Observer-based control algorithms for a distillation column

This paper studies the synthesis of nonlinear observer-based globally linearizing control (GLC) algorithms for a multivariable distillation column. Two closed-loop observers/estimators, namely extended Kalman filter (EKF) and adaptive state observer (ASO), have been designed within the GLC framework to estimate the state variables along with the poorly known parameters. Exactly same basic model structure was used for developing the observers. The model structure is so simple that the estimator design was performed based on only two component balance equations around the condenser-reflux drum and the reboiler-column base systems of the distillation column. To construct these observers, the poorly known parameters, namely component vapor flow rate leaving top tray, component liquid flow rate leaving bottom tray and distribution coefficient in the reboiler, were considered as extra states with no dynamics. The comparative study has been carried out between the proposed GLC in conjunction with ASO (GLC-ASO) and that coupled with EKF (GLC-EKF). The GLC-ASO control scheme showed comparatively better performance in terms of set point tracking and disturbance as well as noise rejections. The control performance of GLC-ASO and a dual-loop proportional integral derivative (PID) controller was also compared under set point step changes and modeling uncertainty. The proposed GLC-ASO structure provided better closed-loop response than the PID controller.     

Polypropylene degradation control during reactive extrusion

In this work, a proportional‐integral‐derivative (PID) control scheme with two different tuning methods to control the degree of degradation of polypropylene (PP) during reactive extrusion is proposed. The concentration of dicumyl peroxide is taken as the manipulated variable. The molten viscosity of PP under processing is taken as the controlled variable. The degree of degradation is determined by a viscosity function derived by an off‐line identification. A first‐order‐plus‐time‐delay empirical model is identified to simulate the system plant. Both Ziegler–Nichols tuned PID and internal model control (IMC)‐based PID controllers are implemented on the system. Better performances in settling time and precision can be achieved using the IMC‐based PID controller. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 95: 280–289, 2005     

APPLICATION OF ADAPTIVE PID CONTROL WITH GENETIC ALGORITHM TO A POLYMERIZATION REACTOR

This article describes the application of adaptive PID control with genetic algorithm (GA) to a jacketed batch polymerization reactor. This method was used to keep the polymerization reactor temperature at the desired optimal path, which was determined by the Hamiltonian maximum principle method. The reactor was simulated and the model equations of this jacketed polymerization reactor were solved by means of Runge-Kutta-Felthberg methods. A genetic algorithm can be a good solution for finding the optimum PID parameters because unlike other techniques it does not impose many limitations and it is simple. In this research, suitability of these parameters was checked by the integral absolute error (IAE) criterion. The control parameters in the PID algorithm were changed with time during the control of a polymerization reactor. It was seen that the genetic algorithm was able to tune the PID controller used in this system in terms of higher robustness and reliability by changing the parameters continuously.     

In‐line viscosity control in an extrusion process with a fuzzy gain scheduled PID controller

In the extrusion process, rapidly tracking the set point of quality factor and eliminating its variation to reduce the off‐specification product is important. In this study, the fuzzy gain‐scheduled proportional‐integral‐derivative (PID) controller is used to control the melt viscosity during extrusion processing. A second‐order model related to the viscosity and the extruder screw speed is developed empirically to approximate the extrusion system. It is concluded that, in comparison to the well‐known Zeigler‐Nichols PID tuning control scheme, the performances of the proposed control strategy is preferable both in simulation and implementation. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 541–555, 1999     

PID CONTROLLER TUNING FOR UNSTABLE SYSTEMS BY OPTIMIZATION METHOD

Simple Tuning formulae are provided for optimal PID controller settings for unstable first order plus time delay systems. The method is based on minimization of integral squared errors (ISE). A method of calculating the set point weighting parameter is proposed to reduce the overshoot for servo problems. The performances of the proposed PID settings are compared with the settings recently proposed by Huang and Chen (1997, 1999) for both the servo and regulatory problems. The performance of the controller is also evaluated under parameter uncertainty in time delay and separately in process gain. Tuning formulae are given for PI controller along with the set point weighting. The performance of the PI controller is compared with that of Poulin and Pomerleau (1996). Two simulation studies, one on control of an unstable nonlinear bioreactor and a second on an unstable chemical reactor using the proposed PID controller settings, show improved performances both for servo and regulatory problems.     

Integrating data‐based modeling and nonlinear control tools for batch process control

A data‐based multimodel approach is developed in this work for modeling batch systems in which multiple local linear models are identified using latent variable regression and combined using an appropriate weighting function that arises from fuzzy c‐means clustering. The resulting model is used to generate empirical reverse‐time reachability regions (RTRRs) (defined as the set of states from where the data‐based model can be driven inside a desired end‐point neighborhood of the system), which are subsequently incorporated in a predictive control design. Simulation results of a fed‐batch reactor system under proportional‐integral (PI) control and the proposed RTRR‐based design demonstrate the superior performance of the RTRR‐based design in both a fault‐free and faulty environment. The data‐based modeling methodology is then applied on a nylon‐6,6 batch polymerization process to design a trajectory tracking predictive controller. Closed‐loop simulation results illustrate the superior tracking performance of the proposed predictive controller over PI control. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

A feedback glucose control strategy for type II diabetes mellitus based on fuzzy logic

Most patients with severe Type II diabetes mellitus, characterised by both insulin resistance and β‐cell failure, eventually require insulin therapy. According to the nonlinear dynamics of homeostasis of blood glucose, proportional‐integral (PI) controller, modified by penalising the feedback error using a fuzzy inference system has been developed to maintain normoglycaemia in a simulated patient using a closed‐loop insulin infusion pump. The simulation employs a compartment model proposed by Vahidi et al. [Vahidi et al., Biochem. Eng. J. 2011, 55(1), 7–16]. The results demonstrate that the fuzzy‐based PI controller is superior to a conventional PI controller for the regulation of blood glucose by insulin infusion for Type II diabetic patients. © 2012 Canadian Society for Chemical Engineering     

Application of Model Predictive Control to a Continuous Multiple‐Effect Crystallizer

An infinite horizon model predictive controller (IHMPC) with zone control is applied to a continuous five‐effect evaporative sodium chloride crystallizer. Firstly, a phenomenological dynamic model of the process is developed considering mass, energy, and moment balances coupled to crystallization kinetics. The developed model plays the role of the real system in order to study the proposed optimization/control strategy. The proposed approach is compared to a classical proportional integral derivative (PID) control system. The control strategy based on the prediction of the future state of the plant provides a faster response, a better stability to the process, and a reduction in energy consumption.     

Implementation of Multimodel-Based PID and Intelligent Controller for Simulated and Real-Time Temperature Control of Injection Molding Machine

The proposed real-time multimodel for the injection molding process mainly contributes to the barrel temperature control. Good control of the plastic melt temperature is very important for injection molding in reducing the operator setup time, ensuring product quality, and preventing thermal degradation of the melt. The controllability and set points of the barrel temperature also depend on the precise monitoring and control of the plastic melt temperature. Motivated by the practical temperature control of injection molding, this article proposes a multimodel-based proportional integral derivative (PID) control scheme in real-time and the simulation studies of the PID, fuzzy, and adaptive neuro fuzzy inference system (ANFIS) control schemes. The injection molding process consists of three zones, and the mathematical model for each zone is different. The control output for each zone controller is assigned a weight, based on the computed probability of each model, and the resulting action is the weighted average of the control moves of the individual zone controller.     

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.     

OPTIMALITY CHARACTERISTICS OF PI/PID CONTROLLERS: A COMBINED MIN-MAX/ISE INTERPRETATION

This communication addresses the tuning of PI and PID controllers on the basis of the IMC approach. The tuning is based upon a first order plus time delay (FOPTD) model and aims to achieve a step response specification. Through analysis it has been found that by using the IMC approach we get a PI or a PID depending on the rational approximation used for the time delay term. This article raises the question that the use of a PID instead of a PI controller should be based on another reason more related to the control objectives rather than the use of a better approximation for the time delay. An alternative tuning is presented here, from within the IMC formulation, based on a min-max optimization. From the tuning rule provided by this approach the optimum settings from an integral squared error criterion point of view are derived. The optimal controller results in being a PI controller. From this optimal controller as the starting point, the introduction of the derivative action can be seen as a detuning procedure that can increase the robustness of the controller. This approach provides further insight into the tuning of PI and PID controllers giving the (alternative) parameters a precise engineering meaning.     

A novel two-dimensional PID controller design using two-dimensional model predictive iterative learning control optimization for batch processes

It is known that the key indicators of batch processes are controlled by conventional proportional–integral–derivative (PID) strategies from the view of one-dimensional (1D) framework. Under such conditions, the information among batches cannot be used sufficiently; meanwhile, the repetitive disturbances also cannot be handled well. In order to deal with such situations, a novel two-dimensional PID controller optimized by two-dimensional model predictive iterative learning control (2D-PID-MPILC) is proposed. The contributions of this paper can be summarized as follows. First, a novel two-dimensional PID (2D-PID) controller is developed by combining the advantages of a PID-type iterative learning control (PIDILC) strategy and the conventional PID method. This novel 2D-PID controller overcomes the aforementioned disadvantages and extends the conventional PID algorithm from one-dimension to two-dimensions. Second, the tuning guidelines of the presented 2D-PID controller are obtained from the two-dimensional model predictive control iterative control (2D-MPILC) method. Thus, the proposed approach inherits the advantages of both PID control, PIDILC strategy, and 2D-MPILC scheme. The superiority of the proposed method is verified by the case study on the injection modelling process.     

Evaluation of simple dynamic models and controllers for hydraulic and nozzle pressure in injection molding

Simple pseudo-steady state relations between the hydraulic and nozzle pressures of an injection molding machine were presented and verified experimentally. A simulation study was performed to evaluate the performance of simple controllers using dynamic models developed for the hydraulic and nozzle pressures. The controllers chosen were the discrete proportional, proportional-integral (PI), and proportional-integral-derivative (PID) types, tuned according to the ITAE criterion. The control of hydraulic pressure simulation showed that the PI controller had the best overall performance, whereas the result of nozzle pressure control loop simulation showed that the PID controller performance was better than that of the PI controller. All the controllers, in both loops, gave responses that were about an order of magnitude more rapid than the open loop response.     

Modeling and control of continuous stirred tank reactor for thermal copolymerization

A mathematical model is developed for solution copolymerization in a continuous stirred tank reactor. For the thermal copolymerization of styrene and acrylonitrile (SAN), the kinetic rate expression for thermal initiation is derived by applying the pseudo-steady-state hypothesis to the intermediates, and the kinetic parameters are estimated by experimental investigation. The moment equations of living and dead polymer concentrations are derived by applying the pseudokinetic rate constantmethod. The model is used to calculate the conversion, the copolymer composition, the weight-average molecular weight, and the polydispersity. It is demonstrated that this model can predict the industrial data very well under various operating conditions. The dynamic analysis of the reaction system enables us to determine the polymer properties against the changes in the operation parameters. It is noticed that the monomer conversion is controlled to some extent by the reaction temperature and the feed monomer fraction. The monomer conversion control of a solution copolymerization reactor is treated with different control algorithms. The fuzzy/proportional–integral–derivative controller shows satisfactory performances for both setpoint tracking and disturbance rejection and can be easily applied to continuous polymerization processes. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:921–931, 1998     

Dynamic Matrix Control of a Bubble‐Column Reactor for Microbial Synthesis Gas Fermentation

A spatiotemporal metabolic model of a representative syngas bubble‐column reactor was applied to design and evaluate dynamic matrix control (DMC) schemes for regulation of the desired by‐product ethanol and the undesired by‐product acetate. This model was used to develop linear step response models for controller design and also served as the process in closed‐loop simulations. A 2 × 2 DMC scheme with manipulation of the liquid and gas feed flows to the column provided a superior performance to proportional integral (PI) control due to slow process dynamics combining the multivariable and constrained nature of the control problem. Ethanol concentration control for large disturbances was further improved by adding the flow of a pure hydrogen stream as a third manipulated variable. The advantages of DMC for syngas bubble‐column reactor control are demonstrated and a design strategy for future industrial applications is provided.     

Simulated nonlinear control studies of five-effect evaporator models

This paper is devoted to the simulated nonlinear control studies of two dynamic models of an industrial five-effect evaporator of an alumina refinery. The simulated control studies were carried out to ascertain the performance and robustness of nonlinear control techniques on the five-effect evaporator prior to its implementation on-site. The nonlinear control structure used in the studies was the multi-input multi-output (MIMO) globally linearizing control (GLC) structure of Kravaris and Soroush (1990). The I/O linearizing controller was implemented in a cascade arrangement with the industrial coded velocity form of proportional-integral (PI) controllers in the simulation. The design parameters were chosen such that the desired decoupling control of the ill-conditioned evaporator models was achieved, and such that cascade arrangement of the nonlinear controller was possible. Simulated results indicates that the MIMO GLC structure provides superior servo and regulatory control to multi-loop single-input single-output (SISO) PI controllers that are currently being used to regulate the five-effect evaporator on-site.     

Adaptive Internal Model Control of a High‐Purity Heat‐Integrated Air Separation Column

An internal model control scheme based on a second‐order internal model (SI‐IMC) is proposed for the heat‐integrated air separation column (HIASC). An adaptive internal model control (ASI‐IMC) scheme is further presented to make the model more accurate. The IMC scheme based on the first‐order model (F‐IMC) and the multi‐loop PID (M‐PID) scheme are also explored as the comparison basis of ASI‐IMC and SI‐IMC schemes. Comparative researches among these four control schemes are carried out in detail. The results indicate that ASI‐IMC presents the best performances among the four control schemes in both servo control and regulatory control, which proves the improvement of ASI‐IMC over the SI‐IMC and the superiority of ASI‐IMC for the high‐purity HIASC.     

Experimental validation of the optimal trajectory of initiator concentration in a batch MMA polymerization reactor

This article presents a method to determine the trajectory of initiator concentration that will produce polymer with desired number‐ and weight‐average molecular weights at a prespecified level of monomer conversion. The optimal control theory is applied to the mathematical model for a batch methymethacrylate (MMA) solution polymerization reactor system. By imposing the constraint that initiator concentration should decrease within the range of self‐consumption by the initiation reaction, one can obtain the initiator concentration trajectory that can be tracked by feeding the initiator alone. A control scheme is constructed with a cascade proportional‐integral‐derivative (PID) control algorithm for temperature control and a micropump is installed to manipulate the initiator feed rate. The experimental results show satisfactory tracking control performance despite the nonlinear features of the polymerization reactor system. Also, the monomer conversion and the average molecular weights measured are found to be in fairly good agreement with those of model prediction, respectively. In conclusion, the polymer having desired molecular weight distribution can be produced by operating the batch reactor with the initiator supplement policy calculated from the model. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1256–1266, 2000     

A new predictive PID controller for the processes with time delay

A new proportional-integral-derivative (PID) controller is proposed based upon a simplified generalized predictive control (GPC) control law. The tuning parameters of the proposed predictive PID controller are obtained from the simplified GPC control law for the 1 ^st -order and 2 ^nd -order processes with time delays of integer and non-integer multiples of the sampling time. The internal model technique is employed to compensate the effect of time delay of the target process. The predictive PID controller is equivalent to the PI controller when the target process is 1 ^st -order and to the PID controller when the target process is an integrating process. The performance of the proposed predictive PID controller is almost the same as that of the simplified GPC. The main advantage of the proposed control scheme over other control methods is the ease of tuning and operation.     

Identification and control of a riser‐type FCC unit

This paper addresses the use of feedforward neural networks for the steady‐state and dynamic identification and control of a riser type fluid catalytic cracking unit (FCCU). The results are compared with a conventional PI controller and a model predictive control (MPC) using a state space subspace identification algorithm. A back propagation algorithm with momentum term and adaptive learning rate is used for training the identification networks. The back propagation algorithm is also used for the neuro‐control of the process. It is shown that for a noise‐free system the adaptive neuro‐controller and the MPC are capable of maintaining the riser temperature, the pressure difference between the reactor vessel and the regenerator, and the catalyst bed level in the reactor vessel, in the presence of set‐point and disturbance changes. The MPC performs better than the neuro controller that in turn is superior to the conventional multi‐loop diagonal PI controller.