Multivariable control strategy based on bifurcation analysis of an industrial gas-phase polymerization reactor

In an industrial gas-phase polyethylene reactor, the safe operating range of temperature is rather narrow. Even within this temperature range, temperature excursions must be avoided because they can result in low catalyst productivity and significant changes in product properties. If the manipulated variable for temperature control saturates (i.e., the cooling water valve position is completely open), then the reactor operates without a feedback temperature controller, leading to oscillatory behavior and limit cycles. In this work, it has been demonstrated that the saturation in the manipulated variable and the complex non-linear dynamic behavior are removed when auxiliary manipulated variables, obtained by bifurcation analysis, are used in a multivariable control strategy for the reactor temperature control. Two control structures are proposed and compared considering their impact in the reactor production and polymer melt index. In the first control structure, the designed PID controller for the reactor temperature is considered and a switching strategy with a PI controller for the auxiliary manipulated variables is included. In the second control structure, the designed PID controller for the reactor temperature is also used, however, a MPC controller for the auxiliary manipulated variables is considered. The results suggest that the use of gain-scheduling strategy in the PID temperature controller with a MPC controller for the auxiliary manipulated variables avoids the saturation of the manipulated variable and, hence, the undesired non-linear dynamic behavior, reducing the production loss and improving the product quality.     

Profile control in distributed parameter systems using lexicographic optimization based MPC

Process equipment that exhibits significant spatial variation of system properties, such as temperature or concentration in a fixed bed reactor, are typically modeled as distributed parameter systems. While some properties of the final product exiting the equipment may depend on the states concerning the endpoint, others may be a function of the history of processing within the equipment. In such instances, control of the spatial property profile may be beneficial. In this work, we explore the idea of profile control using extended MPC and outline the additional challenges that must be addressed in this context. In case that the target profile is unachievable, we present an MPC formulation that uses lexicographic optimization to prioritize the different sections of the profile. Simulation of a simple representative system namely a hypothetical plug flow reactor is used to demonstrate that the lexicographic optimization based MPC provides a systematic approach to profile control and spans between the endpoint control strategy and the whole profile control strategy. The benefits of lexicographic optimization based MPC were also demonstrated on a large-scale distributed parameter system of industrial size, namely the continuous pulp digester.     

Nonlinear inferential control of an autonomous periodic fixed-bed reactor

This paper deals with the control of an autonomous periodic fixed-bed reactor, which is called circulation loop reactor (CLR). This process can be described by a distributed parameter system with sustained oscillations. The state variables at some positions of such a process, e.g. the conversion at the reactor exit, may be required to vary in a smooth fashion, which in general is a difficult task due to the process's inherent complex behavior. Here, a straightforward control strategy of the CLR based on direct exit concentration regulation is presented. A relay feedback controller is found to be effective for achieving overall conversion while using relatively small external heating. In order to implement the control scheme without on-line concentration measurement, a nonlinear inferential control concept is adopted. A newly-developed nonlinear distributed parameter observer is used to infer the exit concentration from the temperature measurements at only a few positions. Moreover, an approach based on integrating a disturbance estimator is presented for improving the performance of the observer in the case of unmeasured inlet concentration. It is found that there exist simple determinate relations between the inlet variables or the model parameters and the maximum amplitude or the period of the oscillatory temperature at an axial position for the considered cases. By employing the oscillatory feature of the CLR, a method of estimating the inlet concentration is proposed, and a parameter estimation method based on the least square technique is given to update offline model parameters. It is shown that substantial benefits could be realized using the proposed nonlinear inferential control scheme for the CLR because it can provide excellent disturbance rejection capabilities and strong robustness.     

A self-tuning regulator for distributed parameter systems

The control of distributed parameter systems with constant, but unknown parameters is considered. A weighted average of the distributed output on the spatial domain is defined as a new variable and is used to generate the control. The parameters of the model are estimated using recursive least squares estimation. The control is obtained using a minimum variance strategy based on the estimated parameters. Distributed disturbances and measurement noise are allowed to be present. Measurements at a finite number of points in the spatial domain are used in obtaining a discrete-time model. From the simulation of a one-sided heating diffusion process the self-tuning regulator is shown to have attractive characteristics and hence can be recommended for practical on-line control of distributed parameter systems.     

Nonlinear inferential multi-rate control of Kappa number at multiple locations in a continuous pulp digester

The continuous pulp digester represents a large-scale, distributed parameter system. Control of the spatial profile of degree of cooking, characterized by the Kappa number, rather than its endpoint value can effectively control properties that are dependent on the history of cooking. However, profile control of such large-scale distributed parameter systems throws up new challenges in estimation and control. We design a nonlinear model predictive controller using a multi-rate extended Kalman filter to infer and control discrete points along the Kappa number profile. Both, the plant and controller models are based on first principles. The design is tested for significant mismatches in parameters, initial state errors, and stochastic disturbances in the entering wood composition.     

Estimation and coordinated control for distributed parameter processes with a moving radiant actuator

This paper presents an estimation and control scheme for a class of industrial processes described by distributed parameter models with a moving radiant actuator. To overcome the lack of direct sensing alternatives for process state, a dual extended Kalman filter is established for estimating process status online based on a reduced process model and available output measurements. A distinct challenge that is addressed is the selection and construction of a suitable feedback signal from the distributed state estimate following the moving radiant actuator. The estimated status is then integrated into a rule-based feedback controller, which coordinates two manipulated variables of the moving radiant actuator to achieve the control objective. The two manipulated variables are the velocity and the radiant flux or power of the moving actuator. Both the estimation and feedback control strategies are demonstrated using computer simulations of one-dimensional distributed parameter models for an ultraviolet (UV) coating curing process involving a moving UV source. The results show that the proposed estimation and control schemes can significantly improve process quality and compensate for unknown disturbances on the target.     

Model predictive control of an industrial packed bed reactor using neural networks

This paper discusses an industrial application of a multivariable nonlinear feedforward/feedback model predictive control where the model is given by a dynamic neural network. A multi-pass packed bed reactor temperature profile is modelled via recurrent neural networks using the backpropagation through time training algorithm. This model is then used in conjunction with an optimizer to build a nonlinear model predictive controller. Results show that, compared with conventional control schemes, the neural network model based controller can achieve tighter temperature control for disturbance rejection     

Steady state optimization of an ammonia reactor

A hybrid simulation technique for identification and steady state optimization of a tubular reactor used in ammonia synthesis is presented. The parameter identification program finds the catalyst activity factor and certain heat transfer coefficients that minimize the sum of squares of deviation from simulated and actual temperature measurements obtained from an operating plant. The optimization program finds the values of three flows to the reactor to maximize the ammonia yield using the estimated parameter values. Powell's direct method of optimization is used in both cases. The results obtained here are compared with the plant data.     

Modeling and control of an LDPE autoclave reactor

A two-compartment four-cell model is developed for the adiabetic slim type autoclave reactor for free radical polymerization of low density polyethylene (LDPE). It is possible to determine not only the reactor performance represented by the monomer conversion and the reaction temperature but also the properties of the polymer product characterized by the average molecular weight and the polydispersity. It turns out that the reactor performance predicted is in good agreement with the plant data and the properties of the polymer product are estimated within reasonable ranges of actual values. The steady state multiplicity is found to exist and is examined by constructing the bifurcation diagram. The effects of various operation parameters on the reactor performance and the polymer properties are investigated systematically to show that the temperature distribution plays the central role for the properties of the polymer products. Therefore, it is essential to establish a good control strategy for the temperature in each compartment. The adaptive pole-placement control algorithm is applied to the temperature control of the adiabatic slim type autoclave reactor. The recursive least square method is used for the model identification. To accomplish a satisfactory control, the estimator and controller are initialized during the period of start-up. It is shown that the reactor system can be adaptively controlled by the pole-placement control algorithm, especially when the reactor temperature distribution is changed.     

基于T-S模糊模型的状态反馈预测控制

将T-S模糊模型和状态反馈预测控制相结合,提出了一种基于T-S模糊模型的预测控制算法.该算法把T-S模糊模型作为预测模型得到状态和输出的预估值,并利用可测的过程变量对输出预估值进行反馈修正,然后利用最优控制理论,由修正后的预估值和给定值计算出控制整个系统的控制律.本文还对串级CSTR控制系统的不同的初态、设定值及干扰情况下进行了仿真,仿真结果表明了该方法的有效性和可行性.     

Self-tuning control application to a nuclear power plant

The aim of this paper is to investigate the application possibilities of a self-tuning control method to a pressurized-water reactor (PWR) nuclear power plant. A self-tuning control algorithm which incorporates pole assignment into the generalized minimum variance strategy with a particular form of cost function is employed. This algorithm enables closed-loop system stability characteristics to be readily specified and facilitates reference following. The control system design is based on a second-order linear model with unknown, time-varying parameters. To ensure that this low-order model describes the complex real dynamics well enough for control purposes, control parameters are updated on-line with a recursive estimation sequences of the extended least-squares method. Weighting polynomials are also adjusted on-line to keep closed-loop poles at the desired location and to satisfy the zero steady-state condition and disturbance rejection. The purpose of this control system is to hold the average coolant temperature in the reactor as near as possible to a desired but changing reference value in the load-following mode of the nuclear power plant. The position of the control rods is an appropriate control variable. Simulation results are very successful and show the possibilities of the adaptive control application to actual plants.     

Distributed attitude synchronization control for multiple flexible spacecraft without modal variable measurement

This paper solves the attitude synchronization and tracking problem for a group of flexible spacecraft without flexible‐mode variable measurement. The spacecraft formation is studied in a leader‐following synchronization scheme with a dynamic virtual leader. With the application of adaptive sliding‐mode control technique, a distributed modified Rodriguez parameters‐based dynamic controller is proposed for flexible spacecraft without requiring modal variable measurement. It is proved that the attitude synchronization and tracking can be achieved asymptotically under the control strategy through the Lyapunov's stability analysis. Furthermore, a distributed robust continuous control algorithm is designed to guarantee the ultimate boundedness of both the attitude tracking error and the modal variable observation error when bounded external disturbances exist. Some numerical simulation examples for multiple flexible spacecraft formation are given to demonstrate the effectiveness of the proposed method.     

LPV model development and control of a solution copolymerization reactor

In this paper, linear parameter-varying (LPV) control is considered for a solution copolymerization reactor, which takes into account the time-varying nature of the parameters of the process. The nonlinear model of the process is first converted to an exact LPV model representation in the state-space form that has a large number of scheduling variables and hence is not appropriate for control design purposes due to the complexity of the LPV control synthesis problem. To reduce such complexity, two approaches are proposed in this paper. First, an approximate LPV representation with only one scheduling variable is obtained by means of a parameter set mapping (PSM). The second approach is based on reformulating the nonlinear model so that it provides an LPV model with a fewer number of scheduling parameters but preserves the same input–output behavior. Moreover, in the implementation of the LPV controllers synthesized with the derived models, the unmeasurable scheduling variables are estimated by an extended Kalman filter. Simulation results using the nonlinear model of the copolymerization reactor are provided in order to illustrate the performance of the proposed controllers in reducing the convergence time and the control effort.     

Model-based temperature control of a diesel oxidation catalyst

The problem studied in this article is the control of a DOC (diesel oxidation catalyst) as used in aftertreatment systems of diesel vehicles. This system is inherently a distributed parameter system due to its elongated geometry where a gas stream is in contact with a spatially distributed catalyst. A first contribution is a model for the DOC system. It is obtained by successive simplifications justified either experimentally (from observations, estimates of orders of magnitude) or by an analysis of governing equations (through asymptotic developments and changes of variables). This model can reproduce the complex temperature response of DOC output to changes in input variables. In particular, the effects of gas velocity variations, inlet temperature and inlet hydrocarbons are well represented. A second contribution is a combination of algorithms (feedback, feedforward, and synchronization) designed to control the thermal phenomena in the DOC. Both contributions have been tested and validated experimentally. In conclusion, the outcomes are evaluated: using the approach presented in this article, it is possible to control, in conditions representative of vehicle driving conditions, the outlet temperature of the DOC within ±15 °C.     

动态输出反馈鲁棒模型预测控制离线算法

研究具有多包不确定性和有界噪声系统的动态输出反馈鲁棒模型预测控制(Robust model predictive control, RMPC)的离线方法. 先前的在线方法中, 在估计状态和估计误差集合已知的情况下, 在每一采样时刻通过近似最优算法求解控制器参数. 本文采用先前的方法计算离线控制器参数和吸引域. 首先, 选定一系列估计状态, 其中,每个估计状态对应同样一组嵌套的估计误差集合. 然后,针对每一估计状态和每一估计误差集合的组合,离线计算唯一的控制器参数和对应的吸引域. 这些控制器参数和对应的吸引域存储在表中. 如果离线确定的吸引域包含实时的扩展状态, 则该离线控制器参数是实时可行的. 在线时, 根据实时估计状态和选取实时估计误差集合, 在表中搜索包含实时扩展状态且优化性能指标最小的吸引域所对应的控制器参数. 通过连续搅拌釜式反应器控制系统验证了该方法的有效性.     

Modelling and simulation of semi-batch polymerisation reactor for improved reactants dosing control

This paper presents a temperature model of an industrial, semi-batch, emulsion-polymerisation reactor, which together with the already designed chemical reactions model is able to predict the temperature in the reactor as a result of varying operating conditions. The model was derived from the energy balance equations and validated on real-plant data. The model was used to analyse the influence of reactants dosing during the batch on the reactor temperature. The analysis shows that during the batch dosing of the two reactants, initiator and monomer, needs to be mutually balanced and adjusted to the current process situation, otherwise, the temperature in the reactor may become oscillatory and unstable towards the end of the batch because of the limited heat removal capacity of the condenser. To keep the reactor temperature in a narrow region also the control strategy was proposed that adjusts the monomer flow and initiator addition, using reactor temperature as a controlled variable. Simulation results show that the proposed reactants dosing control significantly reduces the variations in the reactor temperature and at the same time results in more uniform final batch results.     

Nonlinear adaptive control of robotic manipulators - hyperstability approach

A nonlinear model reference adaptive controller based on hyperstability approach, is presented for the control of robot manipulators. Use of hyperstability approach simplifies the stability proof of the adaptive system. The unknown parameters of the system, as well as its variable payload, are estimated on line and are adaptive to their actual values; tending to reduce the system error. In addition, any sudden change in the system parameters or payload is detected by the proposed intelligent controller. Robot path tracking, with unknown parameter values and variable payload, is simulated to show the effectiveness of the proposed adaptive control algorithm. Both system output error and parameter estimation error vanish under the proposed parameter adaptation algorithm.     

Multivariable PID estimation and control in systems with biased disturbances

A solution is given to yield reset control action in multivariable control systems, where the controller consists of a state reconstructor and feedback from estimated process and environmental states. Integral action in the estimation loop follows from the assumptions about the disturbance model, and if a special choice for the “feed-forward” matrix operating on the estimated environmental states is made, integral, or reset, control action results. The classical least squares optimal control with modeling of the environment is illustrated using a linearized model of a plug flow tubular reactor as a basis for the design. As a second example which illustrates the reset control action, i.e. the tracking of a constant reference vector with zero control error, a simple third order linear system is used.     

Adaptive control of an open tubular heterogeneous enzyme reactor for extracorporeal leukaemia treatment

This study deals with the control design of a tubular enzymatic reactor to be used in the extracorporeal treatment of leukaemia in children. Tubular reactors are non-linear and time-varying distributed parameter systems with complex dynamics so that it is difficult to have high performance and safe operation when conventional classical control procedures are employed. In this work, an adaptive controller based on a state space approach is developed and tested for the control of a biochemical reactor using L-asparaginase attached to an internal open nylon tube. As a medical system, the design must be simple and safe to operate. It is shown that the control algorithm is adequate to maintain the system in specified operational conditions when the manipulated variable was the electric current, even when significant disturbances take place as well as set-point changes (servo control). This makes the L-asparaginase reactor an efficient method in the treatment of leukaemia.