Feasibility analysis and online adjustment of constraints in model predictive control integrated with soft sensor

Feasibility analysis of soft constraints for input and output variables is critical for model predictive control (MPC).When encountering the infeasible situation,some way should be found to adjust the constraints to guarantee that the optimal control law exists.For MPC integrated with soft sensor,considering the soft constraints for critical variables additionally makes it more complicated and difficult for feasibility analysis and constraint adjustment.Therefore,the main contributions are that a linear programming approach is proposed for feasibility analysis,and the corresponding constraint adjustment method and procedure are given as well.The feasibility analysis gives considerations to the manipulated,secondary and critical variables,and the increment of manipulated variables as well.The feasibility analysis and the constraint adjustment are conducted in the entire control process and guarantee the existence of optimal control.In final,a simulation case confirms the contributions in this paper.     

Koopman Lyapunov-based model predictive control of nonlinear chemical process systems

In this work, we propose the integration of Koopman operator methodology with Lyapunov-based model predictive control (LMPC) for stabilization of nonlinear systems. The Koopman operator enables global linear representations of nonlinear dynamical systems. The basic idea is to transform the nonlinear dynamics into a higher dimensional space using a set of observable functions whose evolution is governed by the linear but infinite dimensional Koopman operator. In practice, it is numerically approximated and therefore the tightness of these linear representations cannot be guaranteed which may lead to unstable closed-loop designs. To address this issue, we integrate the Koopman linear predictors in an LMPC framework which guarantees controller feasibility and closed-loop stability. Moreover, the proposed design results in a standard convex optimization problem which is computationally attractive compared to a nonconvex problem encountered when the original nonlinear model is used. We illustrate the application of this methodology on a chemical process example.     

A Monte-Carlo based model approximation technique for linear model predictive control of nonlinear systems

In this paper we present a model approximation technique based on N-step-ahead affine representations obtained via Monte-Carlo integrations. The approach enables simultaneous linearization and model order reduction of nonlinear systems in the original state space thus allowing the application of linear MPC algorithms to nonlinear systems. The methodology is detailed through its application to benchmark model examples.     

Stability of model predictive control with time-varying weights

In this paper, we show that the stability of constrained Model Predictive Control (MPC) systems can be guaranteed by using time-varying weights. It unifies two popular MPC algorithms with guaranteed stability - Infinite Horizon MPC and MPC with End Constraint. Use of time-varying weights may also be useful in analyzing stability properties of MPC for linear time-varying systems as well as uncertain linear systems.     

Handling sensor malfunctions in control of particulate processes

This work focuses on feedback control of particulate processes in the presence of sensor data losses. Two typical particulate process examples, a continuous crystallizer and a batch protein crystallizer, modeled by population balance models (PBMs), are considered. In the case of the continuous crystallizer, a Lyapunov-based nonlinear output feedback controller is first designed on the basis of an approximate moment model and is shown to stabilize an open-loop unstable steady-state of the PBM in the presence of input constraints. Then, the problem of modeling sensor data losses is investigated and the robustness of the nonlinear controller with respect to data losses is extensively investigated through simulations. In the case of the batch crystallizer, a predictive controller is first designed to obtain a desired crystal size distribution at the end of the batch while satisfying state and input constraints. Subsequently, we point out how the constraints in the predictive controller can be modified as a means of achieving constraint satisfaction in the closed-loop system in the presence of sensor data losses.     

Predictive control of particle size distribution in particulate processes

In this work, we focus on the development and application of predictive-based strategies for control of particle size distribution (PSD) in continuous and batch particulate processes described by population balance models (PBMs). The control algorithms are designed on the basis of reduced-order models, utilize measurements of principle moments of the PSD, and are tailored to address different control objectives for the continuous and batch processes. For continuous particulate processes, we develop a hybrid predictive control strategy to stabilize a continuous crystallizer at an open-loop unstable steady-state. The hybrid predictive control strategy employs logic-based switching between model predictive control (MPC) and a fall-back bounded controller with a well-defined stability region. The strategy is shown to provide a safety net for the implementation of MPC algorithms with guaranteed stability closed-loop region. For batch particulate processes, the control objective is to achieve a final PSD with desired characteristics subject to both manipulated input and product quality constraints. An optimization-based predictive control strategy that incorporates these constraints explicitly in the controller design is formulated and applied to a seeded batch crystallizer. The strategy is shown to be able to reduce the total volume of the fines by 13.4% compared to a linear cooling strategy, and is shown to be robust with respect to modeling errors.     

过程预测控制中约束可行性研究与在线调整

化工过程控制中,普遍存在着各种对输入和输出变量的约束条件。系统与约束之间的矛盾有可能造成约束预测控制的优化问题不可行,为生产带来负面影响。基于线性系统离散状态空间的动态模型,从凸多面体距离角度,对有约束预测控制的可行性分析和不可行时的约束处理问题进行讨论,提出在每步求解约束预测控制律之前进行必要的可行性分析和合理的约束调整的在线滚动算法,从而使约束条件在整个时域得到满足,并且保证系统的控制性能。通过CSTR模型的控制仿真实验证明了该算法的有效性。     

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     

Considerations on nonlinear model predictive control techniques

The nonlinear model predictive control (NMPC) is an on-line application based on nonlinear convolution models. It is an appealing control methodology, but it is difficult to implement and its solution is not so performing since it unavoidably means to solve a usually large-scale, constrained, and multidimensional optimization. To increase the difficulty, this optimization problem is subject to computationally heavy differential and algebraic constraints constituting the same convolution model and the least squares nature of the objective function easily leads to narrow valleys and multimodality issues.Beyond a short review of the state-of-the-art, the paper is aimed at highlighting the possibility to exploit at best the intrinsic features of the specific system one is going to control using the NMPC. The idea is to give the NMPC the possibility to automatically select the best combination of algorithms (differential solvers and optimizers) in accordance with the specific problem to be solved. From this perspective, the NMPC could be easily extended to many scientific fields traditionally far from process systems and computer-aided process engineering and the user has not to worry about which specific differential solvers and optimizers are needed to solve his/her problem.     

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     

Sequential and iterative architectures for distributed model predictive control of nonlinear process systems

In this work, we focus on distributed model predictive control of large scale nonlinear process systems in which several distinct sets of manipulated inputs are used to regulate the process. For each set of manipulated inputs, a different model predictive controller is used to compute the control actions, which is able to communicate with the rest of the controllers in making its decisions. Under the assumption that feedback of the state of the process is available to all the distributed controllers at each sampling time and a model of the plant is available, we propose two different distributed model predictive control architectures. In the first architecture, the distributed controllers use a one‐directional communication strategy, are evaluated in sequence and each controller is evaluated only once at each sampling time; in the second architecture, the distributed controllers utilize a bi‐directional communication strategy, are evaluated in parallel and iterate to improve closed‐loop performance. In the design of the distributed model predictive controllers, Lyapunov‐based model predictive control techniques are used. To ensure the stability of the closed‐loop system, each model predictive controller in both architectures incorporates a stability constraint which is based on a suitable Lyapunov‐based controller. We prove that the proposed distributed model predictive control architectures enforce practical stability in the closed‐loop system and optimal performance. The theoretical results are illustrated through a catalytic alkylation of benzene process example. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

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     

Robust decision making for hybrid process supply chain systems via model predictive control

Model predictive control (MPC) is a promising solution for the effective control of process supply chains. This paper presents an optimization-based decision support tool for supply chain management, by means of a robust MPC strategy. The proposed formulation: (i) captures uncertainty in model parameters and demand by stochastic programming, (ii) accommodates hybrid process systems with decisions governed by logical conditions/rulesets, and (iii) addresses multiple supply chain performance metrics including customer service and economics, within an integrated optimization framework. Two mechanisms for uncertainty propagation are presented – an open-loop approach, and an approximate closed-loop strategy. The performance of the robust MPC framework is analyzed through its application to two process supply chain case studies. The proposed approach is shown to provide a substantial reduction in the occurrence of back orders when compared to a nominal MPC implementation.     

Robust model predictive control of an industrial partial combustion fluidized-bed catalytic cracking converter

It is presented here in the study of the application of a robust model predictive control to an industrial partial combustion fluidized-bed catalytic cracking (FCC) converter. This particular type of FCC converter shows an interesting dynamics in which most of the system outputs are integrating with respect to the manipulated inputs. Time delays are also present and the model parameters can change depending on the operating point. Then, the system model should be represented by a set of possible plants, which can stand for different operating conditions of this process system. Moreover, one needs to include a comprehensive model formulation in order to accommodate time-delays for both stable and integrating outputs. The proposed control strategy was tested through simulation for the disturbances commonly found in the FCC converter unit, taking into consideration the plant/model mismatch. Results obtained from the simulated scenarios point out a fine prospective method. The robust controller shows a good potential to be implemented in the real process.     

Constrained model predictive control in ball mill grinding process

Stable control of grinding process is of great importance for improvements of operation efficiency, the recovery of the valuable minerals, and significant reductions of production costs in concentration plants. Decoupled multi-loop PID controllers are usually carried out to manage to eliminate the effects of interactions among the control loops, but they generally become sluggish due to imperfect process models and a close control of the process is usually impossible in real practice. Based on its inherent decoupling scheme, model predictive control (MPC) is employed to handle such highly interacting system. For high quality requirements, a three-input three-output model of the grinding process is constructed. Constrained dynamic matrix control (DMC) is applied in an iron ore concentration plant, and operation of the process close to their optimum operating conditions is achieved. Some practical problems about the application of MPC in grinding process are presented and discussed in detail.     

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     

A dynamic programming based approach for explicit model predictive control of hybrid systems

This work presents an algorithm for explicit model predictive control of hybrid systems based on recent developments in constrained dynamic programming and multi-parametric programming. By using the proposed approach, suitable for problems with linear cost function, the original model predictive control formulation is disassembled into a set of smaller problems, which can be efficiently solved using multi-parametric mixed-integer programming algorithms. It is also shown how the methodology is applied in the context of explicit robust model predictive control of hybrid systems, where model uncertainty is taken into account. The proposed developments are demonstrated through a numerical example where the methodology is applied to the optimal control of a piece-wise affine system with linear cost function.     

Safe-parking of nonlinear process systems: Handling uncertainty and unavailability of measurements

This work considers the problem of handling actuator faults in nonlinear process systems subject to input constraints, uncertainty and availability of limited measurements. A framework is developed to handle faults that preclude the possibility of continued operating at the nominal equilibrium point using the existing robust or reconfiguration-based fault-tolerant control approaches. The key consideration is to operate the plant using the depleted control action at an appropriate ‘safe-park’ point to prevent onset of hazardous situations as well as enable smooth resumption of nominal operation upon fault-repair. First, we consider the presence of constraints and uncertainty and develop a robust Lyapunov-based model predictive controller that enhances the set of initial conditions from which closed-loop stability is achieved. The stability region characterization provided by the robust predictive controller is subsequently utilized in a safe-parking algorithm that appropriately selects ‘safe-park’ points from the safe-park candidates (equilibrium points subject to failed actuators) to preserve closed-loop stability upon fault-repair. Specifically, a candidate parking point is termed a safe-park point if (1) the process state at the time of failure resides in the stability region of the safe-park candidate (subject to depleted control action and uncertainty) and (2) the safe-park candidate resides within the stability region of the nominal control configuration. Then we consider the problem of availability of limited measurements. An output feedback Lyapunov-based model predictive controller, utilizing an appropriately designed state observer (to estimate the unmeasured states), is formulated and its stability region explicitly characterized. An algorithm is then presented that accounts for the estimation errors in the implementation of the safe-parking framework. The proposed framework is illustrated using a chemical reactor example and demonstrated on a styrene polymerization process.     

Analysis of linear programming in model predictive control

The linear programming formulations of model predictive control are known to exhibit degenerate solution behavior. In this work, a multi-parametric linear programming technique is utilized to analyze the control laws that are generated from various linear programming based MPC routines. These various routines explore a number of factors, including objective function selection and constraint handling on the control laws generated from LP based MPC. A single input single output system is used to demonstrate that the use of input velocity penalties, input blocking, and ∞-norm objective functions can limit or eliminate this undesirable behavior. Finally, a paper machine cross directional control problem is used to demonstrate the control laws generated from LP based MPC for a multivariable example.