A safe-parking framework for plant-wide fault-tolerant control

This work addresses the problem of handling actuator faults in a chemical plant. We consider a multi-unit nonlinear process system subject to input constraints and actuator faults in one unit that preclude the possibility of operating the unit at its nominal equilibrium point. The interconnected nature of the units in a plant brings forth unique opportunities as well as challenges that simply do not exist when handling faults in isolated units. In particular, the fact that the outlet streams from a faulty unit go through subsequent (well functioning) units raises the possibility of better restricting the effects of the fault to the faulty unit. At the same time, handling a fault in a unit may necessitate appropriate action in the downstream unit, which is not a result of a fault in the downstream unit. To address such issues that arise when handling faults in chemical plants, in this work we present a safe-parking framework (we define, in a previous work on handling faults in isolated units, a safe-park point as an operating point where in the event of a fault, a unit can be operated in a way that prevents onset of hazardous situation and allows smooth resumption of nominal operation) for plant-wide fault-tolerant control. We first consider the case where there exists a safe-park point for the faulty unit such that the effect of safe-parking can be completely rejected (via changing the nominal values of the manipulated variables) in the downstream unit. Steady-state as well as dynamic considerations (including the presence of input constraints) is used in determining the necessary conditions for safe-parking the multi-unit system. We next consider the problem where no viable safe-park point for the faulty unit exists such that its effect can be completely rejected in the subsequent unit. A methodology is presented to simultaneously safe-park the consecutive units. Finally, we incorporate performance considerations in the safe-parking framework and illustrate the implementation of the safe-parking framework using a multi-unit chemical reactor system.     

ROBUST CONTROL OF BATCH REACTORS

The design of robust nonlinear feedback controller is analysed for a trajectory tracking in a single-input single-output nonlinear state variable system x = f(x) + g(x)u, y=cx which arises in nonlinear chemical processes particularly in batch reactor control problems. Simulation results for the batch reactor temperature tracking problem show the effectiveness of the control scheme and its robustness to modelling errors. The method is also applicable to multi-input multi-output system where the number of inputs is equal to that of outputs. The controller design is also analyzed for situations wrier: the kinetics, the activation energy and Ihe heat of reaction are unknown and also only limited measurement of state-variables are available. The method of Youcef-Toumi and Ito (1987) is applied to such problems and the effectiveness of control system is shown by simulation.     

ADAPTIVE CONTROL OF A BATCH REACTOR

A globally stable adaptive predictive control system (APCS) is evaluated by application to a simulated PVC batch reactor. The reactor is run under APCS control with the objective of either temperature setpoint tracking or constant reaction rate. The batch nature of this system makes it possible to learn about the physical problem from successive runs. This knowledge is incorporated into the control strategy to improve the performance of the reactor. The problem of excessive manipulation of the control variable has been recognized and resolved by using control weighting. Performance of the adaptive technique is compared with previous results using self-tuning and PID control of the same reactor. APCS provides good, robust control despite the nonlinear dynamics of the system.     

ADAPTIVE FUZZY MODEL BASED PREDICTIVE CONTROL OF AN EXOTHERMIC BATCH CHEMICAL REACTOR*

An adaptive fuzzy model based predictive control (AFMBPC) approach is presented to track the desired temperature trajectories in an exothermic batch chemical reactor. The AFMBPC incorporates an adaptive fuzzy modeling framework into a model based predictive control scheme to derive analytical controller output. This approach has the flexibility to cope with different fuzzy model structures whose choice also lead to improve the controller performance. In this approach, adaptation of fuzzy models using dynamic process information is carried out to build a predictive controller, thus eliminating the determination of a predefined fixed fuzzy model based on various sets of known input-output relations. The performance of the AFMBPC is evaluated by comparing to a fixed fuzzy model based predictive controller (FFMBPC) and a conventional PID controller. The results show the better suitability of AFMBPC for the control of highly nonlinear and time varying batch chemical reactors.     

Dynamic Modelling and Process Control of ZnS Precipitation

Abstract

This paper presents the dynamic modelling and design of a control strategy for the ZnS precipitation process. During lab‐scale experiments, the sulfide concentration in a precipitator was controlled at a prespecified pS value by manipulating the flow from a buffer vessel. Batch tests showed that the optimal condition for zinc sulfide precipitation is at a sulfide concentration of 10^?15 mole/l (pS 15). Experiments with the precipitator showed that the sulfide concentration highly deviates from a given setpoint when proportional (P) control is used, but this deviation can be decreased using a Proportional Integral (PI) controller. Moreover, the PI controller was able to handle sudden disturbances in the process conditions (pH, influent flow rate, or zinc and sulfide concentration). Additional precipitation experiments were conducted using effluent from a sulfate reducing gas‐lift reactor to determine if the compounds present in the effluent influence the control process. With the gas‐lift reactor effluent and a PI controller, the desired sulfide concentration was reached almost instantaneously (within 15 minutes) within acceptable margins (2–5%).     

A nonlinear pi(d) controller

The PID control algorithm remains the most widely used in the process industries. This is due to its simplicity (three tuning parameters, fixed structure) and its ability to satisfy the majority of process control needs. Here, a new nonlinear algorithm (the PI(D)) is presented, which maintains the simplicity of the PID, but is nevertheless able to outperform it in both load and set point changes. Tuning formulae and response curves for the PI(D) controller are presented.     

Passivity-based control of the phthalic anhydride fixed-bed reactor

The control of tubular fixed-bed reactors with highly exothermic reactions is approached from a passivity-based control perspective. The proposed controller solves dynamic tracking of the reactor exit conversion and stabilization of the reactor temperature by exploiting the passivity properties of the process. The model-based control structure proposed in this paper provides a suitable framework for developing the passivity-based control law and the state predictor. The integrated controller is designed and its performance in the face of parameter variation and model uncertainty is tested by numerical simulation. Digital simulation on an industrial phthalic anhydride fixed-bed reactor shows that the proposed control scheme can give satisfactory dynamic tracking ability and disturbance rejection performance, which is robust in the presence of process variation and model uncertainty. This paper provides a basic insight into the characterization and solution of control problems that are particular to tubular fixed-bed reactor systems and constitutes the application of passivity-based control theory to complex chemical processes.     

Batch-to-batch iterative learning control and within-batch on-line control for end-point qualities using MPLS-based dEWMA

A new feedback batch control strategy based on multiway partial least squares (MPLS) model and dEWMA (double exponentially weighted moving average) control for the end-point product quality system is proposed in this paper. It combines batch-to-batch (BtB) control with on-line tracking control within a batch. In the BtB operation, MPLS-based dEWMA control is done by applying feedback from the final output quality of the batch process. It utilizes the information from the current batch to improve quality for the next batch. The advantage of MPLS is to extract the strongest relationship between the input and the output variables in the reduced space of the latent variables model rather than in the real space of the highly dimensional manipulated variable trajectories. It is particularly useful for inherent noise suppression. Then the optimal manipulated variable trajectories in the score space without decoupler design can be directly and individually applied to each control loop under the MPLS modeling structure. Then the dEWMA controller can be applied to each SISO control loop respectively to address the model errors gradually reduced from model-plant mismatches and unmeasured disturbances. In on-line tracking control within a batch, the MPLS-based dEWMA control strategy is developed to explore the possible adjustments of the future input trajectories. It fixes up the disturbances just in time instead of until the next batch run and maintains the product specification when this batch is finished. To demonstrate the potential applications of the proposed design method, a typical batch reactor with processes of different dynamics is applied. Comparisons between MPLS-based dEWMA BtB control and MPLS-based dEWMA within-batch control are also made.     

核反应堆稳压器水位和压力控制系统研究

利用前馈补偿控制方法实现水位和压力系统的解耦后,利用模糊自适应PID控制方法对系统进行控制。仿真结果表明：稳压器水位和压力的稳态性能都得到了较大的改善。     

Nonlinear adaptive temperature control of multi-product, semi-batch polymerization reactors

This paper considers the temperature control of semi-batch polymerization reactors in which some of the following issues must be considered: (i) production of multiple products in the same reactor; (ii) changing heat transfer characteristics, during a batch and from batch to batch; (iii) time varying and nonlinear reaction rate due to changing monomer concentration and diffusion controlled termination reactions (gel effect); (iv) the absence of detailed kinetic models for the reactors. The industrial challenge problem published by Chylla and Haase [Chylla, R. W. and Haase, D. R. (1993) Temperature control of semi-batch polymerization reactors (with corrected updates). Comput. Chem. Eng. 17, 257–264) is used as the simulation basis for evaluating these problems.

A nonlinear adaptive controller consisting of a nonlinear controller (based on differential geometric concepts) coupled with an extended Kalman filter (which uses only readily available data and knowledge) is shown to provide excellent control in all the above situations. In particular, the on-line estimation is critical for the strong performance of the nonlinear controller over a broad range of conditions. PID controllers with feedforward terms can perform well at one set of conditions, however, they require retuning as conditions and products change.     

Recursive data-based prediction and control of product quality for a PMMA batch process

In many batch processes, frequent process/feedstock disturbances and unavailability of direct on-line quality measurements make it very difficult to achieve tight control of product quality. Motivated by this, we present a simple data-based method in which measurements of other process variables are related to end product quality using a historical data base. The developed correlation model is used to make on-line predictions of end quality, which can serve as a basis for adjusting the batch condition/time so that desired product quality may be achieved. This strategy is applied to a methyl methacrylate (MMA) polymerization process. Important end quality variables, the weight average molecular weight and the polydispersity, are predicted recursively based on the measurements of reactor cooling rate. Subsequently, a shrinking-horizon model predictive control approach is used to manipulate the reaction temperature. The results in this study show promise for the proposed inferential control method.     

Robust temperature control for batch chemical reactors

Since batch chemical reactors exhibit an integrating response, temperature control for these systems can be a real problem for conventional PID controllers. Tuning can be extremely difficult due to the reduced stability margins proved for this type of processes. In this work, a simple robust control strategy for temperature regulation in batch and semi-batch chemical reactors is proposed. The feedback controller is composed by an approximate I/O linearizing feedback equipped with a calorimetric balance estimator. Based on standard results from singular perturbations, it is proven that the proposed feedback controller (i) can track a bounded temperature trajectory as close as desired (i.e., practical stability) by adjusting a single estimation parameter, and (ii) after a short transient, the performance of the exact I/O linearizing feedback can be recovered as the calorimetric balance estimation rate is increased.     

A DIRECT NONLINEAR ADAPTIVE CONTROL OF STATE FEEDBACK LINEARIZABLE SYSTEMS

A direct nonlinear adaptive control of state feedback linearizable single-input single-output systems is proposed in the case when parametric uncertainties are represented linearly in the unknown parameters. The main feature of the proposed nonlinear adaptive control system is that the linearizing coordinate transformation and the state feedback are updated by parametric adaptive law, derived using the second method of Lyapunov. The proposed adaptive control scheme is relatively straightforward and simple in the sense that it does not use the concept of augmented error. This adaptive control scheme is numerically applied to an exothermic chemical reactor system and is compared with the nonadaptive stale feedback linearization which has an integral action. The simulation shows that the proposed adaptive control scheme can be applied effectively to highly nonlinear, uncertain chemical systems.     

无模型控制器与PI控制器的性能对比分析

通过仿真,比较CyboCon无模型单输入单输出控制器、基于鲁棒性能指标设计的PI控制器和基于经验整定方法设计的PI控制器在对象模型精确和模型变化情况下的控制性能,得出CyboCon无模型单输入单输出控制器与基于经验整定方法设计的Pl控制器在性能上是相同的,基于鲁棒性能指标设计的PI控制器设计时应该考虑约束条件。     

Feedback linearizing control of a fluidized bed reactor

The design of an adaptive nonlinear controller for the control of a fluidized bed reactor is derived by using exact linearization techniques. Reset action and parameter adaptation are used to make more robust the precise compensation of nonlinear terms, which is called for in the linearization technique. A nonlinear antiwindup mechanism is introduced to handle reset windup problem and to provide fast response without large overshoot. Simulation results show that the proposed adaptive controller guarantees good setpoint tracking. The developed estimation algorithm allows accurate estimation of the parameters for which the regressor component is not zero.     

Evaluation and improvement of dynamic optimality in electrochemical reactors

A systematic approach for the dynamic optimization problem statement to improve the dynamic optimality in electrochemical reactors is presented in this paper. The formulation takes an account of the diffusion phenomenon in the electrode/electrolyte interface. To demonstrate the present methodology, the optimal time-varying electrode potential for a coupled chemical-electrochemical reaction scheme, that maximizes the production of the desired product in a batch electrochemical reactor with/without recirculation are determined. The dynamic optimization problem statement, based upon this approach, is a nonlinear differential algebraic system, and its solution provides information about the optimal policy. Optimal control policy at different conditions is evaluated using the best-known Pontryagin's maximum principle. The two-point boundary value problem resulting from the application of the maximum principle is then solved using the control vector iteration technique. These optimal time-varying profiles of electrode potential are then compared to the best uniform operation through the relative improvements of the performance index. The application of the proposed approach to two electrochemical systems, described by ordinary differential equations, shows that the existing electrochemical process control strategy could be improved considerably when the proposed method is incorporated.     

Nonlinear control of the dissolved oxygen concentration integrated with a biomass estimator for production of Bacillus thuringiensis δ-endotoxins

Bacillus thuringiensis is a microorganism that allows the biosynthesis of δ-endotoxins with toxic properties against some insect larvae, being often used for the production of biological insecticides. A key issue for the bioprocess design consists in adequately tracking a pre-specified optimal profile of the dissolved oxygen concentration. To this effect, this paper aims at developing a novel control law based on a nonlinear dynamic inversion method. The closed-loop strategy includes an observer based on a Bayesian Regression with Gaussian Process, which is used for on-line estimating the biomass present in the bioreactor. Unlike other approaches, the proposed controller leads to an improved response time with effective disturbance rejection properties, while simultaneously prevents undesired oscillations of the dissolved oxygen concentration. Simulation results based on available experimental data were used to show the effectiveness of the proposal.