Multi-model predictive control of an industrial C3/C4 splitter

In this paper, the application of a linear predictive controller to an industrial distillation column that presents a nonlinear behavior is described. The system is represented by a set of linear approximating models, where each model corresponds to a possible operating point of the system. The control sequence computed by the control algorithm is based on a min–max optimization problem where the controller cost is minimized for the worst process model. The control algorithm makes use of a particular form of the state-space model, which preserves the structure of conventional model predictive control controllers that are based on the step response model. The performance of the proposed controller applied to an industrial system is illustrated with results of the real system at typical plant conditions with the controller performing as a regulator and as an output reference tracker.     

Nonlinear identification and control of a high-purity distillation column: a case study

Identification and control of ill-conditioned, interactive and highly nonlinear processes pose a challenging problem to the process industry. In the absence of a reasonably accurate model, these processes are fairly difficult to control. Using a high-purity distillation column as an example, model identification and control issues are addressed in this paper. The structure of the identified models is that of the polynomial type nonlinear autoregressive models with exogenous inputs (NARX). While most of the work in this area has concentrated on linear models (one-time scale and two-time scale models), this work is aimed at identifying the inherent nonlinearities. Comparisons are drawn between the identified models based on statistical criteria (AIC etc.) and other validation tests. Simulation results are provided to demonstrate the closed-loop performance of the nonlinear ARX models in the control of the distillation column. The controller employed is based on a nonlinear model predictive scheme with state and parameter estimation.     

Linear controller design and performance limits of binary distillation column subject to disturbances with bounds on magnitudes and rates of change

In this paper, we present an application of linear controller design via convex optimization to a binary distillation column and determine its limits of performance. Disturbances of distillation process are characterized as input signals with bounded magnitudes and rates of change. Performance measures of top and bottom control loops are defined as the maximum deviation magnitudes of top and bottom compositions, respectively. This performance is often referred to as the worst-case norm of convolution systems under such disturbances. The convex optimization and the ellipsoid algorithm are applied to design linear controllers and, at the same time, determine the best achievable performance of the closed-loop system. Then, a series of convex optimization problems are efficiently solved to give a trade-off curve representing limits of performance between the top and bottom compositions. The trade-off curve provides a practical insight into the design specification that cannot be achieved for the distillation column control with dynamic controller configuration. To confirm the results, we undertake computer simulation using nonlinear dynamical model of the distillation column. Closed-loop responses of the chosen optimal linear controller are consistent with the trade-off curve and yields superior performance than that of a conventional decentralized PI controller.     

基于模型匹配的精馏塔产品质量非线性控制

将非线性系统模型匹配问题 (MMP)应用于精馏塔产品质量控制器的设计 ,得到精馏塔的MMP非线性控制器。理论分析和仿真表明 ,该控制器实现了对部分干扰的解耦 ,具有良好的跟踪和调节特性。     

A wave propagation approach for reduced dynamic modeling of distillation columns: Optimization and control

Reduced models enable real-time optimization of large-scale processes. We propose a reduced model of distillation columns based on multicomponent nonlinear wave propagation (Kienle 2000). We use a nonlinear wave equation in dynamic mass and energy balances. We thus combine the ideas of compartment modeling and wave propagation. In contrast to existing reduced column models based on nonlinear wave propagation, our model deploys a hydraulic correlation. This enables the column holdup to change as load varies. The model parameters can be estimated solely based on steady-state data. The new transient wave propagation model can be used as a controller model for flexible process operation including load changes. To demonstrate this, we implement full-order and reduced dynamic models of an air separation process and multi-component distillation column in Modelica. We use the open-source framework DyOS for the dynamic optimizations and an Extended Kalman Filter for state estimation. We apply the reduced model in-silico in open-loop forward simulations as well as in several open- and closed-loop optimization and control case studies, and analyze the resulting computational speed-up compared to using full-order stage-by-stage column models. The first case study deals with tracking control of a single air separation distillation column, whereas the second one addresses economic model predictive control of an entire air separation process. The reduced model is able to adequately capture the transient column behavior. Compared to the full-order model, the reduced model achieves highly accurate profiles for the manipulated variables, while the optimizations with the reduced model are significantly faster, achieving more than 95% CPU time reduction in the closed-loop simulation and more than 96% in the open-loop optimizations. This enables the real-time capability of the reduced model in process optimization and control.     

Control of integrated processes: A case study on reactive distillation in a medium-scale pilot plant

This paper deals with the systematic design of a multivariable controller for a medium-scale reactive distillation column that is operated in semi-batch mode. This is a challenging problem because of the time-varying and strongly nonlinear dynamics of the process and considerable deviations of the behaviour of the real plant from the rigorous model used for process design. The design procedure consists of three steps: first, a suitable control structure that enables the operation of the column near the economically optimal operating point is determined based upon the rigorous nonlinear process model. In a second step, a linear model of the column is identified from experiments and used to compute the best attainable control performance for the chosen control structure. In this step, actuator limitations and model uncertainties described by confidence intervals that were obtained in the identification procedure are considered. In the third step, the resulting high-order controller is approximated by a low-order controller that gives nearly the same performance and preserves robust stability for the computed uncertainty bounds. The controller performance is demonstrated in a series of experiments that were performed at the real reactive distillation column.     

A feedforward control strategy for distillation columns

The prime objective of this work is to demonstrate the potential of neural network modeling for advanced nonlinear control applications. In particular, for the case of a single composition distillation column, a model-based neural controller is developed to regulate the composition of the distillate stream. The neural controller relies on process inversion for the evaluation of the actuator action on the manipulated variable (reflux flowrate) to maintain the controlled variable (distillate composition) at the prescribed value.The performance of the neural controller is assessed and compared with that of a conventional temperature control loop and of a neural inferential control structure. The neural controller by far outperforms the other two in terms of the response speed by which the upsetting loads are compensated.     

非线性系统多步预测控制的复合神经网络实现

提出一种基于神经网络的非线性多步预测控制,采用由线性网络和动态递归神经网络构成的复合神经网络。在此基础上将线性系统的广义预测控制器扩展为非线性系统的多步预测控制器。通过对非线性过程ＣＳＴＲ的仿真表明,该方法的稳定性和鲁棒性明显优于线性ＤＭＣ预测控制。     

Performance analysis of a dynamic phenomenological controller for a pellet cooling process

The cooling zone of an induration furnace exhibits a nonlinear dynamic behavior in addition to a strong coupling between output pressure and temperature. Simulation studies show that linear controller performance is unacceptable from an industrial point of view. In order to obtain adequate performance on a wide operating range, a nonlinear predictive controller (NLMPC) based on a phenomenological process model is proposed. Since the furnace simulation model shows that the equipment behaves as a Hammerstein model, a variable change is performed and a linear model predictive controller (MPC) is developed for the cooling zone. Both controllers are tested for set-point changes and disturbance rejection and give relatively similar performances. It is concluded that for processes having structured nonlinearities, as the cooling zone considered here, linear MPC should be preferred to NLMPC since the computation time is far less demanding and the industrial implementation easier.     

Nonlinear model predictive control of a reactive distillation column

This paper considers the application of nonlinear model predictive control (NLMPC) to a highly nonlinear reactive distillation column. NLMPC was applied as a nonlinear programming problem using orthogonal collocation on finite elements to approximate the ODEs that constitute the model equations for the reactive distillation column. Diagonal PI controls were used to identify that the [L/D,V] and the [L/D,V/B] configurations performed best. NLMPC was applied using the [L/D,V] configuration and found to provide a factor of 2–3 better performance than the corresponding PI controller. The effect of process/model mismatch on the performance of the NLMPC controller was also evaluated.     

High-purity control of internal thermally coupled distillation columns based on nonlinear wave model

Internal thermally coupled distillation column (ITCDIC) is a frontier of energy saving distillation researches, which is a great improvement on conventional distillation column (CDIC). However its high degree thermal coupling makes the control design a bottleneck problem, where data-driven model leads to obvious mismatch with the real plant in the high-purity control processes, and a first-principle model which is comprised of complex mass balance relations and thermally coupled relations could not be directly used as control model for the bad online computing efficiency. In the present work, wave theory is extended to the control design of ITCDIC with variable molar flow rates, where a general nonlinear wave model of ITCDIC processes based on the profile trial function of the component concentration distribution is proposed firstly; combined with the thermally coupled relations, a novel wave model based generic model controller (WGMC) of ITCDIC processes is developed. The benzene-toluene system for ITCDIC is studied as illustration, where WGMC is compared with another generic model controller based on a data-driven model (TGMC) and an internal model controller (IMC). In the servo control and regulatory control, WGMC exhibits the greatest performances. Detailed research results confirm the efficiency of the proposed wave model and the advantage of the proposed WGMC control strategy.     

Nonlinear control of a reactive distillation column

Control of reactive distillation columns is a challenging task due to the complex dynamics arising from the coupling of reaction and separation. In this paper, asymptotically exact input/output-linearization is applied in simulation studies to an industrial reactive distillation column which is operated by Bayer AG. The resulting control law is rather general and can be easily adopted for other reactive distillation columns. This control scheme requires knowledge of the complete state of the process and therefore an observer is designed. Asymptotically exact input/output-linearization inherits robust stability from a robust observer. It is intuitively argued that the proposed observer is robust w.r.t. both model structure and parameter errors. In order to compensate for steady state observer offsets an outer control loop with simple PI-controllers is implemented. Simulation studies evidence that in comparison with a well-tuned linear controller the nonlinear controller shows a superior performance with respect to setpoint-changes and disturbances, even in the presence of unknown input delays.     

A data-based approach for multivariate model predictive control performance monitoring

An intelligent statistical approach is proposed for monitoring the performance of multivariate model predictive control (MPC) controller, which systematically integrates both the assessment and diagnosis procedures. Model predictive error is included into the monitored variable set and a 2-norm based covariance benchmark is presented. By comparing the data of a monitored operational period with the “golden” user-predefined one, this method can properly evaluate the performance of an MPC controller at the monitored operational stage. Characteristic direction information is mined from the operating data and the corresponding classes are built. The eigenvector angle is defined to describe the similarity between the current data set and the established classes, and an angle-based classifier is introduced to identify the root cause of MPC performance degradation when a poor performance is detected. The effectiveness of the proposed methodology is demonstrated in a case study of the Wood-Berry distillation column system.     

大型炼油蒸馏塔的多输入预报自校正控制

本文针对一个大型炼油蒸馏塔的控制,设计了一种适用于具有多个确定性扰动对象的多 输入预报自校正控制器,其特点是综合了在线辨识、多输入前馈、最小方差和PI规律各自的优 点,并采用变遗忘因子的最小二乘估计算法在线修正参数,使控制器的收敛性、稳定性与自适应能力较一般自校正控制器大为提高.实践表明,该控制器很好地克服了生产中的干扰和波 动,平稳了操作,成功地实现了对蒸馏塔的产品质量控制.     

Nonlinear control of high purity distillation column under input saturation and parametric uncertainty

This paper presents a systematic methodology for designing adaptive feedback linearization controller for high purity binary distillation column having uncertain parameters and input saturation. Main goal of the controller is to control the top and bottom compositions of a binary distillation column in presence of both structured and unstructured uncertainty. An adaptive control strategy is used for the estimating uncertain parameters in the system model. Process input saturation always causes an added nonlinearity to the process, leading the process to become uncontrollable. A cascade reduced order nonlinear adaptive controller is designed and implemented to handle both forms of structured and unstructured uncertainty and input saturation problem.     

永磁同步电机高效非线性模型预测控制

永磁电机控制器要求电机有很强的转速跟踪能力,并且要保证系统参数变化及负荷扰动下系统的鲁棒性. 永磁电机包含很多不确定因素,是强耦合的非线性系统,传统的线性控制器很难对其进行控制. 针对永磁电机的转速控制构造非线性模型预测控制方法. 非线性永磁电机模型通过输入-输出反馈线性化策略解耦成为新的线性系统. 为保证可行解的收敛性,提出一种迭代二次规划方法来处理由输入-输出反馈线性化导致的非线性约束. 仿真结果表明,控制器能有效降低计算负担,具有很好的动态控制性能,能抑制转矩脉动,并保证在参数变化和负荷扰动下控制系统的鲁棒性.     

Application of Wiener model predictive control (WMPC) to an industrial C2-splitter

Dual composition control of a high-purity distillation column is recognized as an industrially important, yet notoriously difficult control problem. It is proposed, however, that Wiener models, consisting of a linear dynamic element followed in series by a static nonlinear element, are ideal for representing this and several other nonlinear processes. They are relatively simple models requiring little more effort in development than a standard linear step response model, yet offer superior characterization of systems with highly nonlinear gains. Wiener models may be incorporated into MPC schemes in a unique way that effectively removes the nonlinearity from the control problem, preserving many of the favorable properties of linear MPC, especially in the analysis of stability. In this paper, Wiener model predictive control is applied to an industrial C2-splitter at the Orica Olefines plant with promising results.     

间歇精馏过程的模糊逻辑与增益自调整PID混合控制

针对间歇精馏过程的强非线性和非平稳时变特性,结合模糊逻辑控制和增益自调整PID控制的优点,提出了一种模糊逻辑和增益自调整PID混合控制的先进控制策略,详细推导了其控制算法,设计了相应的控制器,并在EuroBEEB工控机上用实时BASIC语言编程实现,对一套甲醇/水二元间歇精馏塔的塔顶浓度进行了推断控制实验,获得了比单独采用模糊逻辑控制时更好的控制结果。这说明,模糊逻辑和增益自调整PID混合控制是强非线性和非平稳时变过程的一种有效控制策略。     

基于神经网络与多模型的非线性自适应广义预测解耦控制

针对一类非线性多变量离散时间动态系统,提出了基于神经网络与多模型的非线性自适应广义预测解耦控制方法.该控制方法由线性鲁棒广义预测解耦控制器和神经网络非线性广义预测解耦控制器以及切换机构组成.线性鲁棒广义预测解耦控制器用于保证闭环系统输入输出信号有界,神经网络非线性广义预测解耦控制器能够改善系统性能.切换策略通过对上述两种控制器的切换,保证系统稳定的同时,改善系统性能.同时本文给出了所提自适应解耦控制方法的稳定性和收敛性分析.最后,通过仿真实例验证了该方法的有效性.     

Predictive proportional nonlinear control for stable-target tracking of a mobile robot: an experimental study

Two new types of control method have been developed based on model predictive control for stable-target tracking of a nonholonomic mobile robot. One method (Method 1) is a new nonlinear control method. This was developed based on model predictive control (predictive nonlinear control) to predict the next position of a mobile robot using the current velocities of the right and left wheels. This technique uses a tuning guideline in predictive nonlinear control. The other method (Method 2) is a combination of Method 1 and proportional control (predictive proportional nonlinear control). Method 2 involves a tuning guideline not only in a predictive nonlinear controller, but also in a proportional controller. In this technique, the selection of a tuning guideline in the proportional controller is enhanced, and thereby increases the control action in closed-loop responses. In Method 1, the nonlinear controller is derived from Liapunov stability theory, and is used to control the linear and angular velocities for locomotion control. Tuning parameters in the nonlinear controller (in Method 1) are selected to satisfy various design criteria, such as stability, performance, and robustness. Method 1 has certain limitations that result in a decrease of the performance criteria specified. Strong nonlinearities in the mobile robot system result in accumulated errors. To enhance performance further, we developed Method 2 as the solution for decreasing cumulative errors. Hence, the proportional controller is added to Method 1 in the closed-loop form in order to eliminate errors. The advantage of Method 2 is that it can cope with strong nonlinearities in the mobile vehicle system. The results of the performances of Method 1 and Method 2 are shown to demonstrate the effectiveness of both methods, and also the better performance of Method 2. The two new methods are effective in stable-target tracking, yielding an increase in performance and stability.