Distributed economic model predictive control for operational safety of nonlinear processes

Achieving operational safety of chemical processes while operating them in an economically‐optimal manner is a matter of great importance. Our recent work integrated process safety with process control by incorporating safety‐based constraints within model predictive control (MPC) design; however, the safety‐based MPC was developed with a centralized architecture, with the result that computation time limitations within a sampling period may reduce the effectiveness of such a controller design for promoting process safety. To address this potential practical limitation of the safety‐based control design, in this work, we propose the integration of a distributed model predictive control architecture with Lyapunov‐based economic model predictive control (LEMPC) formulated with safety‐based constraints. We consider both iterative and sequential distributed control architectures, and the partitioning of inputs between the various optimization problems in the distributed structure based on their impact on process operational safety. Moreover, sufficient conditions that ensure feasibility and closed‐loop stability of the iterative and sequential safety distributed LEMPC designs are given. A comparison between the proposed safety distributed EMPC controllers and the safety centralized EMPC is demonstrated via a chemical process example. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3404–3418, 2017     

Distributed model predictive control of switched nonlinear systems with scheduled mode transitions

A method for the design of distributed model predictive control (DMPC) systems for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule is presented. Under appropriate stabilizability assumptions on the existence of a set of feedback controllers that can stabilize the closed‐loop switched, nonlinear system, a cooperative DMPC architecture using Lyapunov‐based model predictive control (MPC) in which the distributed controllers carry out their calculations in parallel and communicate in an iterative fashion to compute their control actions is designed. The proposed DMPC design is applied to a nonlinear chemical process network with scheduled mode transitions and its performance and computational efficiency properties in comparison to a centralized MPC architecture are evaluated through simulations. © 2013 American Institute of Chemical Engineers AIChE J, 59:860‐871, 2013     

Real‐time economic model predictive control of nonlinear process systems

Closed‐loop stability of nonlinear systems under real‐time Lyapunov‐based economic model predictive control (LEMPC) with potentially unknown and time‐varying computational delay is considered. To address guaranteed closed‐loop stability (in the sense of boundedness of the closed‐loop state in a compact state‐space set), an implementation strategy is proposed which features a triggered evaluation of the LEMPC optimization problem to compute an input trajectory over a finite‐time prediction horizon in advance. At each sampling period, stability conditions must be satisfied for the precomputed LEMPC control action to be applied to the closed‐loop system. If the stability conditions are not satisfied, a backup explicit stabilizing controller is applied over the sampling period. Closed‐loop stability under the real‐time LEMPC strategy is analyzed and specific stability conditions are derived. The real‐time LEMPC scheme is applied to a chemical process network example to demonstrate closed‐loop stability and closed‐loop economic performance improvement over that achieved for operation at the economically optimal steady state. © 2014 American Institute of Chemical Engineers AIChE J, 61: 555–571, 2015     

Economic model predictive control of nonlinear time‐delay systems: Closed‐loop stability and delay compensation

Closed‐loop stability of nonlinear time‐delay systems under Lyapunov‐based economic model predictive control (LEMPC) is considered. LEMPC is initially formulated with an ordinary differential equation model and is designed on the basis of an explicit stabilizing control law. To address closed‐loop stability under LEMPC, first, we consider the stability properties of the sampled‐data system resulting from the nonlinear continuous‐time delay system with state and input delay under a sample‐and‐hold implementation of the explicit controller. The steady‐state of this sampled‐data closed‐loop system is shown to be practically stable. Second, conditions such that closed‐loop stability, in the sense of boundedness of the closed‐loop state, under LEMPC are derived. A chemical process example is used to demonstrate that indeed closed‐loop stability is maintained under LEMPC for sufficiently small time‐delays. To cope with performance degradation owing to the effect of input delay, a predictor feedback LEMPC methodology is also proposed. The predictor feedback LEMPC design employs a predictor to compute a prediction of the state after the input delay period and an LEMPC scheme that is formulated with a differential difference equation (DDE) model, which describes the time‐delay system, initialized with the predicted state. The predictor feedback LEMPC is also applied to the chemical process example and yields improved closed‐loop stability and economic performance properties. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4152–4165, 2015     

Transition from Batch to Continuous Operation in Bio‐Reactors: A Model Predictive Control Approach and Application

This work considers the problem of determining the transition of ethanol‐producing bio‐reactors from batch to continuous operation and subsequent control subject to constraints and performance considerations. To this end, a Lyapunov‐based non‐linear model predictive controller is utilized that stabilizes the bio‐reactor under continuous mode of operation. The key idea in the predictive controller is the formulation of appropriate stability constraints that allow an explicit characterization of the set of initial conditions from where feasibility of the optimization problem and hence closed‐loop stability is guaranteed. Additional constraints are incorporated in the predictive control design to expand on the set of initial conditions that can be stabilized by control designs that only require the value of the Lyapunov function to decay. Then, the explicit characterization of the set of stabilizable initial conditions is used in determining the appropriate time for which the reactor must be run in batch mode. Specifically, the predictive control approach is utilized in determining the appropriate batch length that achieves stabilizable values of the state variables at the end of the batch. Application of the proposed method to the ethanol production process using Zymomonas mobilis as the ethanol producing micro‐organism demonstrates the effectiveness of the proposed model predictive control strategy in stabilizing the bio‐reactor.     

A delay‐dependent robust fuzzy MPC approach for nonlinear CSTR

Based on Takagi–Sugeno (T–S) fuzzy models, a robust fuzzy model predictive control (MPC) algorithm is presented for a class of nonlinear time‐delay systems with input constraints. Delay‐dependent sufficient conditions for the robust stability of the closed‐loop system are derived, and the condition for the existence of the fuzzy model predictive controller is formulated in terms of nonlinear matrix inequality via the parallel distributed compensation (PDC) approach. By using a novel matrix transform technique, a receding optimization problem with linear matrix inequality (LMIs) constraints is constructed to design the desired controllers with an on‐line optimal receding horizon guaranteed cost. Finally, an example of continuous stirred tank reactors (CSTR) is given to demonstrate the effectiveness of the proposed results.     

Economic model predictive control of nonlinear process systems using empirical models

Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained either through application of first principles or through system identification techniques. In industrial practice, it may be difficult in general to obtain an accurate first‐principles model of the process. Motivated by this, in the present work, Lyapunov‐based EMPC (LEMPC) is designed with a linear empirical model that allows for closed‐loop stability guarantees in the context of nonlinear chemical processes. Specifically, when the linear model provides a sufficient degree of accuracy in the region where time varying economically optimal operation is considered, conditions for closed‐loop stability under the LEMPC scheme based on the empirical model are derived. The LEMPC scheme is applied to a chemical process example to demonstrate its closed‐loop stability and performance properties as well as significant computational advantages. © 2014 American Institute of Chemical Engineers AIChE J, 61: 816–830, 2015     

Error‐triggered on‐line model identification for model‐based feedback control

In industry, it may be difficult in many applications to obtain a first‐principles model of the process, in which case a linear empirical model constructed using process data may be used in the design of a feedback controller. However, linear empirical models may not capture the nonlinear dynamics over a wide region of state‐space and may also perform poorly when significant plant variations and disturbances occur. In the present work, an error‐triggered on‐line model identification approach is introduced for closed‐loop systems under model‐based feedback control strategies. The linear models are re‐identified on‐line when significant prediction errors occur. A moving horizon error detector is used to quantify the model accuracy and to trigger the model re‐identification on‐line when necessary. The proposed approach is demonstrated through two chemical process examples using a model‐based feedback control strategy termed Lyapunov‐based economic model predictive control (LEMPC). The chemical process examples illustrate that the proposed error‐triggered on‐line model identification strategy can be used to obtain more accurate state predictions to improve process economics while maintaining closed‐loop stability of the process under LEMPC. © 2016 American Institute of Chemical Engineers AIChE J, 63: 949–966, 2017     

Smart manufacturing: Handling preventive actuator maintenance and economics using model predictive control

Integrating components and systems of the manufacturing process is an important area of research to enable the future development and deployment of the Smart Manufacturing paradigm. An economic model predictive control (EMPC) scheme is proposed that effectively integrates scheduled preventive control actuator maintenance, process economics, and process control into a unified methodology. To accomplish this goal, a Lyapunov‐based EMPC (LEMPC) scheme is formulated for handling changing number of online actuators (i.e., changing number of manipulated inputs). Closed‐loop stability under the proposed LEMPC is proven. Subsequently, the LEMPC is applied to a chemical process network used for benzene alkylation to demonstrate that the LEMPC can maintain stability and improve dynamic economic performance of the process network in the presence of changing number of available control actuators resulting from scheduled preventive maintenance tasks. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2179–2196, 2014     

Economic model predictive control with time‐varying objective function for nonlinear process systems

Economic model predictive control (EMPC) is a control scheme that combines real‐time dynamic economic process optimization with the feedback properties of model predictive control (MPC) by replacing the quadratic cost function with a general economic cost function. Almost all the recent work on EMPC involves cost functions that are time invariant (do not explicitly account for time‐varying process economics). In the present work, we focus on the development of a Lyapunov‐based EMPC (LEMPC) scheme that is formulated with an explicitly time‐varying economic cost function. First, the formulation of the proposed two‐mode LEMPC is given. Second, closed‐loop stability is proven through a theoretical treatment. Last, we demonstrate through extensive closed‐loop simulations of a chemical process that the proposed LEMPC can achieve stability with time‐varying economic cost as well as improve economic performance of the process over a conventional MPC scheme. © 2013 American Institute of Chemical Engineers AIChE J 60: 507–519, 2014     

Actuator stiction compensation via model predictive control for nonlinear processes

The problem of valve stiction is addressed, which is a nonlinear friction phenomenon that causes poor performance of control loops in the process industries. A model predictive control (MPC) stiction compensation formulation is developed including detailed dynamics for a sticky valve and additional constraints on the input rate of change and actuation magnitude to reduce control loop performance degradation and to prevent the MPC from requesting physically unrealistic control actions due to stiction. Although developed with a focus on stiction, the MPC‐based compensation method presented is general and has potential to compensate for other nonlinear valve dynamics which have some similarities to those caused by stiction. Feasibility and closed‐loop stability of the proposed MPC formulation are proven for a sufficiently small sampling period when Lyapunov‐based constraints are incorporated. Using a chemical process example with an economic model predictive controller (EMPC), the selection of appropriate constraints for the proposed method is demonstrated. The example verified the incorporation of the stiction dynamics and actuation magnitude constraints in the EMPC causes it to select set‐points that the valve output can reach and causes the operating constraints to be met. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2004–2023, 2016     

分布式预测控制全局协调及稳定性分析

实际的化工过程系统维数都较高,对系统进行关联分解并使各子系统进行协调来实现整个大系统全局最优是必要的。对于关联作用存在反馈的化工过程大系统,分散式预测控制算法和基于串联过程推导的邻域优化分布式预测控制算法都不适用,因此在这两个算法的基础上推导出约束条件下基于全局协调的分布式预测控制算法。针对分解后得到的子系统,假设子系统间关联信息的传递存在一个采样时间的滞后,建立每个子系统的预测模型时考虑滞后的关联信息;建立子系统的目标函数时,综合考虑所有关联子系统的输入和输出对本子系统的关联作用;每个子系统滚动优化并行求解各自的最优控制作用。然后,在一定条件下分析了基于全局协调的分布式预测控制算法与集中预测控制算法的一致性,并说明了闭环系统的全局稳定性。最后,通过对Shell公司重油分馏塔和TE过程两个例子进行仿真并与其他算法进行比较,验证了本文提出算法的可行性和有效性。     

Distributed model predictive control based on dissipativity

A noncooperative approach to plant‐wide distributed model predictive control based on dissipativity conditions is developed. The plant‐wide process and distributed control system are represented as two interacting process and controller networks, with interaction effects captured by the dissipativity properties of subsystems and network topologies. The plant‐wide stability and performance conditions are developed based on global dissipativity conditions, which in turn are translated into the dissipative trajectory conditions that each local model predictive control MPC must satisfy. This approach is enabled by the use of dynamic supply rates in quadratic difference forms, which capture detailed dynamic system information. A case study is presented to illustrate the results. © 2012 American Institute of Chemical Engineers AIChE J, 59: 787–804, 2013     

Multi‐controller scheme for load rejection and set‐point tracking

To acheive complete compensation for loads, a novel multi‐controller scheme with feedforward control is proposed. This scheme has four controllers, a set‐point controller, two load controllers, and a feedforward controller. This results in the separation of the load response from the set‐point response in a closed‐loop system. These four controllers can then be designed independently to achieve good system performance for both set‐point tracking and load rejection. One of the load controllers can be chosen as a proportional controller; this guarantees physical realizability and provides excellent compensation. The results of simulation and real time control show that the proposed multi‐controller scheme is superior to a double‐controller system and a Smith predictor in the presence of large uncertainty in process dynamics especially for load disturbances.     

Economic model predictive control of nonlinear process systems using Lyapunov techniques

In this work, we develop model predictive control (MPC) designs, which are capable of optimizing closed‐loop performance with respect to general economic considerations for a broad class of nonlinear process systems. Specifically, in the proposed designs, the economic MPC optimizes a cost function, which is related directly to desired economic considerations and is not necessarily dependent on a steady‐state—unlike conventional MPC designs. First, we consider nonlinear systems with synchronous measurement sampling and uncertain variables. The proposed economic MPC is designed via Lyapunov‐based techniques and has two different operation modes. The first operation mode corresponds to the period in which the cost function should be optimized (e.g., normal production period); and in this operation mode, the MPC maintains the closed‐loop system state within a predefined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the economic MPC to an appropriate steady‐state. In this operation mode, suitable Lyapunov‐based constraints are incorporated in the economic MPC design to guarantee that the closed‐loop system state is always bounded in the predefined stability region and is ultimately bounded in a small region containing the origin. Subsequently, we extend the results to nonlinear systems subject to asynchronous and delayed measurements and uncertain variables. Under the assumptions that there exist an upper bound on the interval between two consecutive asynchronous measurements and an upper bound on the maximum measurement delay, an economic MPC design which takes explicitly into account asynchronous and delayed measurements and enforces closed‐loop stability is proposed. All the proposed economic MPC designs are illustrated through a chemical process example and their performance and robustness are evaluated through simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Distributed lyapunov‐based model predictive control with neighbor‐to‐neighbor communication

This work considers distributed predictive control of large‐scale nonlinear systems with neighbor‐to‐neighbor communication. It fulfills the gap between the existing centralized Lyapunov‐based model predictive control (LMPC) and the cooperative distributed LMPC and provides a balanced solution in terms of implementation complexity and achievable performance. This work focuses on a class of nonlinear systems with subsystems interacting with each other via their states. For each subsystem, an LMPC is designed based on the subsystem model and the LMPC only communicates with its neighbors. At a sampling time, a subsystem LMPC optimizes its future control input trajectory assuming that the states of its upstream neighbors remain the same as (or close to) their predicted state trajectories obtained at the previous sampling time. Both noniterative and iterative implementation algorithms are considered. The performance of the proposed designs is illustrated via a chemical process example. © 2014 American Institute of Chemical Engineers AIChE J 60: 4124–4133, 2014     

Enhanced Performance Assessment of Subspace Model‐Based Predictive Controller with Parameters Tuning

This study focuses on performance assessment of model predictive control. An MPC‐achievable benchmark for the unconstrained case is proposed based on closed‐loop subspace identification. Two performance measures can be constructed to evaluate the potential benefit to update the new identified model. Potential benefit by tuning the parameter can be found from trade‐off curves. Effect of constraints imposed on process variables can be evaluated by the installed controller benchmark. The MPC‐achievable benchmark for the constrained case can be estimated via closed‐loop simulation provided that constraints are known. Simulation of an industrial example was done using the proposed method.     

Robust distributed economic model predictive control based on differential dissipativity

In this article, a robust distributed economic model predictive control (DEMPC) approach is developed for plant-wide chemical processes. The proposed approach achieves arbitrary feasible setpoints that may vary frequently, attenuates the plant-wide effects of unknown disturbances and minimizes a plant-wide economic cost. In this approach, a plant-wide process is represented as a network of process units and each process unit is controlled by an individual controller which shares a plant-wide optimization economic objective and stability conditions through the network. To ensure the convergence of process variables to arbitrary setpoints, a contraction condition is developed for the DEMPC, based on the contraction theory. To deal with the effects of interactions among process units, the concept of dissipativity is adopted. Using sum-separable control contraction metrics, a reference-independent robust stability condition is developed to ensure the plant-wide disturbance effects (under interactions among process units) to be attenuated in terms of differential ℒ₂ gain and represented by a plant-wide differential dissipativity condition, which is converted into the differential dissipativity conditions that individual controllers need to satisfy. This approach facilitates the optimization of plant-wide economic costs with global constraints in a distributed way, allowing efficient implementation of alternating direction method of multipliers (ADMM). The proposed approach is illustrated using a reactor-separator process.