LQ (optimal) control of hyperbolic PDAEs

The linear quadratic control synthesis for a set of coupled first-order hyperbolic partial differential and algebraic equations is presented by using the infinite-dimensional Hilbert state-space representation of the system and the well-known operator Riccati equation (ORE) method. Solving the algebraic equations and substituting them into the partial differential equations (PDEs) results in a model consisting of a set of pure hyperbolic PDEs. The resulting PDE system involves a hyperbolic operator in which the velocity matrix is spatially varying, non-symmetric, and its eigenvalues are not necessarily negative through of the domain. The C₀-semigroup generation property of such an operator is proven and it is shown that the generated C₀-semigroup is exponentially stable and, consequently, the ORE has a unique and non-negative solution. Conversion of the ORE into a matrix Riccati differential equation allows the use of a numerical scheme to solve the control problem.     

二甲醚精馏装置的模拟与分析

二甲醚精馏是甲醇制二甲醚工艺中的重要工段。本文应用PRO/II流程模拟软件,采用PR方程计算气相组分的逸度系数,利用NRTL法计算液相活度系数,实现了对二甲醚精馏过程的流程模拟。在操作压力为0.83 MPa下,考察了年产20万吨甲醇气相脱水制二甲醚工艺中二甲醚精馏塔进料温度、原料进料位置和回流比对二甲醚分离效果的影响。模拟结果和实际操作数据吻合良好,可用于指导生产装置的改造和设计。     

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.     

乙二醇单丁醚催化精馏塔开车过程的动态模拟研究

对以环氧乙烷和正丁醇为原料,通过催化精馏法合成乙二醇单丁醚的催化精馏塔开车过程的动态行为进行了模拟研究。提出了1项适用于本工艺体系特点的开车策略。建立了催化精馏塔开车过程的动态数学模型,通过模拟计算得到了从开车至达到系统稳定需要的时间,研究和分析了开车过程中塔内温度、组分浓度、热负荷、反应速率及汽液相流量等的动态分布特征,并同试验结果进行了比较。研究揭示了催化精馏塔开车过程的基本规律,为工艺优化和控制策略的建立奠定了重要基础。     

LQ optimal control for a class of pulse width modulated systems

We consider linear quadratic optimal control for a class of pulse width modulated systems. The problem is motivated from a practical application—digital control of switching power converters. The control synthesis problem is posed based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the intersampling behavior into account.     

Nonlinear parametric predictive temperature control of a distillation column

The integration of a nonlinear reduced process model with Parametric Predictive Control (PPC) is discussed for the bottom temperature control of a stabilizer distillation column. One of the main objectives is ensure the quality of the bottom product despite disturbances and complex dynamics. The purpose is to balance nonlinear control with simplicity, facilitating implementation in a DCS. The controllers developed were first tested in a simulated environment and then in the field, showing good performance under a wide range of operating conditions. The use of an estimator to compensate for modeling errors and unmeasured disturbances is also discussed.     

Identification and bilinear control of a binary distillation column

A reduced bilinear model of a binary distillation column is presented. This model has as control inputs the reflux rate and the heat flow of the reboiler, as perturbations the feed stream and its concentration, and as outputs the distillate and residual concentrations. A bilinear model is simpler than a non-linear one, and more exact than a linear model. Furthermore, its structure allows the design of a control structure via optimal control theory. In this paper, two optimal control schemes designed by the reduced bilinear model have been applied to a column simulated by an analytical model, obtaining a robust control of the process even in the presence of disturbances.     

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.     

Nonlinear model-based control of a batch reactive distillation column

The inherent trade off between model accuracy and computational tractability for model-based control applications is addressed in this article by the development of reduced order nonlinear models. Traveling wave phenomena is used to develop low order models for multicomponent reactive distillation columns. A motivational example of batch esterification column is used to demonstrate the synthesis procedure. Tight control of the column is obtained with the use of reduced model in a model predictive control algorithm.     

Multivariable adaptive predictive control of a binary distillation column

This paper presents a tutorial review of an adaptive predictive control system (APCS). Special emphasis is given to the key issues involved in the practical application of APCS to real processes. These practical issues are illustrated by actual application of SISO and MIMO control of a pilot scale binary distillation column. The experimental evaluation of this method reveals the simplicity of the adaptive algorithm and its excellent performance in an industrial type environment. The experimental results easily outperformed well-tuned classical PID controllers. A brief review of other applications of adaptive control to chemical processes is also included in this paper.     

Application of predictive control techniques to a distillation column

Model-based predictive control techniques are widely recognized as having useful application to control problems characterized by complex dynamics and severe time delay. The establishment of a representative process model is the key step in the procedure and for anything other than trivially simple systems is a major hurdle. This paper describes the application of predictive control techniques to a distillation problem which embodies a pure time delay of 2–3 h and time constants of 3–4 h. A sampled-data process model is identified from monitored input/output data and from this a predictive control algorithm is designed. The application of the controller has resulted in very effective closed-loop control of the base composition of the distillation column, where previously only manual supervision was possible.     

Robust model predictive control of a pilot plant distillation column

In this paper, the development and application of a robust MPC to a pilot plant ethanol–water distillation column is described. It is shown through experimental tests in the pilot plant, how the linear model can change depending on the operating point. The obtained model has time delays and repeated poles. For this kind of system, the development of an MPC, based on the step response model that is robust to multi-model uncertainty, is presented. The experimental results that confirm the good performance of the proposed controller are also shown.     

Linearizing control of a binary distillation column based on a neuro-estimator

In this work, the LV-control problem in binary distillation columns is addressed. With least prior knowledge, a linear reference model with unknown terms is obtained. The time variations of the unknown terms are estimated using two on-line trained perceptrons. These estimates are subsequently used to design a feedback linearizing-like controller. The closed-loop behavior is analyzed through numerical examples. The resulting controller shows robustness against external disturbances and set-point changes.     

乙酸甲酯催化精馏水解塔过程模拟

分析乙酸甲酯催化精馏水解过程,建立该实验塔物理模型,据此合理简化,建立平衡级与固定床相结合的数学模型及其计算方法.应用该模型方法对本工艺试验的3种催化精馏塔型,分别按2种工况模拟实验过程,得到了与实测数据吻合良好的计算结果.验证了该模型和计算方法的适用性和准确性,能够为过程放大和工艺条件优化提供可靠数据.     

Robust optimal parametric LQ control with a guaranteed cost bound and applications

For an optimal parametric linear quadratic (LQ) control problem, a design objective is to determine a controller of constrained structure such that the closed-loop system is asymptotically stable and an associated performance measure is optimized. In the presence of system uncertainty, the system via a parametric LQ design is further required to be robust in terms of maintaining the closed-loop stability with a guaranteed cost bound. This problem is referred to as ‘robust optimal parametric LQ control with a guaranteed cost bound’ and is addressed in this work. A new design method is proposed to find an optimal controller for simultaneously guaranteeing robust stability and performance over a specified range of parameter variations. The results presented generalize some previous work in this area. A versatile numerical algorithm is also given for computing the robust optimal gains. The usefulness of the design method is demonstrated by numerical examples and a design of the robust control of a VTOL helicopter.     

Triangular decoupling for a binary distillation column under pressure control

The possibility of attaining complete decoupling of a distillation column under pressure control is studied using the state space model. It is shown that under the situation where the distillation column is under pressure control by the manipulation of the condenser duty, the complete decoupling using constant state feedback may not be attained, while the triangular decoupling can be attained with eight measurement variables.     

Constrained multivariable control of a distillation column using a simplified model predictive control algorithm

Distillation columns are important process units in petroleum refining and need to be maintained close to optimum operating conditions because of economic incentives. Model predictive control has been used for control of these units. However, the constrained optimization problem involved in the control has generally been solved in practice in a piece-meal fashion. To solve the problem without decomposition, the use of a linear programming (LP) formulation using a simplified model predictive control algorithm has been suggested in the literature. In this paper, the LP approach is applied for control of an industrial distillation column. The approach involved a very small size optimization problem and required very modest computational resources. The control algorithm eliminated the large cycling in the product composition that was present using SISO controllers. This resulted in a 2.5% increase in production rate, a 0.5% increase in product recovery, and a significant increase in profit.     

Robust control of a distillation column by the method of inequalities

The method of inequalities is applied to design a robust PI controller for the control of distillate composition using the reflux flow as the manipulated variable. The controller design method takes into account wide variations in k,τ and τ_D of the first order plus the delay transfer function of the process. The performance of the controlled system is evaluated for different levels and changes in direction of set point changes on the linear and also on the original non-linear model equations. The performance of the proposed controller is compared with that of a controller with Zieglar-Nichols (Z-N) settings based on a nominal operating point. The closed loop system becomes unstable at other operating points for the Z-N method whereas the present controller gives good response for wide operating points.     

浆态床法合成二甲醚的模拟研究

对于直接以合成气作为原料,使用Cu-Zn-Al和γ-Al2O3构成的双重催化剂、采用浆态床法合成二甲醚的反应体系,使用全混流反应器模型结合化学反应动力学进行模拟。组分方程使用超松弛迭代方法并结合C 编程进行求解,编制了计算机程序。通过模拟计算,讨论了压力、温度、空速、催化剂配比、反应气中不同氢碳比以及CO2含量对反应收率、DME选择性的影响,并讨论了在不同氢碳比下对CO转化率和CO与H2总转化率的影响,从而寻找合适的反应条件,为工业化生产提供参考。