Modeling and control of Wiener-type processes

We develop a simple relay feedback method to identify Wiener-type nonlinear processes. It separates the identification problem of the nonlinear static function from that of the linear dynamic subsystem to simplify the identification procedure significantly. Owing to the separation, the unmeasurable output of the linear dynamic subsystem can be obtained in a straightforward manner. Then, determining the model structure of the nonlinear static function becomes very simple and the estimates are robust to additive output noises. We can identify the whole activated region of the nonlinear static function as well as the ultimate information of the linear dynamic subsystem from only one relay feedback test. More information on the linear dynamic subsystem can be estimated by well-established linear system identification methods from additional tests. We use a nonlinear control strategy to compensate the nonlinear dynamics of the Wiener process so that the design parameters can be determined by usual tuning rules developed for linear processes and a high control performance can be achievable as in linear processes.     

A model predictive formulation for control of open-loop unstable cascade systems

Cascade control is commonly used in the operation of chemical processes to reject disturbances that have a rapid effect on a secondary measured state, before the primary measured variable is affected. In this paper, we develop a state estimation-based model predictive control approach that has the same general philosophy of cascade control (taking advantage of secondary measurements to aid disturbance rejection), with the additional advantage of the constraint handling capability of model predictive control (MPC). State estimation is achieved by using a Kalman filter and appending modeled disturbances as augmented states to the original system model. The example application is an open-loop unstable jacketed exothermic chemical reactor, where the jacket temperature is used as a secondary measurement in order to infer disturbances in jacket feed temperature and/or reactor feed flow rate. The MPC-based cascade strategy yields significantly better performance than classical cascade control when operating close to constraints on the jacket flow rate.     

Decentralized fault-tolerant control system design for unstable processes

Fault-tolerant control is an important issue in control of mission critical processes. In this paper, a new approach to fault-tolerant control of unstable processes is proposed based on the Passivity Theorem. The control system is designed in two sequential steps: A multi-loop proportional controller is used to stabilize the unstable process; a passivity-based decentralized unconditionally stabilizing (DUS) controller is then applied to the stabilized process. While the multi-loop stabilizing controllers need to be built with redundancy, the DUS controller is inherently fault tolerant and can maintain closed-loop stability when any of its loops fail. By using a stabilizing proportional controller with the fewest loops, control redundancy can be reduced to the minimum level.     

Use of bifurcation analysis for development of nonlinear models for control applications

Nonlinear system identification poses challenging questions because a closed general theory is not available for this field. Particularly, nonlinear models based on neural networks (NN) may present incompatible general dynamic process behavior, leading to improper closed-loop responses, even when they allow for satisfactory one step ahead prediction of process dynamics, as required by traditional validation methods. It is shown here that performing detailed bifurcation and stability analysis may be very helpful for the adequate development and implementation of nonlinear models and model based controllers. The study of many parameters that are defined a priori during the training of the NN shows that the spurious dynamic behavior is related mostly to the use of incomplete data sets during the learning process. This is an indication that, for each kind of process, the number, range and distribution of the data points in the operation region of interest are of paramount importance for proper training of the nonlinear model. Strategies to improve the quality of the training procedure are provided and analyzed both theoretically and experimentally, using the solution polymerization of styrene in a tubular reactor as a case study.     

An optimal control-based safety system for cost efficient risk management of chemical processes

The design of conventional safety systems is based on failure likelihood and accident severity, which is normally obtained empirically, leaving the system vulnerable to process nonlinearities. To ensure process safety, control actions are conservative and small deviations from setpoints may lead to shutdown, generating economic losses. In this work, periodic simulations of system behavior against failures is proposed in order to determine the potential risk to which the system is subjected. Depending on this potential, preventive actions can be taken in order to guarantee the system safety and integrity and avoid potential shutdown. These actions are calculated to provoke least possible disturbance in order to reduce impact on product quality, while keeping the process operating. The goal is to increase annual operating time of the plant without compromising safety and product quality. Results show that the proposal is feasible to real time applications and unnecessary shutdowns can be avoided.     

Recent developments in the control of constrained hybrid systems

We review recently developed schemes for the constrained control of systems integrating logic and continuous dynamics. The control paradigm we focus on is model predictive control (MPC) and its derivatives, with the emphasis on explicit solution. The exposition of the basic theory is supplemented by a number of application case studies showing the effectiveness as well as the limitations of the deployed algorithms. Current and future lines of research are briefly discussed.     

Two observer-based nonlinear control approaches for temperature control of a class of continuous stirred tank reactors

In this paper, two nonlinear observer based controllers for temperature control of a continuous stirred tank reactor in which a special class of parallel exothermic reactions take place are proposed. A reduced order nonlinear observer is constructed to estimate the concentration in the reactor. The observer is coupled with two nonlinear controllers, designed based on two well-known techniques, namely input-output linearization and backstepping for controlling the reactor temperature. For dampening the effect of observer error dynamics, a compensating term is used in each control law. The asymptotical stability of the closed-loop system is shown by the Lyapunov's stability theorem. The effectiveness of the proposed controllers has been demonstrated through computer simulations.     

Observer-based nonlinear control law for a continuous stirred tank reactor with recycle

This paper proposes new results concerning the problem of the control of a continuous stirred tank reactor with recycle. The novelty of the proposed results consists of a new nonlinear observer-based controller which is found by means of recent results of differential geometry for time-delay nonlinear systems, without using linear approximations of the model. Local convergence of the system state to the arbitrarily chosen operating point is theoretically proved. The significance of the proposed control law is shown by many simulations, which show high performances with any initial conditions, even at the start-up, and with critical cases of mismatched parameter values.     

A variational approach to the control of electrochemical hydrogen reactions

Optimal control problems for the hydrogen evolution reaction (HER) system are solved for different cost objectives and admissible control strategies. The solution for the set-point-change process is given in analytical terms when the admissible controls are continuous functions of time. For piecewise-continuous controls the problem admits a solution as a feedback law. In both cases the cost functional penalizes the electrochemical power spent in the process, which translates into a Lagrangian more involved than classical quadratic. The theoretical framework remains into the Calculus of Variations for infinite-horizon problems. The Hamiltonian control formalism is adapted to treat the problem when the final time is bounded.     

Approximation of the optimal minimum-phase output for control of nonlinear nonminimum-phase processes

Nonminimum-phase parts are better removed in the feedback loop like the time delay term. For this, Wright and Kravaris [1992] proposed the concept of optimal minimum-phase output to control nonlinear nonminimumphase processes. However, their optimal minimum-phase output has no analytic solutions for processes with more than three state variables. Here, methods for analytic minimum-phase outputs approximating the optimal ones are proposed, having no limitations in the number of state variables. The proposed methods provide analytic solutions for processes with three state variables and simple numerical solutions for those with more state variables.     

Enhancement of laminar mixing by optimal control methods

Calculus of variations is applied to the problem of optimal mixing of two immiscible fluids in a laminar flow where stretching of the interface between the liquids is treated as an objective function. Under the action of an optimal control, the system behaves like that driven by a negative surface tension, i.e., an initially flat interface evolves in long tongues that are stretched and twisted by the flow. The method was tested for mixing by Stokes flow in lid-driven two-dimensional rectangular cavity.     

Nonlinear process monitoring using kernel principal component analysis

In this paper, a new nonlinear process monitoring technique based on kernel principal component analysis (KPCA) is developed. KPCA has emerged in recent years as a promising method for tackling nonlinear systems. KPCA can efficiently compute principal components in high-dimensional feature spaces by means of integral operators and nonlinear kernel functions. The basic idea of KPCA is to first map the input space into a feature space via nonlinear mapping and then to compute the principal components in that feature space. In comparison to other nonlinear principal component analysis (PCA) techniques, KPCA requires only the solution of an eigenvalue problem and does not entail any nonlinear optimization. In addition, the number of principal components need not be specified prior to modeling. In this paper, a simple approach to calculating the squared prediction error (SPE) in the feature space is also suggested. Based on T² and SPE charts in the feature space, KPCA was applied to fault detection in two example systems: a simple multivariate process and the simulation benchmark of the biological wastewater treatment process. The proposed approach effectively captured the nonlinear relationship in the process variables and showed superior process monitoring performance compared to linear PCA.     

连续搅拌釜式反应器的鲁棒最优控制

针对一类带不确定性的连续搅拌釜式反应器,提出基于滑模控制理论的鲁棒最优控制算法。输入输出线性化方法用于线性化对象模型,假设系统的不确定因素有界,滑模面采用积分型滑模面以确保系统稳态误差为零,将线性二次型理论用于等效控制律的设计中,保证了系统的性能指标最优,自适应滑模切换控制增益的选取在降低系统抖振的前提下补偿了系统的不确定因素及外部扰动,实现了控制器的鲁棒最优。通过仿真实验表明,提出的控制器对匹配的不确定性因素及外部扰动具有鲁棒性,且闭环系统的性能指标最优。     

Control of a solution copolymerization reactor using multi-model predictive control

We study the control of a solution copolymerization reactor using a model predictive control algorithm based on multiple piecewise linear models. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function which has finite and infinite horizon cost components and uses multiple linear models in its predictions. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and takes the system to the final operating point. Simulation results on an industrial scale methyl methacrylate vinyl acetate solution copolymerization reactor model demonstrate the ability of the algorithm to rapidly transition the process between different operating points.     

化工过程约束优化控制的可行性分析及约束处理

在化工领域过程控制中,普遍存在着各种对输出变量、输入变量甚至中间变量的约束。不同约束条件之间的矛盾会造成约束条件无法全部满足,优化控制器无可行解,给实际生产造成负面影响。从凸体几何角度,将化工生产过程中约束优化控制的可行性判定转化为凸多面体是否相交的问题,将不可行时合理的约束处理方案转化为一系列线性规划或非线性规划问题,提出无需人为参与的自动进行约束优化控制可行性分析和约束调整的算法。Shell公司提供的重油分馏塔典型案例实验证明,该算法能够在约束优化控制不可行时自动有效地进行合理的约束调整,超调量小,控制作用变化平缓,且有一定控制裕量。     

Constrained Unscented Gaussian Sum Filter for state estimation of nonlinear dynamical systems

This work presents a novel constrained Bayesian state estimation approach for nonlinear dynamical systems. The proposed approach uses the recently proposed Unscented Gaussian Sum Filter to represent the underlying non-Gaussian densities as sum of Gaussians, and explicitly incorporates constraints on states during the measurement update step. This approach, labeled Constrained-Unscented Gaussian Sum Filter (C-UGSF), can thus model non-Gaussianity in constrained, nonlinear state estimation problems. Its applicability is demonstrated using three nonlinear, constrained state estimation case studies taken from literature, namely, (i) a gas phase batch reactor, (ii) an isothermal batch process, and (iii) a continuous polymerization process. Results demonstrate superior estimation performance along with a significant improvement in computational time when compared to Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR), which is a popular nonlinear, constrained state estimation approach available in literature.     

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.     

Bang‐Bang solution of nonlinear time‐optimal control problems using a semi‐exhaustivesearch

At times, the objective is to seek a bang‐bang control policy for nonlinear time‐optimal control problems. The usefulness of iterative dynamic programming (IDP) has been shown in the literature for solving such problems. However, the convergence to the optimal solution has been obtained from about 50% of the guessed values near the optimum. In this paper, we present a semiexhaustive search method for seeking such solutions and a comparison is made with the IDP. The results show that the convergence can be obtained from a significantly higher number of guessed values chosen over a much wider region around the optimum.     

A comparison of nonlinear control performance assessment techniques for nonlinear processes

Assessing the quality of industrial control loops is an important auditing task for the control engineer. However, there are complications when considering the ubiquitous nonlinearities present in many industrial control loops. If one simply ignores these nonlinearities, there is the danger of over‐estimating the performance of the control loop in rejecting disturbances and thereby possibly overlooking loops that need attention. To address this problem, several techniques have been recently developed to extend the control performance assessment (CPA) of single input/single output linear systems to nonlinear systems. This article surveys these nonlinear CPA techniques and compares their performances using three case studies. These results can be used to guide control engineers to select the most suitable CPA techniques for their particular applications. © 2012 Canadian Society for Chemical Engineering     

Effect of the choice of final time in optimal control of nonlinear systems

The choice of the final time, t_j, in the optimal control of nonlinear systems is shown to be very important. By choosing t_f to be small, and repeatedly optimizing the system operation over the short time intervals gives a highly oscillatory type of control for a particular nonlinear chemical reactor. The cumulative profit as compared to that obtained by choosing t_f to be large, is substantially lower. In the operation of a batch reactor it is shown that if t_f is small, bang-bang control with singular sub-arcs results. When t_f is large, the optimal control policy tends to be relatively smooth and the profitability is substantially improved.