Identification and direct digital stochastic control of a continuous stirred tank process

Several aspects associated with the identification and direct digital stochastic control of a steam-jacketed continuous stirred tank process are investigated. Using data collected under closed-loop conditions by an on-line mini-computer, statistical modelling procedures are used to identify, fit and check a discrete dynamic-stochastic model for the process and its disturbances. Based on these models an optimal stochastic feedback controller is implemented using the minicomputer. A practical modification of this optimal controller is suggested and the modified stochastic controller is implemented and its performance is evaluated.     

Performance assessment of MIMO control systems with time-variant disturbance dynamics

In this paper, we consider performance assessment problem for multivariable control systems subject to piecewise constant time varying disturbance dynamics. The problem is motivated by the observation that most industrial controllers are linear time invariant (LTI) but the process, particularly the disturbance dynamics, can be time varying. We consider a class of disturbance dynamics that can be modelled by piecewise linear disturbance models, namely piecewise linear time varying (LTV) disturbance dynamics. The problem is formulated as searching for a multi-input multi-output (MIMO) benchmark control that is LTI but optimal in regulating the LTV disturbances. The single-input single-output (SISO) case has been previously solved by minimizing the variance of a most representative disturbance or by the minimization of the sum of the weighted variances of all but one of major disturbances, while satisfying a structured regulatory performance requirement for the major disturbance. In this paper, the previous results are extended to MIMO systems. The counterparts of the two SISO benchmarks are defined as the regular linear time varying disturbances (LTVDs) benchmark and the weighted LTVD benchmark for MIMO control systems, respectively. In addition, a new yet more practical LTVD benchmark, the generalized LTVD benchmark, is also proposed, which minimizes the maximum total variance among all different disturbance dynamics. These three LTVD benchmarks are compared by simulation and industrial application examples. The results show that the weighted and generalized LTVD benchmarks can always lead to better trade-offs on the total output variances.     

Disjunctive modeling for optimal control of hybrid systems

In this contribution, a novel approach for the modeling and numerical optimal control of hybrid (discrete–continuous dynamic) systems based on a disjunctive problem formulation is proposed. It is shown that a disjunctive model representation, which constitutes an alternative to mixed-integer model formulations, provides a very flexible, intuitive and effective way to formulate hybrid (discrete–continuous dynamic) optimization problems. The structure and properties of the disjunctive process models can be exploited for an efficient and robust numerical solution by applying generalized disjunctive programming techniques. The proposed modeling and optimization approach will be illustrated by means of optimal control of hybrid systems embedding linear discrete–continuous dynamic models.     

受扰双线性系统的近似最优扰动抑制方法

研究具有外界持续扰动作用下双线性系统的最优控制问题.关于二次型性能指标给出了一种设计最优扰动抑制控制律的逐次逼近方法.利用该算法可将在扰动作用下双线性系统的最优控制问题转化为求解一组线性非齐次两点边值序列问题.通过迭代序列得到的最优扰动抑制控制律由解析的线性前馈-反馈项和序列极限形式的非线性补偿项组成.通过截取非线性补偿序列的有限项,可以得到近似最优扰动抑制控制律.仿真结果表明,该方法抑制外部持续扰动的鲁棒性优于经典反馈最优控制.     

A generalized framework for solving dynamic optimization problems using the artificial chemical process paradigm: Applications to particulate processes and discrete dynamic systems

The solution of optimal control problems (OCPs) becomes a challenging task when the analyzed system includes non-convex, non-differentiable, or equation-free models in the set of constraints. To solve OCPs under such conditions, a new procedure, LARES-PR, is proposed. The procedure is based on integrating the LARES algorithm with a generalized representation of the control function. LARES is a global stochastic optimization algorithm based on the artificial chemical process paradigm. The generalized representation of the control function consists of variable-length segments, which permits the use of a combination of different types of finite elements (linear, quadratic, etc.) and/or specialized functions. The functional form and corresponding parameters are determined element-wise by solving a combinatorial optimization problem. The element size is also determined as part of the solution of the optimization problem, using a novel two-step encoding strategy. These building blocks result in an algorithm that is flexible and robust in solving optimal control problems. Furthermore, implementation is very simple.The algorithm's performance is studied with a challenging set of benchmark problems. Then LARES-PR is utilized to solve optimal control problems of systems described by population balance equations, including crystallization, nano-particle formation by nucleation/coalescence mechanism, and competitive reactions in a disperse system modeled by the Monte Carlo method. The algorithm is also applied to solving the DICE model of global warming, a complex discrete-time model.     

苯氯化侧反应精馏过程的系统设计与控制(英文)

The distillation column with side reactors (SRC) can overcome the temperature/pressure mismatch in the traditional reactive distillation, the column operates at temperature/pressure favorable for vapor-liquid separation, while the reactors operate at temperatures/pressures favorable for reaction kinetics. According to the smooth operation and automatic control problem of the distillation column with side reactors (SRC), the design, simulation calculation and dynamic control of the SCR process for chlorobenzene production are discussed in the paper. Firstly, the mechanism models, the integrated structure optimal design and process simulation systems are established, respectively. And then multivariable control schemes are designed, the controllability of SRC process based on the optimal steady-state integrated structure is explored. The dynamic response performances of closed-loop system against several disturbances are discussed to verify the effectiveness of control schemes for the SRC process. The simulating results show that the control structure using conventional control strategies can effectively overcome feeding disturbances in a specific range.     

Maximum Likelihood Estimates of a Class of One-Dimensional Stochastic Differential Equation Models From Discrete Data

The problem of computing the maximum likelihood estimate of the parameters of a specific class of stochastic differential equation (SDE) models with linear drift whose sample paths are observed at discrete time points is considered. This estimate is obtained as in Cleur and Manfredi (1999) by discretizing the explicit expressions for the estimates which maximize the likelihood function in continuous time, by discretizing the likelihood function through a quadrature approximation before maximizing it, and by maximizing the likelihood function of the Euler scheme approximation to the underlying continuous process. Simulation results indicate that, for the constellation of parameter values considered, all three approaches lead to very similar results.     

Simultaneous process synthesis and control design under uncertainty: A worst‐case performance approach

A new methodology that includes process synthesis and control structure decisions for the optimal process and control design of dynamic systems under uncertainty is presented. The method integrates dynamic flexibility and dynamic feasibility in a single optimization formulation, thus, reducing the costs to assess the optimal design. A robust stability test is also included in the proposed method to ensure that the optimal design is stable in the presence of magnitude‐bounded perturbations. Since disturbances are treated as stochastic time‐discrete unmeasured inputs, the optimal process synthesis and control design specified by this method remains feasible and stable in the presence of the most critical realizations in the disturbances. The proposed methodology has been applied to simultaneously design and control a system of CSTRs and a ternary distillation column. A study on the computational costs associated with this method is presented and compared to that required by a dynamic optimization‐based scheme. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2497–2514, 2013     

On constrained infinite-time nonlinear optimal control

In this work, we consider the infinite-time optimal control of input affine nonlinear systems subject to point-wise in time inequality constraints on both the process inputs and outputs. Fundamental to solving this constrained infinite-time nonlinear optimal control (CITNOC) problem is the ability to calculate the value function of it's unconstrained counterpart, the infinite-time nonlinear optimal control (ITNOC) problem. Unfortunately, the traditional ITNOC solution procedure of specifying an objective function and then solving for the optimal control policy and corresponding value function is computationally intractable in all but the simplest of examples. However, in many cases one can easily identify a stabilizing feedback for near operating point regulation. Building from this local policy, the proposed method is to construct a meaningful optimal control objective function as well as its corresponding value function. These functions are then used to analyze the closed-loop stability of the proposed policy. Upon return to the constrained case the constructed objective and value functions are again used to develop a self-consistent constrained finite-time scheme that will, for the first time, provide an exact solution to the CITNOC problem. The mechanics of the proposed method are then illustrated by an example from chemical reactor control.     

A decomposition algorithm for simultaneous scheduling and control of CSP systems

We present a decomposition algorithm to perform simultaneous scheduling and control decisions in concentrated solar power (CSP) systems. Our algorithm is motivated by the need to determine optimal market participation strategies at multiple timescales. The decomposition scheme uses physical insights to create surrogate linear models that are embedded within a mixed‐integer linear scheduling layer to perform discrete (operational mode) decisions. The schedules are then validated for physical feasibility in a dynamic optimization layer that uses a continuous full‐resolution CSP model. The dynamic optimization layer updates the physical variables of the surrogate models to refine schedules. We demonstrate that performing this procedure recursively provides high‐quality solutions of the simultaneous scheduling and control problem. We exploit these capabilities to analyze different market participation strategies and to explore the influence of key design variables on revenue. Our results also indicate that using scheduling algorithms that neglect detailed dynamics significantly decreases market revenues. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2408–2417, 2018     

Optimal component lumping: Problem formulation and solution techniques

This paper presents a systematic method for optimal lumping of a large number of components in order to minimize the loss of information. In principle, a rigorous composition-based model is preferable to describe a system accurately. However, computational intensity and numerical issues restrict such applications in process modeling, simulation and design. A pseudo-component approach that lumps a large number of components in a system into a much smaller number of hypothetical groups reduces the dimensionality at the cost of losing information. Moreover, empirical and heuristic approaches are commonly used to determine the lumping scheme. Given an objective function defined with a linear weighting rule, an optimal lumping problem is formulated as a mixed integer nonlinear programming (MINLP) problem both in discrete and in continuous settings. A reformulation of the original problem is also presented, which significantly reduces the number of independent variables. The application to a system with 144 components demonstrates that the optimal lumping problem can be efficiently solved with a stochastic optimization method, Tabu Search (TS) algorithm. The case study also reveals that the discrete formulation is preferable due to the reduced search space compared to a continuous model formulation.     

Optimal quality control of baker's yeast drying in large scale batch fluidized bed

Optimal quality control of drying process of baker's yeast in large scale batch fluidized bed dryer is presented using neural network based models and modified genetic algorithm (GA). The objective of this study is to determine optimal conditions to maximize product quality while minimizing energy consumption. For this purpose, the drying process and quality models based on neural network with delay units are combined for predicting the dry matter, product temperature, change in dry matter and the quality loss while minimizing energy consumption and this model is then used for optimal quality control. A stochastic method based optimization structure is designed in order to solve the optimization problem whose the objective function is discontinuous, non-differentiable, complex and highly non-linear. The results obtained by optimal quality control based on modified GA showed that the performance of the existing industrial scale drying process was improved. The constructed optimal quality control structure is very convenient for the production process applications and may be applied without too much modification.     

受扰动非线性系统的反馈线性化最优控制

研究具有外界扰动作用下的非线性系统基于状态反馈精确线性化的最优控制器设计问题。首先基于微分同胚将受扰动非线性系统模型转变为无扰动的伪线性系统模型,然后给出了在关系度等于系统阶数情况下基于二次型性能指标的最优控制器设计方法,通过求解Riccati方程得到系统最优扰动抑制控制律。最后通过仿真实例表明了该方法的有效性。     

过程动态优化问题的自热式求解策略

分析了基于微分代数方程（DAE）的动态优化问题的联立求解原理,提出了基于Lobatto配置的全离散模型的简洁描述形式。根据离散化模型的最优解具有结构相似性的特点,利用低密度离散的解来近似高密度离散的解,并且配合内点法求解的暖启动技术与障碍参数初值设定方法,提出了能实现动态优化问题快速求解的自热式策略。最后通过求解一个结晶过程的动态优化算例,证实了所提出的自热式策略能够将求解速度提高6倍左右。     

先进控制条件下化工过程操作裕量与控制性能分析

引言化工过程的设计裕量可以定义为考虑过程不确定参数(包括工艺条件、设备条件、外来扰动)发生变化时为满足生产和操作要求需要在正常操作的标称设计值上增加的量。设计裕量根据其属性可以     

Nonlinear predictive control using multi-rate sampling

A nonlinear predictive control (NLPC) strategy based on a nonlinear, lumped parameter model of the process is developed in this paper. A constrained optimization approach is used to estimate unmeasured state variables and load disturbances. Additional model/process mismatch is handled by using an additive output term which is equivalent to the Internal Model Control approach. Similar to linear predictive control methods, an optimal sequence of future control moves is determined in order to minimize an objective function based on a desired output trajectory, subject to manipulated variable constraints (absolute and velocity). Deadtime is explicitly included in the model formulation, giving NLPC the same deadtime compensation feature of linear model-predictive techniques. The multi-rate sampling nature of most chemical processes is also used to improve estimates of process disturbances. Infrequent composition measurements in conjunction with frequent temperature measurements are used to improve the “inferential” control of the composition in a continuous flow stirred tank reactor (CSTR).     

Multistage adaptive optimization using hybrid scenario and decision rule formulation

Scenario-based stochastic programming and linear decision rule (LDR)-based robust optimization are prevalent methods for solving multistage adaptive optimization (MSAP) problems. In practical applications such as capacity expansion planning of chemical processes, often multiple sources of uncertainty affect the problem which introduces challenges to traditional stochastic optimization methods. While a large number of uncertain parameters exist in the problem, using scenario-based method results in very large problem size and the solution becomes computationally expensive. In addition, when the constraints include multiplication of uncertain parameters and adaptive variables, the constraints are not linear with respect to uncertain parameters when the LDR method is used. In order to address these challenges, we propose two different hybrid methods where scenario and decision rule methods are combined to solve the MSAP problem. The article demonstrates the computational performance of the proposed hybrid methods using two chemical process planning examples.     

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.     

Inferential Control of Reactive Destillation Columns – An Algorithmic Approach

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. Here, mixed integer optimization is used to determine the optimal control structure and the optimal controller parameters simultaneously. The process dynamics is included explicitly into the constraints using a rigorous nonlinear dynamic process model. Depending on the objective function, which is used for the evaluation of competing control systems, two different formulations are proposed which lead to mixed‐integer dynamic optimization (MIDO) problems. A MIDO solution strategy based on the sequential approach is adopted in the present paper. Here, the MIDO problem is decomposed into a series of nonlinear programming (NLP) subproblems (dynamic optimization) where the binary variables are fixed, and mixed‐integer linear programming (MILP) master problems which determine a new binary configuration for the next NLP subproblem. The proposed methodology is applied to inferential control of reactive distillation columns as a challenging benchmark problem for chemical process control.     

Control of pH neutralization process using simulation based dynamic programming

The pH neutralization process has long been taken as a representative benchmark problem of nonlinear chemical process control due to its nonlinearity and time-varying nature. For general nonlinear processes, it is difficult to control with a linear model-based control method so nonlinear controls must be considered. Among the numerous approaches suggested, the most rigorous approach is the dynamic optimization. However, as the size of the problem grows, the dynamic programming approach suffers from the curse of dimensionality. In order to avoid this problem, the Neuro-Dynamic Programming (NDP) approach was proposed by Bertsekas and Tsitsiklis [1996]. The NDP approach is to utilize all the data collected to generate an approximation of optimal cost-to-go function which was used to find the optimal input movement in real time control. The approximation could be any type of function such as polynomials, neural networks, etc. In this study, an algorithm using NDP approach was applied to a pH neutralization process to investigate the feasibility of the NDP algorithm and to deepen the understanding of the basic characteristics of this algorithm. As the approximator, the neural network which requires training and the k-nearest neighbor method which requires querying instead of training are investigated. The approximator has to use data from the optimal control strategy. If the optimal control strategy is not readily available, a suboptimal control strategy can be used instead. However, the laborious Bellman iterations are necessary in this case. For pH neutralization process it is rather easy to devise an optimal control strategy. Thus, we used an optimal control strategy and did not perform the Bellman iteration. Also, the effects of constraints on control moves are studied. From the simulations, the NDP method outperforms the conventional PID control.