Continuous Stirred Tank Reactor Plant Research Articles

Self-Evolving Fuzzy Controller Composed of Univariate Fuzzy Control Rules

The paper proposes a methodology to online self-evolve direct fuzzy logic controllers (FLCs), to deal with unknown and time-varying dynamics. The proposed methodology self-designs the controller, where fuzzy control rules can be added or removed considering a predefined criterion. The proposed methodology aims to reach a control structure easily interpretable by human operators. The FLC is defined by univariate fuzzy control rules, where each input variable is represented by a set of fuzzy control rules, improving the interpretability ability of the learned controller. The proposed self-evolving methodology, when the process is under control (online stage), adds fuzzy control rules on the current FLC using a criterion based on the incremental estimated control error obtained using the system’s inverse function and deletes fuzzy control rules using a criterion that defines “less active” and “less informative” control rules. From the results on a nonlinear continuously stirred tank reactor (CSTR) plant, the proposed methodology shows the capability to online self-design the FLC by adding and removing fuzzy control rules in order to successfully control the CSTR plant.

Soft sensor design for variable time delay and variable sampling time

Often industrial variables can be difficult to measure due to such factors as extreme conditions or complex compositions. In such cases, soft sensors have been developed that use available system information and measurements to estimate these difficult-to-obtain variables. In practice, the measurements that are to be estimated by a soft sensor are often infrequently measured or delayed. Occasionally, these sampling times or delays are time varying. At present, most research has considered these parameters to be time invariant, and thus, there is a need to consider the time-varying case. Therefore, this paper will evaluate the impact of time-varying delays and sampling times for the design of a data-driven soft sensor. Modifications will be proposed that will increase the robustness and performance of the soft sensor. The reliability of the estimate will be shown using the Bauer–Premaratne–Durán Theorem. Furthermore, the proposed soft sensor system will be tested using simulations of a continuous stirred tank reactor (CSTR) and an reverse osmosis plant. Simulation showed that the modified soft sensor gives good estimates, whereas the traditional soft sensor gives an unstable estimate for the CSTR and reverse osmosis plant.

A Neural Network-Based Adaptive Backstepping Control Law With Covariance Resetting for Asymptotic Output Tracking of a CSTR Plant

A robust nonlinear adaptive controller merging a backstepping approach with neural networks is proposed for a nonlinear non-affine model. The work presented here is evaluated on a complex uncertain model of a continuous stirred tank reactor plant including an unknown varying parameter that enters the complexity model. By exploiting NN and adaptive backstepping approximation methods, an equivalent adaptive NN controller is constructed to achieve robust asymptotic output tracking control. The robustness to uncertainties as well as the lack of informative process data is the main enhancement of this work. This is attained through the implementation of the covariance resetting algorithm in the least square estimation of the NN weight tuning algorithm. The proposed novel control algorithm has been analyzed using Lyapunov analysis. In addition to excellent output trajectory tracking performance, the proposed approach has a profound benefit in terms of substantially lower control effort in comparison to the established work in the literature. In terms of applications in the petrochemical industry, lower control effort can translate to a more energy-efficient actuator, leading to lower costs over a long-run operation. The proposed method's feasibility for chemical process control was shown via numerical simulation.

An Advanced PID Based Control Technique With Adaptive Parameter Scheduling for A Nonlinear CSTR Plant

The continuous stirred tank reactor (CSTR) tends to reveal unstable severe nonlinear behavior when the operating level changes. As investigated in an earlier work, the hard nonlinearity nature of the CSTR originates from multiple probable sets of states for the same reaction in the same CSTR under identical ongoing inlet conditions. The previous work concluded, and this paper will discuss, that nonlinear processes with dynamic trajectories will involve a degrading control performance whenever the measured process variable evolves away from the designed level of the desired output trajectory. In this work, this problem will be examined for temperature tracking control on a CSTR with an adaptive fuzzy gain-scheduling proportional-integral-derivative (AFGS-PID) controller scheduled for a dynamic output trajectory. It will be proven that the AFGS-PID has better tracking performance than the fuzzy gain scheduling (FGS-PID) and conventional PID. Although all three controllers demonstrate the same level of control efforts, AFGS-PID has the smallest IAE and ISE. The lowest settling time being exhibited by AFGS-PID also proves that the intended regulator can rapidly track the desired coolant jacket temperature. A Lyapunov analysis is presented to prove the stability of the closed-loop and support the simulated result in the comparative study.

Robust synergetic control design under inputs and states constraints

ABSTRACTIn this paper, a novel robust-constrained control methodology for discrete-time linear parameter-varying (DT-LPV) systems is proposed based on a synergetic control theory (SCT) approach. It is shown that in DT-LPV systems without uncertainty, and for any unmeasured bounded additive disturbance, the proposed controller accomplishes the goal of stabilising the system by asymptotically driving the error of the controlled variable to a bounded set containing the origin and then maintaining it there. Moreover, given an uncertain DT-LPV system jointly subject to unmeasured and constrained additive disturbances, and constraints in states, input commands and reference signals (set points), then invariant set theory is used to find an appropriate polyhedral robust invariant region in which the proposed control framework is guaranteed to robustly stabilise the closed-loop system. Furthermore, this is achieved even for the case of varying non-zero control set points in such uncertain DT-LPV systems. The controller is characterised to have a simple structure leading to an easy implementation, and a non-complex design process. The effectiveness of the proposed method and the implications of the controller design on feasibility and closed-loop performance are demonstrated through application examples on the temperature control on a continuous-stirred tank reactor plant, on the control of a real-coupled DC motor plant, and on an open-loop unstable system example.

Online identification of non-linear dynamic systems by Wiener model using subspace method and neural networks

This paper presents a method for online identification of non-linear dynamic systems using the Wiener model. For the linear dynamic part the subspace identification method with the multivariable output-error state-space algorithm is employed, whereas for the non-linear static part the multi-layer perceptron neural network with Levenberg–Marquardt algorithm is used. The stability and convergence of the proposed method is shown using the Lyapunov direct method and the region solution of the linear matrix inequality (LMI) approach. The proposed method is tested by simulations performed on the continuous stirred tank reactor (CSTR) plant, which is presented by non-linear differential equations. Moreover, the method is applied on the input–output data that are obtained from a practical system of the CSTR plant as well as the pH neutralization plant. The results show significant improvements in online identification of the non-linear dynamic systems compared with the recently reported methods in literature.

Adaptive control of uncertain continuously stirred tank reactors with unknown actuator nonlinearities

Adaptive nonlinear control is investigated for continuously stirred tank reactor (CSTR) systems using neural networks. The CSTR plant under study belongs to a class of nonaffine nonlinear systems, and contains an unknown parameter that enters the model nonlinearly. Using adaptive backstepping and neural network (NN) approximation techniques, an alternative adaptive NN controller is developed that achieves asymptotic output tracking control. A novel integral-type Lyapunov function, which includes both system states and control input as its arguments, is constructed to solve the difficulty associated with the nonaffine control problem. Numerical simulation is performed to show the feasibility of the proposed approach for chemical process control.

SLIDING MODE CONTROL OF AEROBIC BIOPROCESS USING RECURRENT NEURAL IDENTIFIER

The paper proposed a new adaptive control system containing a Recurrent Neural Network (RNN) identifier, a Sliding Mode (SM) controller, and an integral term. The SM control is derived defining the sliding surface with respect to the output tracking error. The state and parameter information to resolve the SM control is obtained from a RNN identifier, which permits the SM control to maintain the sliding regime when the plant parameters changed. The simulation results obtained with a continuous stirred tank reactor plant model confirmed the good quality of the control.