Predictive Control For Batch Processes Research Articles

Event-Based Switching Iterative Learning Model Predictive Control for Batch Processes With Randomly Varying Trial Lengths.

Iterative learning model predictive control (ILMPC) has been recognized as an excellent batch process control strategy for progressively improving tracking performance along trials. However, as a typical learning-based control method, ILMPC generally requires the strict identity of trial lengths to implement 2-D receding horizon optimization. The randomly varying trial lengths extensively existing in practice can result in the insufficiency of learning prior information, and even the suspension of control update. Regarding this issue, this article embeds a novel prediction-based modification mechanism into ILMPC, to adjust the process data of each trial into the same length by compensating the data of absent running periods with the predictive sequences at the end point. Under this modification scheme, it is proved that the convergence of the classical ILMPC is guaranteed by an inequality condition relative with the probability distribution of trial lengths. Considering the practical batch process with complex nonlinearity, a 2-D neural-network predictive model with parameter adaptability along trials is established to generate highly matched compensation data for the prediction-based modification. To best utilize the real process information of multiple past trials while guaranteeing the learning priority of the latest trials, an event-based switching learning structure is proposed in ILMPC to determine different learning orders according to the probability event with respect to the trial length variation direction. The convergence of the nonlinear event-based switching ILMPC system is analyzed theoretically under two situations divided by the switching condition. The simulations on a numerical example and the injection molding process verify the superiority of the proposed control methods.

A two-stage robust iterative learning model predictive control for batch processes

Iterative learning model predictive control (ILMPC) has been considered as potential control strategy for batch processes. ILMPC can converge to the desired reference trajectory with high precision along batches and ensure system stability within batches. However, as a model-based control method, the control performance of the ILMPC algorithm deteriorates when exists model parameter uncertainty. Therefore, guaranteeing system tracking performance in the case of model parameter uncertainty is a challenging task in the framework designing of ILMPC method. To this end, we develop a two-stage robust ILMPC strategy for batch processes, which integrates the robust iterative learning control (ILC) in the domain of batch-axis and robust model predictive control (MPC) in the domain of time-axis into one comprehensive control scheme. The integrated control law of the developed two-stage robust ILMPC algorithm is obtained by solving two convex optimization problems. As a result, the developed control method obtains faster convergence speed and better tracking performance in the case of model parameter uncertainty. Moreover, the convergence analysis of the system is presented. Finally, comparative simulations are provided to verify the superiority of the developed control algorithm.

Tube-based iterative-learning-model predictive control for batch processes using pre-clustered just-in-time learning methodology

Iterative-learning-model predictive control (ILMPC) has been considered a potential control strategy for batch processes. ILMPC can converge to the desired reference trajectory with high precision along cycles and reject real-time disturbances within cycles. However, as a model-based control method, the control performance of the ILMPC algorithm deteriorates when it suffers the problem of model-plant mismatches. Therefore, simultaneously guaranteeing system convergence along the cycle-axis and robust stability on the time-axis is a challenging task in the framework designing of ILMPC control systems. To this end, we present a type of tube-based ILMPC strategy based on an empirical model for nonlinear batch processes. First, to describe the dynamic behavior of nonlinear batch processes as much as possible with the goal of low computational cost and high modeling accuracy, a pre-clustered just-in-time learning (JITL) model focused on operation data is developed. Then, an ancillary MPC controller is combined with the ILMPC algorithm to form a tube scheme to relieve the impact of model error. In addition, we construct an inverse model system (IMS) to systematically determine the first cycle control input trajectory of the proposed tube-based ILMPC algorithm. As a result, they simultaneously ensure the system convergence along the cycle-axis and robust stability on the time-axis. Still, they can improve convergence speed and tracking performance. Finally, comparative simulations demonstrate the superiority of the proposed control algorithm.

Two-Dimensional Iterative Learning Model Predictive Control for Batch Processes: A New State Space Model Compensation Approach

To achieve improved control performance of batch processes under uncertainty, a novel two-dimensional model predictive iterative learning control (2D-MPILC) scheme is proposed. First, a new two-dimensional (2-D) extended nonminimal state space model is formulated where more degrees of freedom are offered for further controller design; second, a new error compensation strategy is introduced in the controller design to improve the ensemble control performance. The two merits are combined together to form a new control strategy where the model predictive control and iterative learning control are united based on the 2-D framework. By employing the novel model formulation and the system error compensation approaches, the effects caused by uncertainty in the batch processes can be eliminated gradually from cycle-to-cycle such that the desired control performance will be obtained finally. The effectiveness of the proposed 2D-MPILC is tested on the packing pressure in the injection molding batch process.

A 2D-FM model-based robust iterative learning model predictive control for batch processes

The work deals with composite iterative learning model predictive control (CILMPC) for uncertain batch processes via a two dimensional Fornasini–Marchesini (2D-FM) model. A novel equivalent error system is first presented which is composed of state error and tracking error. Then an iterative learning predictive updating law is constructed by 2D state feedback control and the ‘worst’ case linear quadratic function is also designed. Besides, the update controller considering the input and output constraint will be optimized using the worst-case objective function along the infinite moving horizon. The solvable conditions that can be optimized online in real time are constructed using linear matrix inequalities (LMIs). The stability of the proposed control scheme can be achieved with the feasibility of the optimization problem. Compared with robust traditional MPC using one-dimensional models, the presented control approach can guarantee more degrees of tuning to achieve faster convergence of tracking error, which is of more significance since uncertainties exist inevitably in industrial batch processes. Finally, an injection molding process and a three-tank are introduced as two cases to demonstrate the feasibility and superiority of the proposed MPC strategy.

Integrated process design, scheduling, and model predictive control of batch processes with closed‐loop implementation

AbstractSimultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed‐integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed‐loop implementation. We use multi‐parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base‐2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.

Successive Linearization based Stochastic Model Predictive Control for batch processes described by DAEs

This paper presents a formulation of Stochastic Model Predictive Control (SMPC) for control of batch processes modeled by nonlinear Differential algebraic Equations (DAEs). In presence of additive stochastic disturbances, states become stochastic variables and measurements are also corrupted with noise. Hence, to obtain refined state estimates we employ DAE-Extended Kalman Filter (EKF). Linear prediction model obtained by successive linearization is used in the SMPC formulation. Our proposed SMPC solves a chance constrained optimization problem in receding horizon window to calculate future control moves with pre-specified degree of constraint violation for trajectory tracking. Further, the probabilistic constraints are converted to hard constraints by accommodating necessary back-off. We present a simulation case study of batch transesterification reactor modeled by non-linear DAEs to validate the proposed SMPC framework.

A two-dimensional design of model predictive control for batch processes with two-dimensional (2D) dynamics using extended non-minimal state space structure

A modified two-dimensional (2D) structure based control strategy that incorporates model predictive control (MPC) and iterative learning control (ILC) in 2D sense is developed for batch processes in this article. To enhance the control effect of the conventional 2D model predictive iterative learning control (2D-MPILC), an improved non-minimal form of state space model is utilized in the developed method. Through employing such model, the dynamics of the closed-loop system can be regulated by tuning extra process variables. In other words, additional degrees of freedom are achieved in the novel controller design, and the modified control performance is expected for the proposed algorithm. The simulation results on two processes evaluate the effectiveness of the presented 2D-MPILC strategy finally.

Output feedback stochastic nonlinear model predictive control for batch processes

Batch processes play a vital role in the chemical industry, but are difficult to control due to highly nonlinear behaviour and unsteady state operation. Nonlinear model predictive control (NMPC) is therefore one of the few promising approaches. Batch process models are however often affected by uncertainties, which can lower the performance and cause constraint violations. In this paper we propose a shrinking horizon NMPC algorithm accounting for these uncertainties to optimize a probabilistic objective subject to chance constraints. At each sampling time only noisy output measurements are observed. Polynomial chaos expansions (PCE) are used to express the probability distributions of the uncertainties, which are updated at each sampling time using a PCE state estimator and exploited in the NMPC formulation. The approach considers feedback by using time-invariant linear feedback gains, which alleviates the conservativeness of the approach. The NMPC scheme is verified on a polymerization semi-batch reactor case study.

Handling sensor faults in economic model predictive control of batch processes

The problem of sensor fault detection and isolation (FDI) and fault‐tolerant economic model predictive control (FT‐EMPC) for batch processes is addressed. To this end, we first model batch processes using subspace‐based system identification techniques. The analytical redundancy within the identified model is subsequently exploited to detect, isolate, and handle the faulty measurements. The reconciled fault‐free measurements are then incorporated in an economic model predictive controller formulation. Simulation case studies involving the application of the proposed data‐driven FDI and FT‐EMPC algorithms to the energy intensive electric arc furnace process illustrate the improvement in economic performance under various fault scenarios. © 2018 American Institute of Chemical Engineers AIChE J, 65: 617–628, 2019

Model predictive control of batch processes based on two-dimensional integration frame

A novel integrated model predictive control (MPC) strategy for batch processes is proposed in this paper. Both batch-axis and time-axis information are integrated into a two-dimensional control frame. The control law is obtained through the solution of a MPC optimization with time-varying prediction horizon, which leads to superior tracking performance and robustness against disturbance and uncertainty. Moreover, both model identification and dynamic R-parameter are employed to compensate the model-plant mismatch and make zero-error tracking possible. Next, the convergence analysis and tracking performance of the proposed integrated model predictive learning control system are described and proved strictly. Lastly, the effectiveness of the proposed method is verified by an example.

Handling multi‐rate and missing data in variable duration economic model predictive control of batch processes

In the present work, we consider the problem of variable duration economic model predictive control of batch processes subject to multi‐rate and missing data. To this end, we first generalize a recently developed subspace‐based model identification approach for batch processes to handle multi‐rate and missing data by utilizing the incremental singular value decomposition technique. Exploiting the fact that the proposed identification approach is capable of handling inconsistent batch lengths, the resulting dynamic model is integrated into a tiered EMPC formulation that optimizes process economics (including batch duration). Simulation case studies involving application to the energy intensive electric arc furnace process demonstrate the efficacy of the proposed approach compared to a traditional trajectory tracking approach subject to limited availability of process measurements, missing data, measurement noise, and constraints. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2705–2718, 2017

Model predictive control for batch processes: Ensuring validity of predictions

The intuitive and simple ideas that support model predictive control (MPC) along with its capabilities have been the key to its success both in industry and academia. The contribution this paper makes is to further enhance the capabilities of MPC by easing its application to industrial batch processes. Specifically, this paper addresses the problem of ensuring the validity of predictions when applying MPC to such processes. Validity of predictions can be ensured by constraining the decision space of the MPC problem. The performance of the MPC control strategy relies on the ability of the model to predict the behaviour of the process. Using the model in the region in which it is valid improves the resulting performance. In the proposed approach four validity indicators on predictions are defined: two of them consider all the variables in the model, and the other two consider the degrees of freedom of the controller. The validity indicators are defined from the latent variable model of the process. Further to this, these are incorporated as constraints in the MPC optimization problem to bound the decision space and ensure the proper use of the model. Finally, the MPC cost function is modified to enable fine case-specific tuning if desired. Provided the indicators are quadratic, the controller yields a quadratic constrained quadratic programming problem for which efficient solvers are commercially available. A fed-batch fermentation example shows how MPC ensuring validity of predictions improves performance and eases tuning of the controller. The target in the example provided is end-point control accounting for variations in the initial measurable conditions of the batch.

Robust nonlinear model predictive control of batch processes

AbstractNMPC explicitly addresses constraints and nonlinearities during the feedback control of batch processes. This NMPC algorithm also explicitly takes parameter uncertainty into account in the state estimation and state feedback controller designs. An extended Kalman filter estimates the process noise covariance matrix from the parameter uncertainty description and employs a sequential integration and correction strategy to reduce biases in the state estimates due to parameter uncertainty. The shrinking horizon NMPC algorithm minimizes a weighted sum of the nominal performance objective, an estimate of the variance of the performance objective, and an integral of the deviation of the control trajectory from the nominal optimal control trajectory. The robust performance is quantified by estimates of the distribution of the performance index along the batch run obtained by a series expansion about the control trajectory. The control and analysis approaches are applied to a simulated batch crystallization process with a realistic uncertainty description. The proposed robust NMPC algorithm improves the robust performance by a factor of six compared to open loop optimal control, and a factor of two compared to nominal NMPC. Monte Carlo simulations support the results obtained by the distributional robustness analysis technique.

Convergence of constrained model-based predictive control for batch processes

The convergence property of constrained model-based predictive control for batch processes (BMPC) is investigated. BMPC is a recently developed control technique that combines iterative learning control with real-time predictive control. It is proven for a general class of linear constrained systems that the tracking error converges to zero as the run number increases.