Application of state estimation based NMPC to an unstable nonlinear process

Model predictive control (MPC) has become very popular both in process industry and academia due to its effectiveness in dealing with nonlinear, multivariable and/or hard-constrained plants.Although linear MPC can be applied for controlling nonlinear processes by obtaining a linearized model of the plant, this is only valid in a limited region. Therefore, a substantial improvement can be achieved by using the whole knowledge of the process dynamics, specially in the presence of marked nonlinearities. This effect can be strong if the process to control is open-loop unstable.The purpose of this paper is to introduce a nonlinear model predictive controller (NMPC) based on nonlinear state estimation, in order to exploit the knowledge of the nonlinear dynamics and to avoid modeling simplifications or linearization.A state-space formulation is proposed to achieve the control objective. To update the optimization involved in NMPC strategy, state estimation based on the measured outputs is proposed.As a particular application, we consider an open-loop unstable jacketed exothermic chemical reactor. This CSTR is widely recognized as a difficult problem for the purpose of control. In order to achieve the control goal, a NMPController coupled with a state observer are designed. The observer is also used to estimate some unmeasured disturbances. Finally, computer simulations are developed for showing the performance of both the nonlinear observer and the control strategy.     

Model based robust control approach for batch crystallization product design

The paper presents a novel control approach for crystallization processes, which can be used for designing the shape of the crystal size distribution to robustly achieve desired product properties. The approach is based on a robust optimal control scheme, which takes parametric uncertainties into account to provide decreased batch-to-batch variability of the shape of the crystal size distribution. Both open-loop and closed-loop robust control schemes are evaluated. The open-loop approach is based on a robust end-point nonlinear model predictive control (NMPC) scheme which is implemented in a hierarchical structure. On the lower level a supersaturation control approach is used that drives the system in the phase diagram according to a concentration versus temperature trajectory. On the higher level a robust model-based optimization algorithm adapts the setpoint of the supersaturation controller to counteract the effects of changing operating conditions. The process is modelled using the population balance equation (PBE), which is solved using a novel efficient approach that combines the quadrature method of moment (QMOM) and method of characteristics (MOC). The proposed robust model based control approach is corroborated for the case of various desired shapes of the target distribution.     

A CLOSED-LOOP REACTION-CURVE METHOD FOR CONTROLLER TUNING

This article proposes a closed-loop, reaction-curve method to provide a procedure for establishing controller settings on the classical three-mode (P1D) controllers. It uses the partial extreme data available during the early period of step set-point change under porportional control mode to determine the ultimate period and the ultimate gain of the open-loop process. The resulting ultimate data are critical for subsequent controller settings according to Ziegler-Nichols rules. Simulation examples and test on a pilot-scale stirred-tank reactor demonstrate that the method can provide adequate critical process data, and that it is applicable to processes that are underdamped, characterized by large dead-times, open-loop unstable or with inverse-response.     

Dynamic optimization oriented modeling and nonlinear model predictive control of the wet limestone FGD system

Nonlinear model predictive control (NMPC) scheme is an effective method of multi-objective optimization control in complex industrial systems. In this paper, a NMPC scheme for the wet limestone flue gas desulphurization (WFGD) system is proposed which provides a more flexible framework of optimal control and decision-making compared with PID scheme. At first, a mathematical model of the FGD process is deduced which is suitable for NMPC structure. To equipoise the model's accuracy and conciseness, the wet limestone FGD system is separated into several modules. Based on the conservation laws, a model with reasonable simplification is developed to describe dynamics of different modules for the purpose of controller design. Then, by addressing economic objectives directly into the NMPC scheme, the NMPC controller can minimize economic cost and track the set-point simultaneously. The accuracy of model is validated by the field data of a 1000 MW thermal power plant in Henan Province, China. The simulation results show that the NMPC strategy improves the economic performance and ensures the emission requirement at the same time. In the meantime, the control scheme satisfies the multiobjective control requirements under complex operation conditions (e.g., boiler load fluctuation and set point variation). The mathematical model and NMPC structure provides the basic work for the future development of advanced optimized control algorithms in the wet limestone FGD systems.     

Model based control of a liquid swelling constrained batch reactor subject to recipe uncertainties

This work presents the application of nonlinear model predictive control (NMPC) to a simulated industrial batch reactor subject to safety constraint due to reactor level swelling, which can occur with relatively fast dynamics. Uncertainties in the implementation of recipes in batch process operation are of significant industrial relevance. The paper describes a novel control-relevant formulation of the excessive liquid rise problem for a two-phase batch reactor subject to recipe uncertainties. The control simulations are carried out using a dedicated NMPC and optimization software toolbox OptCon which implements efficient numerical algorithms. The open-loop optimal control problem is computed using the multiple-shooting technique and the arising nonlinear programming problem is solved using a sequential quadratic programming (SQP) algorithm tailored for large-scale problems, based on the freeware optimization environment HQP. The fast response of the NMPC controller is guaranteed by the initial value embedding and real-time iteration technologies. It is concluded that the OptCon implementation allows small sampling times and the controller is able to maintain safe and optimal operation conditions, with good control performance despite significant uncertainties in the implementation of the batch recipe.     

A method to coordinate decentralized NMPC controllers in oxygen distribution networks

This paper deals with the optimal operation of large scale systems composed by local processes liked by shared resources. A decentralized architecture plus a coordinator, which guarantees the satisfaction of the global constraints of the process, is presented. The decomposition of the control problem into smaller ones is based on Lagrangean decomposition and on price coordination methods to update the prices. A coordination method that allows formulating the price assignment as a control problem is presented besides a formulation based on market behaviour. Both approaches are driven by the difference between the total shared resources available and demanded by the local NMPC controllers. One advantage of this approach is that in the low layer only requires adding an extra term in the cost function of the existing NMPC controllers. Moreover, there is no communication between local controllers, only between each local controller and the coordinator.     

一类非线性系统的变负荷预测控制

生产过程的变负荷运行使得其非线性动态特性的影响凸显。针对变负荷生产过程中机理模型为常微分方程或半显式Heisenberg微分-代数方程的一类非线性动态系统,采用非线性预测控制算法,构造出稳态优化与动态优化的两层控制结构,并采用联立法进行优化数值求解。最后对化工过程的夹套CSTR进行仿真验证,表明该算法的有效性。     

Differential-geometric model-based control (DGMBC): A software package for controller design

This paper presents a new software package, called differential-geometric model-based control (DGMBC), which carries out symbolic manipulations to automatically generate differential-geometric, model-based controllers and subsequently tests the designed controller. This prototype software was developed to simplify the industrial implementation and testing of differential-geometric, model-based controllers on lumped-parameter processes. DGMBC has a user-friendly interface that allows a user to enter process model equations and parameters easily. The user interface was developed using Visual Basic and linked to MATHEMATICA using MathLink. The user enters the process model (set of ordinary differential equations), and the software generates an analytical model-based controller, if an analytical solution exists. The resulting analytical model-based controller (set of ordinary differential and algebraic equations) can be in FORTRAN, C, or MATLAB format. DGMBC can also simulate the closed-loop process responses. The application and implementation of DGMBC 1.0 are shown using three chemical and biochemical process examples with varying levels of complexity. An analytical model-based controller is designed for each of the processes, and simulation results showing the closed-loop process responses are presented.     

Model predictive control of an industrial pyrolysis gasoline hydrogenation reactor

This study focuses on the implementation of a nonlinear model predictive control (MPC) algorithm for controlling an industrial fixed-bed reactor where hydrogenations of raw pyrolysis gasoline occur. An orthogonal collocation method is employed to approximate the original reactor model consisting of a set of partial differential equations. The approximate model obtained is used in the synthesis of a MPC controller to control the temperature rising across a catalyst bed within the reactor. In the MPC algorithm, a sequential optimization approach is used to solve an open-loop optimal control problem. Feedback information is incorporated in the MPC to compensate for modeling error and unmeasured disturbances. The control studies are demonstrated in cases of set point tracking and disturbance rejection.     

MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

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.     

APPLICATION OF FUZZY ADAPTIVE CONTROLLER IN NONLINEAR PROCESS CONTROL

In general, physical processes are usually nonlinear and control system design based on the linearization technique cannot control the process well for a wide range of operation. Use of the variable transformation method may not always solve the problem. In this paper, a fuzzy adaptive controller is proposed to control the nonlinear process. The CSTR control problem has also been considered. The results are compared with the method of nonlinear model predictive control (NMPC) with constrained and unconstrained control variables. A fuzzy model-following control system scheme is also proposed. The results show that the proposed controller is a feasible control structure for a nonlinear or parameter-variations process control.     

Two-degree-of-freedom output feedback controllers for discrete-time nonlinear systems

A discrete-time, model-based output feedback control structure for nonlinear processes is developed in the present work. The structure makes use of a closed-loop observer, while at the same time it guarantees that the overall feedback controller possesses integral action. An algebraic transformation is applied on the observer states to insure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The resulting control algorithm is a two-degree-of-freedom control law, in the sense that the output and the set point are processed in different ways. The control structure is shown not only to have the same properties as the standard model-state feedback structure, but also that it emerges from a model algorithmic control framework. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to evaluate the closed-loop performance of the proposed method.     

Robust continuous velocity control of convective spatially distributed systems

In this work a robust nonlinear scheme is proposed to control spatially distributed convective systems described by first-order hyperbolic partial differential equations by manipulating the flow velocity. The proposed scheme is designed after the method of characteristics is used to establish key structural properties of the system dynamics. The resulting feedback control, which can be seen as a proportional integral controller with variable integration time, does not require measurements for several axial points nor infinite dimensional state estimations. The proposed controller is applied successfully to two heat exchange simulation examples and a nonisothermical plug flow reactor. It is shown that it is robust in the face of uncertain parameters and load disturbances. Finally, the performance of the robust controller is compared to other control applications.     

MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

Dynamic output feedback covariance control of stochastic dissipative partial differential equations

In this work, we develop a method for dynamic output feedback covariance control of the state covariance of linear dissipative stochastic partial differential equations (PDEs) using spatially distributed control actuation and sensing with noise. Such stochastic PDEs arise naturally in the modeling of surface height profile evolution in thin film growth and sputtering processes. We begin with the formulation of the stochastic PDE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation is then obtained to capture the dominant mode contribution to the surface roughness profile (i.e., the covariance of the surface height profile). Subsequently, a state feedback controller and a Kalman-Bucy filter are designed on the basis of the finite-dimensional approximation. The dynamic output feedback covariance controller is subsequently obtained by combining the state feedback controller and the state estimator. The steady-state expected surface covariance under the dynamic output feedback controller is then estimated on the basis of the closed-loop finite-dimensional system. An analysis is performed to obtain a theoretical estimate of the expected surface covariance of the closed-loop infinite-dimensional system. Applications of the linear dynamic output feedback controller to both the linearized and the nonlinear stochastic Kuramoto-Sivashinsky equations (KSEs) are presented. Finally, nonlinear state feedback controller and nonlinear output feedback controller designs are also presented and applied to the nonlinear stochastic KSE.     

On‐Line PEMFC Control Using Parameterized Nonlinear Model‐Based Predictive Control

In this work, a fast nonlinear model‐based predictive control (NMPC) strategy is designed and experimentally validated on‐line on a real fuel cell. Regarding NMPC strategies, the most challenging part remains to achieve on‐line implementation, especially when dealing with fast dynamic systems. As previously demonstrated in a recent work, the proposed control strategy is ideally suited to address this problem. Indeed, it is 30 times faster than classical NMPC controllers. This strategy relies on a specific parameterization of the control actions to reduce the computational time and achieve on‐line implementation. Due to its short computational time compared to mechanistic models, an artificial neural network model is designed and experimentally validated. This model is employed as internal model in the NMPC controller to predict the system behavior. To confirm the applicability and the relevance of the proposed NMPC controller varying control scenarios are investigated on a test bench. The built‐in controller is overridden and the NMPC controller is implemented externally and executed on‐line. Experimental results exhibit the outstanding tracking capability and robustness against model‐process mismatch of the proposed strategy. The parameterized NMPC controller turns out to be an excellent candidate for on‐line applications.     

积分和不稳定时滞对象的改进内模控制

针对化工过程中一阶积分和不稳定时滞对象,基于内模控制提出了两自由度控制方案。首先根据鲁棒控制理论H2最优性能指标设计设定值跟踪控制器,然后采用期望闭环补灵敏度函数确定扰动抑制控制器。设定值跟踪控制器和扰动抑制控制器可通过性能参数独立调节而无需再取折衷,同时保证系统具有较好的鲁棒稳定性。最后通过仿真实例验证了该控制方案的有效性。     

Integrated nonlinear model predictive fault tolerant control and multiple model based fault detection and diagnosis

In this paper, a new fault-tolerant control approach is presented for a class of nonlinear systems, which preserves system stability despite a time delay in fault detection. The faults are assumed to occur in the actuators and are modeled for the general form of affine nonlinear systems. A fault detection and diagnosis (FDD) block is designed based on the multiple model method. The bank of extended Kalman filters (EKF) is used to detect predefined actuator faults and to estimate the unknown parameters of actuator position. The estimated parameters are then used to correct the model of the faulty system and to reconfigure the controller. The reconfigurable controller is designed based on the stabilizing nonlinear model predictive control (NMPC) scheme. On the other hand, in the duration between fault occurrence and fault detection, because of the mismatch between the process and the model, the system states may go off the attraction region. The proposed method is based on designing multiple local controllers for individual predefined faults. Depending on the value of a system variable at the moment of fault detection, one of these controllers will operate. This leads to a stability region of a set of auxiliary equilibrium points (AEPs), which is larger than the attraction region. Moreover, a framework for preserving system stability is presented. Finally, a practical chemical process example is presented to illustrate the effectiveness of this method.     

A nested online scheduling and nonlinear model predictive control framework for multi-product continuous systems

In the pursuit of integrated scheduling and control frameworks for chemical processes, it is important to develop accurate integrated models and computational strategies such that optimal decisions can be made in a dynamic environment. In this study, a recently developed switched system formulation that integrates scheduling and control decisions is extended to closed-loop operation embedded with nonlinear model predictive control (NMPC). The resulting framework is a nested online scheduling and control loop that allows to obtain fast and accurate solutions as no model reduction is needed and no integer variables are involved in the formulations. In the outer loop, the integrated model is solved to calculate an optimal product switching sequence such that the process economics is optimized, whereas in the inner loop, an NMPC implements the scheduling decisions. The proposed scheme was tested on two multi-product continuous systems. Unexpected large disturbances and rush orders were handled effectively.