Model predictive control of reactive distillation for benzene hydrogenation

Benzene hydrogenation via reactive distillation is a process that has been widely adopted in the process industry. However, studies in the open literature on control of this process are rare and seem to indicate that conventional decentralized PI control results in sluggish responses when the reactive distillation column is subjected to disturbances in the feed concentration. In order to overcome this performance limitation, this work investigates model predictive control (MPC) strategies of a reactive distillation column model, which has been implemented in gPROMS. Several MPCs based upon different sets of manipulated and controlled variables are investigated where the remaining variables remain under regular feedback control. Further, MPC controllers with output disturbance correction and, separately, with input disturbance correction have been investigated. The results show that the settling time of the column can be reduced and the closed loop dynamics significantly improved for the system under MPC control compared to a decentralized PI control structure.     

Design of a Robust Optimal Decentralized PI Controller Based on Nonlinear Constraint Optimization For Level Regulation: An Experimental Study

This paper presents the development of a new robust optimal decentralized PI controller based on nonlinear optimization for liquid level control in a coupled tank system. The proposed controller maximizes the closed-loop bandwidth for specified gain and phase margins, with constraints on the overshoot ratio to achieve both closed-loop performance and robustness. In the proposed work, a frequency response fitting model reduction technique is initially employed to obtain a first order plus dead time (FOPDT) model of each higher order subsystem. Furthermore, based on the reduced order model, a proposed controller is designed. The stability and performance of the proposed controller are verified by considering multiplicative input and output uncertainties. The performance of the proposed optimal robust decentralized control scheme has been compared with that of a decentralized PI controller. The proposed controller is implemented in real-time on a coupled tank system. From the obtained results, it is shown that the proposed optimal decentralized PI controller exhibits superior control performance to maintain the desired level, for both the nominal as well as the perturbed case as compared to a decentralized PI controller.      

Model predictive pressure control of steam networks

The control scheme of industrial power plants leads typically to a complex multivariable control structure with active constraints to be taken care of. Then Model Predictive Control method (MPC) handles multivariate control problems naturally and optimal control result is calculated considering actuator limitations and constraints of process variables. MPC is applied to control the pressure stability in a multilevel steam network. The system is demonstrated in a simulator environment. MPC can also be used as a convenient tool for analyzing and designing the structure of the steam network. A power plant simulator controlled by MPC helps to decide the location and the capacity of steam levelling components needed to stabilize the operation of the process.     

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.     

Adaptive neural model-based decentralized predictive control

This paper considers the problem of developing an adaptive neural model-based decentralized predictive controller for general multivariable non-linear processes, where the equations governing the system are unknown. It derives a method for implementing a neural network model for unknown non-linear process dynamics for adaptive control. The performance of this controller is demonstrated and evaluated using a simulated chemical process: multivariable non-linear control of distillation column. The simulation results indicate that the proposed control strategies have good practical potential for adaptive control of multivariable non-linear processes.     

Decentralized model predictive control of a multi-evaporator air conditioning system

Temperature control of multiple zones with a multi-evaporator vapor compression system is a common problem in modern air conditioning. Due to the coupled system dynamics, standard decoupled controllers can interfere with each unit′s performance. This paper proposes an architecture that is decentralized and modular, avoiding competing controllers and the practical difficulty of implementing a centralized controller. A model predictive control (MPC) supervisor calculates evaporator cooling and pressure setpoints for each zone, balancing temperature regulation with energy efficiency; these setpoints are tracked by local level controllers, which rely upon MPC's ability to respect constraints in order to maintain safe, efficient operation.     

Constrained model predictive force control of an electrohydraulic actuator

An analytical MPC controller was designed for force control of a single-rod electrohydraulic actuator. The controller based on a difference equation uses short control horizon. The constraints on both input and output variables are taken into consideration by the controller. The mechanism of output constraints satisfaction uses output prediction and makes possible to constrain the output values many sampling instants ahead. Thus, it extends capabilities of the analytical MPC controllers to the field reserved so far for much more computationally expensive numerical MPC algorithms. Results of real life experiments illustrate efficiency of the proposed controller. The results also show that the MPC controller has better tracking performance than conventional P and PI controllers. The MPC controller with the constraint handling mechanisms, though relatively simple, offers very good performance. As the design process is detailed, it is possible to relatively easy adapt the proposed approach to other control plants.     

Decentralized filtering adaptive constrained tracking control for interconnected nonlinear systems

This paper presents a novel decentralized filtering adaptive constrained tracking control framework for uncertain interconnected nonlinear systems. Each subsystem has its own decentralized controller based on the established decentralized state predictor. For each subsystem, a piecewise constant adaptive law will generate total uncertainty estimates by solving the error dynamics between the host system and decentralized state predictor with the neglection of unknowns, whereas a decentralized filtering control law is designed to compensate both local and mismatched uncertainties from other subsystems, as well as achieve the local objective tracking of the host system. The achievement of global objective depends on the achievement of local objective for each subsystem. In the control scheme, the nonlinear uncertainties are compensated for within the bandwidth of low‐pass filters, while the trade‐off between tracking and constraints violation avoidance is formulated as a numerical constrained optimization problem which is solved periodically. Priority is given to constraints violation avoidance at the cost of deteriorated tracking performance. The uniform performance bounds are derived for the system states and control inputs as compared to the corresponding signals of a bounded closed‐loop reference system, which assumes partial cancelation of uncertainties within the bandwidth of the control signal. Compared with model predictive control (MPC) and unconstrained controller, the proposed control architecture is capable of solving the tracking control problems for interconnected nonlinear systems subject to constraints and uncertainties.     

Performance evaluation of two industrial MPC controllers

This paper presents case studies of the performance evaluation of two industrial multivariate model predictive control (MPC) based controllers at the Mitsubishi chemical complex in Mizushima, Japan: (1) a 6-output, 6-input para-xylene (PX) production process with six measured disturbance variables that are used for feedforward control; and (2) a multivariate MPC controller for a 6-output, 5-input poly-propylene splitter column with two measured disturbances. A generalized predictive controller-based MPC algorithm has been implemented on the PX process. Data from the PX unit before and after the MPC implementation are analyzed to obtain and compare several different measures of multivariate controller performance. The second case study is concerned with performance assessment of a commercial MPC controller on a propylene splitter. A discussion on the diagnosis of poor performance for the second MPC application suggests significant model-plant-mismatch under varying load conditions and highlights the role of constraints.     

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.     

Decentralized robust PI controller design for an industrial boiler

This paper presents a new scheme to design decentralized robust PI controllers for uncertain LTI multivariable systems. Sufficient conditions for closed-loop stability and closed-loop diagonal dominance (almost decoupling) of a multivariable system are obtained. Satisfying these conditions and robust performance of the overall system are modeled as local robust performance problems. Then, by appropriately selecting the time constants of the closed-loop isolated subsystems in the IMC (Internal Model Control) strategy, the defined local robust performance problems are solved. To design a decentralized robust PI controller for a real industrial utility boiler, a control oriented nonlinear model for the boiler is identified. The nonlinearity of the system is modeled as uncertainty for a nominal LTI multivariable system. Using the new proposed method, a decentralized PI controller for the uncertain LTI model is designed. The designed controller is applied to the real system. The simulation results show the effectiveness of the proposed methodology.     

Plant-wide hierarchical optimization and control of an industrial hydrocracking process

Hydrocracking is a crucial refinery process in which heavy hydrocarbons are converted to more valuable, low-molecular weight products. Hydrocracking plants operate with large throughputs and varying feedstocks. In addition the product specifications change due to varying economic and market conditions. In such a dynamic operating environment, the potential gains of real-time optimization (RTO) and control are quite high. At the same time, real-time optimization of hydrocracking plants is a challenging task. A complex network of reactions, which are difficult to characterize, takes place in the hydrocracker. The reactor effluent affects the operation of the fractionator downstream and the properties of the final products. In this paper, a lumped first-principles reactor model and an empirical fractionation model are used to predict the product distribution and properties on-line. Both models have been built and validated using industrial data. A cascaded model predictive control (MPC) structure is developed in order to operate both the reactor and fractionation column at maximum profit. In this cascade structure, reactor and fractionation units are controlled by local decentralized MPC controllers whose set-points are manipulated by a supervisory MPC controller. The coordinating action of the supervisory MPC controller accomplishes the transition between different optimum operating conditions and helps to reject disturbances without violating any constraints. Simulations illustrate the applicability of the proposed method on the industrial process.     

Uniting bounded control and MPC for stabilization of constrained linear systems

In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a logic-based supervisor that constantly monitors the plant, are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under MPC, reconciles the stability and optimality properties of both controllers, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid control scheme is shown to provide, irrespective of the chosen MPC formulation, a safety net for the practical implementation of MPC, for open-loop unstable plants, by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The implementation of the proposed approach is illustrated, through numerical simulations, for an exponentially unstable linear system.     

精馏塔的自适应解耦控制

本文针对某精馏塔提出了一种简单的自适应解耦控制器。该控制器将广义最小方差控制策略和解耦补偿器结合起来,不仅可以对随机多变量系统实现动静态解耦而且具有良好的伺服跟踪性能。该控制器与常规PI控制器在某精馏塔双组分控制中的对比实验结果表明自适应解耦控制的性能优越于常规PI控制。     

An optimal control based approach to designing plantwide control system architectures

An approach to designing decentralized plantwide control system architectures is presented. The approach is based on splitting the optimal controller gain matrix that results from solving an output optimal control problem into feedback and feedforward parts. These two parts are then used to design and evaluate decentralized control systems. Results for the application of the methodology to a realistic, 4 by 4 reactor with recycle process are given. For this system, the optimal control based approach suggests feedback pairings that are significantly different than those suggested by the steady state RGA. The approach presented can give an indication if MPC is preferred over a decentralized approach to plantwide control. Comparison of the results produced by the best decentralized plantwide system and a model predictive control system are presented.     

Adaptive air-fuel ratio control with MLP network

This paper presents an application of adaptive neural network model-based predictive control (MPC) to the air-fuel ratio of an engine simulation. A multi-layer perceptron (MLP) neural network is trained using two on-line training algorithms: a back propagation algorithm and a recursive least squares (RLS) algorithm. It is used to model parameter uncertainties in the nonlinear dynamics of internal combustion (IC) engines. Based on the adaptive model, an MPC strategy for controlling air-fuel ratio is realized, and its control performance compared with that of a traditional PI controller. A reduced Hessian method, a newly developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up nonlinear optimization in the MPC.     

Robust hybrid predictive control of nonlinear systems

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, e.g., to computational difficulties in the optimization or infeasibility) or leads to instability (due, e.g., to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.     

A new robust model predictive control method I: theory and computation

The success of the single-model MPC (SMPC) controller depends on the accuracy of the process model. Modeling errors cause sub-optimal control performance and may cause the control system to become closed-loop unstable. The goal of this paper is to examine the control performance of the robust MPC (RMPC) method proposed by Wang and Rawlings [34] on several illustrative examples. In this paper, we show the RMPC method successfully controls systems with time-varying uncertainties in the process gain, time constant and time delay and achieves offset-free non-zero set point tracking and non-zero disturbance rejection subject to input and output constraints.     

A General Robust MPC Design for the State‐Space Model: Application to Paper Machine Process

Applying model predictive control (MPC) in some cases such as complicated process dynamics and/or rapid sampling leads us to poorly numerically conditioned solutions and heavy computational load. Furthermore, there is always mismatch in a model that describes a real process. Therefore, in this paper in order to prevail over the mentioned difficulties, we design a robust MPC using the Laguerre orthonormal basis in order to speed up the convergence at the same time with lower computation adding an extra parameter “a” in MPC. In addition, the Kalman state estimator is included in the prediction model and accordingly the MPC design is related to the Kalman estimator parameters as well as the error of estimations which helps the controller react faster against unmeasured disturbances. Tuning the parameters of the Kalman estimator as well as MPC is another achievement of this paper which guarantees the robustness of the system against the model mismatch and measurement noise. The sensitivity function at low frequency is minimized to tune the MPC parameters since the lower the magnitude of the sensitivity function at low frequency the better command tracking and disturbance rejection results. The integral absolute error (IAE) and peak of the sensitivity are used as constraints in optimization procedure to ensure the stability and robustness of the controlled process. The performance of the controller is examined via the controlling level of a Tank and paper machine processes.     

Multi-objective constraint optimizing IOL control of distillation column with nonlinear observer

Performance of input–output linearizing (IOL) controllers suffers due to constraints on input and output variables. This problem is successfully tackled by augmenting IOL controllers with quadratic dynamic matrix controller (QDMC). However, this has created a constraint-mapping problem for coupled MIMO systems like distillation column. A multi-objective optimization problem needs to be solved to map the constraints on inputs. A suitable transformation technique is proposed to convert this multi-objective optimization problem to a single objective one. This makes the controller less computationally intensive and easy to implement. This controller (IOL-QDMC) along with nonlinear observer is implemented on a binary distillation column for dual composition control. Its performance is evaluated against a quadratic dynamic matrix controller (QDMC) and input–output linearization with PI controller (IOL-PI).