates the RTO problem. The main advantage of the strategies (ii) and (iii) is in the improved optimality of the stationary operating points reached by the SSTO-MPC control system. The performance of the different SSTO designs is illustrated in simulation for several case studies.     

Multiobjective model predictive control

This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.     

Interactions between control and process design under economic model predictive control

Economic model predictive control (EMPC) is a model-based control scheme that integrates process control and economic optimization, which can potentially allow for time-varying operating policies to maximize economic performance. The manner in which an EMPC operates a process to optimize economics depends on the process dynamics, which are fixed by the process design. This raises the question of how process and EMPC designs interact. Works which have addressed process and control design interactions for steady-state operation have sought to simultaneously develop process designs and control law parameters to find the most profitable way to operate a process that is able to prevent process constraints from being violated and to optimize capital costs in the presence of disturbances. Because EMPC has the potential to operate a process in a transient fashion, this work first focuses on how EMPC and process design interact in the absence of disturbances. Using small-scale process examples, we seek to understand the fundamental nature of the interactions between EMPC and process design, including how these interactions can impact computational complexity of the controller and the design procedure. We subsequently utilize the insights gained to suggest controller design variables which might be considered as decision variables for a simultaneous process and control design problem when disturbances are considered.     

Nonlinear parametric predictive temperature control of a distillation column

The integration of a nonlinear reduced process model with Parametric Predictive Control (PPC) is discussed for the bottom temperature control of a stabilizer distillation column. One of the main objectives is ensure the quality of the bottom product despite disturbances and complex dynamics. The purpose is to balance nonlinear control with simplicity, facilitating implementation in a DCS. The controllers developed were first tested in a simulated environment and then in the field, showing good performance under a wide range of operating conditions. The use of an estimator to compensate for modeling errors and unmeasured disturbances is also discussed.     

Robust moving horizon estimation based output feedback economic model predictive control

In this work, we develop an economic model predictive control scheme for a class of nonlinear systems with bounded process and measurement noise. In order to achieve fast convergence of the state estimates to the actual system state as well as the robustness of the observer to measurement and process noise, a deterministic (high-gain) observer is first applied for a small time period with continuous output measurements to drive the estimation error to a small value; after this initial small time period, a robust moving horizon estimation scheme is used on-line to provide more accurate and smoother state estimates. In the design of the robust moving horizon estimation scheme, the deterministic observer is used to calculate reference estimates and confidence regions that contain the actual system state. Within the confidence regions, the moving horizon estimation scheme is allowed to optimize its estimates. The output feedback economic model predictive controller is designed via Lyapunov techniques based on state estimates provided by the deterministic observer and the moving horizon estimation scheme. The stability of the closed-loop system is analyzed rigorously and conditions that ensure the closed-loop stability are derived. Extensive simulations based on a chemical process example illustrate the effectiveness of the proposed approach.     

Feedforward model predictive control

This paper examines the role played by feedforward in model predictive control (MPC). We contrast feedforward with preview action. The latter is standard in model predictive control, whereas feedforward has been rarely, if ever, used in contemporary formulations of MPC. We argue that feedforward can significantly improve performance in the presence of measurement noise and certain types of model uncertainty.     

Serial advanced-multi-step nonlinear model predictive control using an extended sensitivity method

Nonlinear model predictive control (NMPC) can directly handle multi-input multi-output nonlinear systems and explicitly consider input and state constraints. However, the computational load for nonlinear programming (NLP) of large-scale systems limits the range of possible applications and degrades NMPC performance. An NLP sensitivity based approach, advanced-step NMPC, has been developed to address the online computational load. In addition, for cases where the NLP solving time exceeds one sampling time, two types of advanced-multi-step NMPC (amsNMPC), parallel and serial, have been proposed. However, in previous studies, a serial amsNMPC could not be applied to large-scale problems because of the size of extended Karush–Kuhn–Tucker matrix and its Schur complement decomposition, and the robustness was analyzed under a conservative assumption for memory effects. In this paper, we propose a serial amsNMPC using an extended sensitivity method to increase the online computation speed further. We successfully apply it to a large-scale air separation unit using the sparse matrix handling packages of Python, Pyomo, and k_aug tools. Furthermore, an auxiliary NLP formulation is defined to analyze the robustness. Using this with the key properties of an extended sensitivity matrix, we can prove robustness while avoiding the memory effects term.     

A tutorial review of economic model predictive control methods

An overview of the recent results on economic model predictive control (EMPC) is presented and discussed addressing both closed-loop stability and performance for nonlinear systems. A chemical process example is used to provide a demonstration of a few of the various approaches. The paper concludes with a brief discussion of the current status of EMPC and future research directions to promote and stimulate further research potential in this area.     

Multivariable adaptive predictive control of a binary distillation column

This paper presents a tutorial review of an adaptive predictive control system (APCS). Special emphasis is given to the key issues involved in the practical application of APCS to real processes. These practical issues are illustrated by actual application of SISO and MIMO control of a pilot scale binary distillation column. The experimental evaluation of this method reveals the simplicity of the adaptive algorithm and its excellent performance in an industrial type environment. The experimental results easily outperformed well-tuned classical PID controllers. A brief review of other applications of adaptive control to chemical processes is also included in this paper.     

Application of predictive control techniques to a distillation column

Model-based predictive control techniques are widely recognized as having useful application to control problems characterized by complex dynamics and severe time delay. The establishment of a representative process model is the key step in the procedure and for anything other than trivially simple systems is a major hurdle. This paper describes the application of predictive control techniques to a distillation problem which embodies a pure time delay of 2–3 h and time constants of 3–4 h. A sampled-data process model is identified from monitored input/output data and from this a predictive control algorithm is designed. The application of the controller has resulted in very effective closed-loop control of the base composition of the distillation column, where previously only manual supervision was possible.     

Optimal feedback scheduling of model predictive controllers

Model predictive control （MPC） could not be reliably applied to real-time control systems because its computation time is not well defined. Implemented as anytime algorithm, MPC task allows computation time to be traded for control performance, thus obtaining the predictability in time. Optimal feedback scheduling （FS-CBS） of a set of MPC tasks is presented to maximize the global control performance subject to limited processor time. Each MPC task is assigned with a constant bandwidth server （CBS）, whose reserved processor time is adjusted dynamically. The constraints in the FS- CBS guarantee scheduler of the total task set and stability of each component. The FS-CBS is shown robust against the variation of execution time of MPC tasks at runtime. Simulation results illustrate its effectiveness.     

Economic model predictive control of nonlinear singularly perturbed systems

We focus on the development of a Lyapunov-based economic model predictive control (LEMPC) method for nonlinear singularly perturbed systems in standard form arising naturally in the modeling of two-time-scale chemical processes. A composite control structure is proposed in which, a “fast” Lyapunov-based model predictive controller (LMPC) using a quadratic cost function which penalizes the deviation of the fast states from their equilibrium slow manifold and the corresponding manipulated inputs, is used to stabilize the fast dynamics while a two-mode “slow” LEMPC design is used on the slow subsystem that addresses economic considerations as well as desired closed-loop stability properties by utilizing an economic (typically non-quadratic) cost function in its formulation and possibly dictating a time-varying process operation. Through a multirate measurement sampling scheme, fast sampling of the fast state variables is used in the fast LMPC while slow-sampling of the slow state variables is used in the slow LEMPC. Appropriate stabilizability assumptions are made and suitable constraints are imposed on the proposed control scheme to guarantee the closed-loop stability and singular perturbation theory is used to analyze the closed-loop system. The proposed control method is demonstrated through a nonlinear chemical process example.     

Coalitional model predictive control of an irrigation canal

We present a hierarchical control scheme for large-scale systems whose components can exchange information through a data network. The main goal of the supervisory layer is to find the best compromise between control performance and communicational costs by actively modifying the network topology. The actions taken at the supervisory layer alter the control agents’ knowledge of the complete system, and the set of agents with which they can communicate. Each group of linked subsystems, or coalition, is independently controlled through a decentralized model predictive control (MPC) scheme, managed at the bottom layer. Hard constraints on the inputs are imposed, while soft constraints on the states are considered to avoid feasibility issues. The performance of the proposed control scheme is validated on a model of the Dez irrigation canal, implemented on the accurate simulator for water systems SOBEK. Finally, the results are compared with those obtained using a centralized MPC controller.     

Fast, large-scale model predictive control by partial enumeration

Partial enumeration (PE) is presented as a method for treating large, linear model predictive control applications that are out of reach with available MPC methods. PE uses both a table storage method and online optimization to achieve this goal. Versions of PE are shown to be closed-loop stable. PE is applied to an industrial example with more than 250 states, 32 inputs, and a 25-sample control horizon. The performance is less than 0.01% suboptimal, with average speedup factors in the range of 80-220, and worst-case speedups in the range of 4.9-39.2, compared to an existing MPC method. Small tables with only 25-200 entries were used to obtain this performance, while full enumeration is intractable for this example.     

Evolutionary algorithm enhancement for model predictive control and real-time decision support

Effective decision support and model predictive control of real-time environmental systems require that evolutionary algorithms operate more efficiently. A suite of model predictive control (MPC) genetic algorithms are developed and tested offline to explore their value for reducing combined sewer overflow (CSO) volumes during real-time use in a deep-tunnel sewer system. MPC approaches include the micro-GA, the probability-based compact GA, and domain-specific GA methods that reduce the number of decision variable values analyzed within the sewer hydraulic model, thus reducing algorithm search space. Minimum fitness and constraint values achieved by all GA approaches, as well as computational times required to reach the minimum values, are compared to large population sizes with long convergence times. Optimization results for a subset of the Chicago combined sewer system indicate that genetic algorithm variations with a coarse decision variable representation, eventually transitioning to the entire range of decision variable values, are best suited to address the CSO control problem. Although diversity-enhancing micro-GAs evaluate a larger search space and exhibit shorter convergence times, these representations do not reach minimum fitness and constraint values. The domain-specific GAs prove to be the most efficient for this case study. Further MPC algorithm developments are suggested to continue advancing computational performance of this important class of problems with dynamic strategies that evolve as the external constraint conditions change.     

Distributed model predictive control over network information exchange for large-scale systems

A class of large scale systems, which is naturally divided into many smaller interacting subsystems, are usually controlled by a distributed or decentralized control framework. In this paper, a novel distributed model predictive control (MPC) is proposed for improving the performance of entire system. In which each subsystem is controlled by a local MPC and these controllers exchange a reduced set of information with each other by network. The optimization index of each local MPC considers not only the performance of the corresponding subsystem but also that of its neighbours. The proposed architecture guarantees satisfactory performance under strong interactions among subsystems. A stability analysis is presented for the unconstrained distributed MPC and the provided stability results can be employed for tuning the controller. Experiment of the application to accelerated cooling process in a test rig is provided for validating the efficiency of the proposed method.     

On optimality of nonlinear model predictive control

In this note the optimality property of nonlinear model predictive control (MPC) is analyzed. It is well known that the MPC approximates arbitrarily well the infinite horizon (IH) controller as the optimization horizon increases. Hence, it makes sense to suppose that the performance of the MPC is a not decreasing function of the optimization horizon. This work, by means of a counterexample, shows that the previous conjecture is fallacious, even for simple linear systems.