Safe-parking of nonlinear process systems

This work considers the problem of control of nonlinear process systems subject to input constraints and faults in the control actuators. Faults are considered that preclude the possibility of continued operating at the nominal equilibrium point and a framework (which we call the safe-parking framework) is developed to enable efficient resumption of nominal operation upon fault-recovery. To this end, first Lyapunov-based model predictive controllers, that allow for an explicit characterization of the stability region subject to constraints on the manipulated input, are designed. The stability region characterization is utilized in selecting ‘safe-park’ points from the safe-park candidates (equilibrium points subject to failed actuators). 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 (2) the safe-park candidate resides within the stability region of the nominal control configuration. Performance considerations, such as ease of transition from and to the safe-park point and cost of running the process at the safe-park point, are then quantified and utilized in choosing the optimal safe-park point. The proposed framework is illustrated using a chemical reactor example and robustness with respect to parametric uncertainty and disturbances is demonstrated on a styrene polymerization process.     

A safe-parking framework for plant-wide fault-tolerant control

This work addresses the problem of handling actuator faults in a chemical plant. We consider a multi-unit nonlinear process system subject to input constraints and actuator faults in one unit that preclude the possibility of operating the unit at its nominal equilibrium point. The interconnected nature of the units in a plant brings forth unique opportunities as well as challenges that simply do not exist when handling faults in isolated units. In particular, the fact that the outlet streams from a faulty unit go through subsequent (well functioning) units raises the possibility of better restricting the effects of the fault to the faulty unit. At the same time, handling a fault in a unit may necessitate appropriate action in the downstream unit, which is not a result of a fault in the downstream unit. To address such issues that arise when handling faults in chemical plants, in this work we present a safe-parking framework (we define, in a previous work on handling faults in isolated units, a safe-park point as an operating point where in the event of a fault, a unit can be operated in a way that prevents onset of hazardous situation and allows smooth resumption of nominal operation) for plant-wide fault-tolerant control. We first consider the case where there exists a safe-park point for the faulty unit such that the effect of safe-parking can be completely rejected (via changing the nominal values of the manipulated variables) in the downstream unit. Steady-state as well as dynamic considerations (including the presence of input constraints) is used in determining the necessary conditions for safe-parking the multi-unit system. We next consider the problem where no viable safe-park point for the faulty unit exists such that its effect can be completely rejected in the subsequent unit. A methodology is presented to simultaneously safe-park the consecutive units. Finally, we incorporate performance considerations in the safe-parking framework and illustrate the implementation of the safe-parking framework using a multi-unit chemical reactor system.     

Robust model predictive control of nonlinear process systems: Handling rate constraints

This work considers the problem of stabilization of control affine nonlinear process systems subject to constraints on the rate of change and magnitude of control inputs in the presence of uncertainty. We first handle rate constraints within a soft constraints framework. A new robust predictive controller formulation that minimizes rate constraint violation while guaranteeing stabilization and input constraint satisfaction from an explicitly characterized stability region is designed. We then derive conditions that allow for guaranteed satisfaction of hard rate constraints. Subsequently, a predictive controller is designed that ensures rate constraints satisfaction when the required conditions are satisfied, relaxing them otherwise to preserve feasibility and robust stability. The implementation of the proposed predictive controllers is illustrated via a chemical reactor example.     

Statistical machine-learning–based predictive control of uncertain nonlinear processes

In this study, we present machine-learning–based predictive control schemes for nonlinear processes subject to disturbances, and establish closed-loop system stability properties using statistical machine learning theory. Specifically, we derive a generalization error bound via Rademacher complexity method for the recurrent neural networks (RNN) that are developed to capture the dynamics of the nominal system. Then, the RNN models are incorporated in Lyapunov-based model predictive controllers, under which we study closed-loop stability properties for the nonlinear systems subject to two types of disturbances: bounded disturbances and stochastic disturbances with unbounded variation. A chemical reactor example is used to demonstrate the implementation and evaluate the performance of the proposed approach.     

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.     

Robust model predictive control and fault handling of batch processes

This work considers the control of batch processes subject to input constraints and model uncertainty with the objective of achieving a desired product quality. First, a computationally efficient nonlinear robust Model Predictive Control (MPC) is designed. The robust MPC scheme uses robust reverse‐time reachability regions (RTRRs), which we define as the set of process states that can be driven to a desired neighborhood of the target end‐point subject to input constraints and model uncertainty. A multilevel optimization‐based algorithm to generate robust RTRRs for specified uncertainty bounds is presented. We then consider the problem of uncertain batch processes subject to finite duration faults in the control actuators. Using the robust RTRR‐based MPC as the main tool, a robust safe‐steering framework is developed to address the problem of how to operate the functioning inputs during the fault repair period to ensure that the desired end‐point neighborhood can be reached upon recovery of the full control effort. The applicability of the proposed robust RTRR‐based controller and safe‐steering framework subject to limited availability of measurements and sensor noise are illustrated using a fed‐batch reactor system. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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 robustly stabilizing fault-tolerant MPC: A performance improvement-based approach

In terms of model predictive control (MPC) performance degradation caused by operational faults, in this article, a robust MPC strategy with active fault tolerance properties is proposed. The proposed strategy incorporates a fault supervision layer into the structure of conventional cost-contracting formulation-based robust MPC for the online update of the nominal controller model in the event of faults. The robust MPC is based on multiplant uncertainty, while the supervisory layer consists of a bank of unknown input observers and a decision-making algorithm. Simulation results in a nonlinear polymerization reactor subject to process faults demonstrate that the proposed approach offers superior performance compared to the conventional strategy.     

A MODEL-BASED DIRECT ADAPTIVE PI CONTROLLER FOR NONLINEAR PROCESS CONTROL

This article proposes a model-based direct adaptive proportional-integral (PI) controller for a class of nonlinear processes whose nominal model is input-output linearizable but may not be accurate enough to represent the actual process. The proposed direct adaptive PI controller is composed of two parts: the first is a linearizing feedback control law that is synthesized directly based on the process's nominal model and the second is an adaptive PI controller used to compensate for the model errors. An effective parameter-tuning algorithm is devised such that the proposed direct adaptive PI controller is able to achieve stable and robust control performance under uncertainties. To show the robust stability and performance of the direct adaptive PI control system, a rigorous analysis involving the use of a Lyapunov-based approach is presented. The effectiveness and applicability of the proposed PI control strategy are demonstrated by considering the time-dependent temperature trajectory tracking control of a batch reactor in the presence of plant/model mismatch, unanticipated periodic disturbances, and measurement noises. Furthermore, for use in an environment that lacks full-state measurements, the integration of a sliding observer with the proposed control scheme is suggested and investigated. Extensive simulation results reveal that the proposed model-based direct adaptive PI control strategy enables a highly nonlinear process to achieve robust control performance despite the existence of plant/model mismatch and diversified process uncertainties.     

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.     

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.     

ENHANCED IMC-PID CONTROLLER DESIGN WITH LEAD-LAG FILTER FOR UNSTABLE AND INTEGRATING PROCESSES WITH TIME DELAY

In this article, a design method for a PID controller is proposed based on IMC principles for control of open loop integrating and unstable first-order processes with time delay. The design is based on H₂ optimal closed-loop transfer function for set point changes and step input disturbances. The method has one tuning parameter, and systematic guidelines are provided for the selection of this tuning parameter based on peak value of the sensitivity function. The performance of the designed controller is verified on various integrating and unstable processes, and it is observed that nominal and robust control performance is achieved with the proposed design method. Improved closed-loop performance was obtained when compared to other methods recently reported in the literature. Further, the proposed method provides good closed-loop performance even when there are large uncertainties in the process parameters.     

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.     

LMI-based robust model predictive control for a continuous MMA polymerization reactor

A linear matrix inequality (LMI)-based robust model predictive control (MPC) is applied to a continuous stirred-tank reactor for the polymerization of methyl methacrylate (MMA). The polytopic model is constructed to predict the responses to various control input sequences by using Jacobians of uncertain nonlinear model at several operating points and the controller design is characterized as the problem of minimizing an upper bound on the ‘worst-case’ infinite horizon objective function subject to constraints on the control input and plant output. Simulation studies under different conditions are conducted to validate the feasibility of the optimization problem and evaluate the applicability of such a control scheme. Simulation results show that, despite the model uncertainty, the LMI-based robust model predictive controller performs quite satisfactorily for the property control of the continuous polymerization reactor and guarantees the robust stability.     

Machine learning-based distributed model predictive control of nonlinear processes

This work explores the design of distributed model predictive control (DMPC) systems for nonlinear processes using machine learning models to predict nonlinear dynamic behavior. Specifically, sequential and iterative DMPC systems are designed and analyzed with respect to closed-loop stability and performance properties. Extensive open-loop data within a desired operating region are used to develop long short-term memory (LSTM) recurrent neural network models with a sufficiently small modeling error from the actual nonlinear process model. Subsequently, these LSTM models are utilized in Lyapunov-based DMPC to achieve efficient real-time computation time while ensuring closed-loop state boundedness and convergence to the origin. Using a nonlinear chemical process network example, the simulation results demonstrate the improved computational efficiency when the process is operated under sequential and iterative DMPCs while the closed-loop performance is very close to the one of a centralized MPC system.     

基于Min-Max的预测控制鲁棒参数设计

工业控制中模型的不确定性是不可避免的.提出基于Min-Max的预测控制器鲁棒参数设计方法,充分考虑到模型的不确定性.仿真结果表明,控制器在对象模型一定范围内变化时仍具有较好的控制品质,不需要重新整定控制器参数,提高了系统的鲁棒性能.     

Sontag型构造性预测控制算法的性能分析

Sontag型构造性预测控制策略是为了降低约束非线性预测控制的在线计算量和分离闭环系统稳定性与性能指标而提出的一种有效算法。在算法名义稳定的条件下,运用逆最优控制理论,分析约束连续时间非线性系统Sontag型预测控制器的逆最优性和鲁棒性问题,得到控制器具有鲁棒性的充分条件,为更好地理解该控制算法和算法的实施提供了理论依据。最后,应用仿真实例验证了本文结论的有效性。     

Online machine learning modeling and predictive control of nonlinear systems with scheduled mode transitions

This work develops a model predictive control (MPC) scheme using online learning of recurrent neural network (RNN) models for nonlinear systems switched between multiple operating regions following a prescribed switching schedule. Specifically, an RNN model is initially developed offline to model process dynamics using the historical operational data collected in a small region around a certain steady-state. After the system is switched to another operating region under a Lyapunov-based MPC with suitable constraints to ensure satisfaction of the prescribed switching schedule policy, RNN models are updated using real-time process data to improve closed-loop performance. A generalization error bound is derived for the updated RNN models using the notion of regret, and closed-loop stability results are established for the switched nonlinear system under RNN-based MPC. Finally, a chemical process example with the operation schedule that requires switching between two steady-states is used to demonstrate the effectiveness of the proposed RNN-MPC scheme.