多变量多时滞非方系统的解耦内模控制

多变量复杂控制系统不仅具有多耦合和多时滞性,还具有结构上的复杂性,即输入输出不等,传递函数为奇异矩阵。传统的多变量内模控制是基于对非奇异对象求逆来进行的,因此很难解决这类问题。针对该情况引入矩阵论中的广义逆概念,通过求对象的广义逆矩阵来设计解耦内模控制器,打破了内模控制只能对方系统进行控制的局限性,并利用泰勒近似很好地解决了多滞后的问题,最后通过设计特殊形式的滤波器,不仅能够消除由纯滞后近似引入的不稳定极点,保证系统的稳定性,且能够保证系统的正则性。仿真结果表明,该方法不仅跟踪迅速,且继承了内模控制的无余差和强鲁棒性,动态解耦效果良好,仅对时滞变化较为敏感。由于系统基于内模控制设计,故模型匹配度越高,系统响应越好。     

Experimental study of the ignition behaviour of an adiabatic SRC-II coal liquefaction reactor

Experimental data are presented which describe the thermal behaviour of a bench-scale adiabatic coal liquefaction reactor operating in an open loop. The reactor employed external feedback control for maintaining adiabaticity. Conditions for both ignition and quench have been found for coal liquefaction at SRC-II operating conditions where repeated ignition/quench behaviour was demonstrated. No stable steady states were found between 450 °C and 475 °C for SRC-II operation. Ignition occurred at a feed temperature of ≈415 °C. The low steady states occurred at conditions of essentially no heat generation; at a very low extent of reaction. Some unexpected evidence of a preheater effect on reactor ignition was observed; however, the effect of preheater temperature profiles on reactor performance was not systematically studied.     

Internal model control design for input‐constrained multivariable processes

Multivariable plants under input constraints such as actuator saturation are liable to performance deterioration due to control windup and directionality change. A two‐stage internal model control (IMC) antiwindup design for open loop stable plants is presented. The design is based on the solution of two low‐order quadratic programs at each time step, which addresses both transient and steady‐state behaviors of the system. For analyzing the robust stability of such systems against any infinity‐norm bounded uncertainty, stability test have also been developed. In particular, we note that the controller input‐output mappings satisfy certain integral quadratic constraints. Simulated examples show that the two‐stage IMC has superior performance when compared with other existing optimization‐based antiwindup methods. The stability test is illustrated for a plant with left matrix fraction uncertainty. A scenario where the proposed two‐stage IMC competes favorably with a long prediction horizon model predictive control is described. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Robust discrete control of nonlinear processes: Application to chemical reactors

Trajectory tracking or rejecting persistent disturbances with digital controllers in nonlinear processes is a class of problems where classical control methods breakdown since it is very difficult to describe the dynamic behavior over the entire trajectory. In this paper, a model-based robust control scheme is proposed as a potential solution approach for these systems. The proposed control algorithm is a robust error feedback controller that allows us to track predetermined operation profiles while attenuating the disturbances and maintaining the stability conditions of the nonlinear processes. Various numerical simulation examples demonstrate the effectiveness of this robust scheme. Two examples deal with effective trajectory tracking in chemical reactors over a wide range of operating conditions. The third example analyses the attenuation of periodic load in a biological reactor. All examples illustrate the ability of the robust control scheme to provide good control in the face of parameter uncertainties and load disturbances.     

Simultaneous process and control system design for grade transition in styrene polymerization

We present a comprehensive approach to the simultaneous design and control of a continuous stirred tank reactor (CSTR) for styrene solution polymerization that must be able to produce different polymer grades. The resulting tool allows simultaneous selection of the polymerization equipment, the multivariable feedforward-feedback controller's structure and tuning parameters, the steady states and the transition paths between them. For this purpose a multiobjective optimization is implemented to minimize the annualized reactor cost, the operating costs, the production of off-specification polymer and the transition time between steady states. Trade-offs between the sometimes conflicting objectives are dealt with by the optimization. Unlike many previous grade transition studies, steady states are not known a priori. The only known parameters are the target molecular weights to be produced at each steady state. We have analyzed three different scenarios, and propose practical criteria for selecting the most reasonable optimum when the solution is not unique.     

TUNING METHOD FOR INTERACTIVE MULTILOOP IMC, PI AND PID CONTROLLERS

An efficient method to adjust a multiloop control system based on IMC, PI or PID controllers is presented. The first step of the new method consists in designing and adjusting the individual IMC controllers assuming a noninteractive condition and using information related to model uncertainties. In a second step, a single tuning parameter is used to adjust the multiloop interactive system in order to improve both stability and performance characteristics. The extension to multiloop PI and PID controllers is made through alternative parameterizations of IMC (Rivera el al., 1986).

Several simulation results obtained using transfer function representations of distillation systems from the literature show the convenience of the proposed technique by yielding good settings with a reasonable amount of engineering and computational effort.     

MULTIPLICITY OF STATES IN CONTINUOUS STIRRED COPOLYMERIZATION REACTORS: ITS EXISTENCE AND CONSEQUENCES*

The dynamic behaviour of a continuous copolymerization stirred tank reactor is analyzed. The evolution of multiple steady states due to Trommsdorf or gel effect in free radical bulk copolymerization systems is illustrated for the first time taking into consideration the changes in the cross termination rate constant [or the φ factor] at high extent of reaction. The effect of concentration multiplicity on cumulative copolymer composition is illustrated. The consequences of the results of the present analysis in copolymerisation reactor operation and design have been discussed.     

Control of nonlinear processes using functional expansion models

Functional expansion (FEx) models are a subclass of the general block-oriented model structure for nonlinear process systems. Controller design in this context uses the internal model control (IMC) paradigm, and one can show that the resulting controllers are easily implementable. The primary advantage arises from the fact that inverting the nonlinear dynamic operator is avoided by taking advantage of the partitioned model inverse due to the special structure of FEx models. The robust stability and performance of the closed-loop system can be analyzed by expressing the FEx model as a linear uncertain system and using the structured singular value framework. We present a case study of a polymerization reactor and, for this SISO system, analyze nominal and robust stability and performance conditions as a function of the closed-loop filter constants for a given range of the input variable.     

GLOBALLY OPTIMAL NONLINEAR FEEDBACK: APPLICATION TO NONISOTHERMAL CSTR CONTROL

Approximations of the globally optimal nonlinear quadratic regulator (NQR) strategy are employed to control the unstable steady state of a continuous stirred tank reactor. It is shown that the proposed approximate NQR controllers can be uniquely determined through solution of Riccati and linear matrix equations and can deliver better dynamic performance than the linear quadratic regulator (LQR) if the process model is proper. Stability, optimality, and constraint satisfaction regions for these controllers are identified.     

Robust and optimal control approach for exothermic reactor stabilization

In this paper, the possibility to stabilise open-loop unstable exothermic reactors with temperature measurements is studied. Moreover, the reactors are considered to be multi-input multi-output systems with parametric uncertainties. Robust static output feedback and optimal controllers are designed for stabilization of the exothermic reactors into their open-loop unstable steady states. Stabilization of reactors is simulated using designed controllers. The possibility of using both types of controllers for energy savings is studied and measured by coolant consumption. The approach is tested with a representative example. Obtained simulations results confirm that the robust static output feedback controllers outperform optimal controllers when systems with parametric uncertainties are controlled.     

基于ARX-PLS解耦框架下的多回路约束迭代模型预测控制方法(英文)

A multi-loop constrained model predictive control scheme based on autoregressive exogenous-partial least squares （ARX-PLS） framework is proposed to tackle the high dimension, coupled and constraints problems in industry processes due to safety limitation, environmental regulations, consumer specifications and physical restric-tion. ARX-PLS decoupling character enables to turn the multivariable model predictive control （MPC） controller design in original space into the multi-loop single input single output （SISO） MPC controllers design in latent space. An idea of iterative method is applied to decouple the constraints latent variables in PLS framework and recursive least square is introduced to identify ARX-PLS model. This algorithm is applied to a non-square simulation system and a stirred reactor for ethylene polymerizations comparing with adaptive internal model control （IMC） method based on ARX-PLS framework. Its application has shown that this method outperforms adaptive IMC method based on ARX-PLS framework to some extent.     

Multiple steady states and transitional regimes in a cylindrical fixed-bed catalytic reactor

Heterogeneous catalytic reactions in a cylindrical axial-flow fixed-bed reactor have been investigated using a two-phase mathematical model. Regions of multiple steady states have been mapped for basic process parameters, namely, the flow velocity and coolant temperature. Transitions from one steady state to another and possible pathways of the establishment of various steady states have been examined.     

The design of experiments,training and implementation of nonlinear controllers based on neural networks

In the area of nonlinear predictive control, several control schemes using artificial neural networks have been proposed. In this work, the issues relating to the information contents of the data used to train the neural network components of these nonlinear predictive control schemes are considered. This raises questions about the design of experiments. A class of feedback-feedforward nonlinear controller based on the model predictive structure (also known as Internal Model Control, IMC, structure) is investigated. The implementation and performance of these neural network based controllers, together with comparisons to other nonlinear and linear controllers, are illustrated on two nonlinear continuous-stirred-tank-reactor simulations.     

Fate of commensalistic cultures in identical coupled bioreactors

A comprehensive analysis of static and dynamic behavior of a mixed culture in two identical coupled bioreactors is presented considering anaerobic digestion involving acidogens (X) and methanogens (Y) as the example bioprocess. A single continuous culture may operate at up to seven steady states, including up to four coexistence steady states, with only one coexistence steady state being locally stable. The one-way interaction between X and Y allows for compartmentalization of the system for a stand-alone bioreactor and two coupled bioreactors into two subsystems, which facilitates the analysis of steady state types and stability characteristics of these and classification of dynamic behavior. The bioreactors in the two-reactor system are identical only in terms of feed composition and reactor space time. A two-reactor system may admit up to forty nine steady states, which are comprised of up to forty coexistence steady states, at least at very low interaction rate (R). The static and dynamic analysis of the two-reactor system is facilitated by appropriate grouping of large number of steady states arising for very low R into nine clusters. Numerical illustrations reveal the rich steady state structure of the bioprocess in coupled bioreactors. While a single bioreactor can operate at only one locally stable coexistence steady state, the coupled bioreactors can operate at up to five locally stable coexistence steady states over certain ranges of R. The two-reactor system is operationally more flexible and more robust vis-a-vis single reactor as concerns maintenance of mixed culture. Emergence of four additional steady state clusters and additional coexistence and partial washout steady states at intermediate R reveals that the coupled bioreactors are an example of a complex system.     

多频多变量预测控制系统的IMC结构及其改进算法

Multirate multivariable predictive control system with the sampling mechanism that adjusts the plant inputs only once but detects the plant outputs several times during a period is examined. The IMC structure of the system is derived, and its robust stability and zero steady state error chaxacteristics axe analyzed. A new controlal gorithm is developed by adding the variation of the outputs to the index performance. The simulation results show that the method is effective and has zeros steady-state error.     

Dynamics of a CSTR for styrene polymerization initiated by a binary initiator system

The steady state and dynamic behavior of a continuous stirred tank reactor has been analyzed for free radical solution polymerization of styrene initiated by a mixture of two initiators having different thermal stabilities. From the steady state analysis of the reactor model with a mean residence time as a bifurcation parameter, four unique regions of steady state solutions are identified in an operating parameter space for a given initiator feed composition. A variety of complex bifurcation behavior such as multiple steady states, Hopf bifurcation and limit cycles have been observed and their stability characteristics have been analyzed. The effects of feed initiator composition and the concentration of the initiator in the feed stream on the reactor dynamics are also presented.     

列管式固定床反应器振荡操作研究——以Bang-Bang控制方法产生强制振荡

本文研究了以Bang-Bang控制产生强制振荡的列管式反应器的操作特性.对邻二甲苯催化氧化反应,以热点温度作为控制参数,进行Bang-Bang控制,使反应器在振荡状态下操作,与定态操作相比,苯酐收率提高3%.Bang-Bang控制比传统定值控制提供了更多的工程操作手段,具有更多的灵活性.     

Temperature response to reactant concentration perturbations in a packed‐bed reactor

Unsteady‐state operations are known to enhance the performance of some packed‐bed reactor systems. However, negative effects of this type of operation should not be neglected. Temperature excursions developed during transients may accelerate some deactivation mechanisms, reducing catalyst lifetime and selectivity. Temperature response to perturbations in reactant concentration was studied for CO oxidation over Pt/Al₂O₃ in a packed‐bed reactor. Experiments were conducted in the CO concentration range for which multiple steady states are observed. Temperature and concentration profiles in the packed‐bed reactor at steady state were found to depend on the dynamic history of the reactor prior to the steady‐state condition.     

Control of periodically operated reactors

Control of periodically operated reactors has in common with control of reactors operating at steady state the objective of minimizing the effect of disturbances on an objective function such as the cost of a product or the deviation of an outlet concentration of a pollutant from a statuary target. Simple feedback control employing feedback PID regulators, however, is not “adequate for most disturbances because of problems with tracking a time-varying output and the necessarily non-linear character of the reactors with respect to controlled as well as uncontrolled inputs. This contribution is a review of the literature and a discussion of research needs. The literature on the control of periodically operated reactors is not voluminous. Nevertheless this literature clearly indicates that model based predictive controllers can be used for this type of reactor”. Further research on the limitations, maintenance and implementation costs of model based controllers in this application would be worthwhile. Experimental studies are wholly absent. Unique regulators for other periodic operations, such as adaptive control or forcing the output toward a reference trajectory using an open loop model based control strategy, certainly warrant study of their application to periodically operated reactors. Additionally, proper design of the reactor may lead to configurations that are simpler to control and that may not require complex control strategies for efficient operation.