CSTR (Continuous stirred tank reactor) is employed in process control and chemical industries to improve response characteristics and system efficiency. It has a highly nonlinear characteristic that includes complexities in its control and design. Dynamic performance is compassionate to change in system parameters which need more effort for planning a significant controller for CSTR. The reactor temperature changes in either direction from the defined reference value. It is important to note that the intensity of chemical actions inside the CSTR is dependent on the various levels of temperature, and deviation from reference values may cause degradation of biomass quality. Design and implementation of an appropriate adaptive controller for such a nonlinear system are essential. In this paper, a conventional Proportional Integral Derivative (PID) controller is designed. The conventional techniques to deal with constraints suffer severe limitations like it has fixed controller parameters. Hence, A novel method is applied for computing the PID controller parameters using a swarm algorithm that overcomes the conventional controller's limitation. In the proposed technique, PID parameters are tuned by Particle Swarm Optimization (PSO). It is not easy to choose the suitable objective function to design a PID controller using PSO to get an optimal response. In this article, a multi-objective function is proposed for PSO based controller design of CSTR.

The domain of Chemical engineering always carriages more significant challenges to prevent environmental pollutants and protect its stability with the use of various modeling and control methods. In addition, it can significantly profit the living style and health conditions of humans [

In these conventional offline PID tuning methods, tuning of PID parameters are often not suitable for nonlinear and time-varying systems [

Most of the functions are obtained from the analysis of error signals ranging among the desired output and the input signal of a system [

On the other hand, the weighting factor's selection for the objective function is a challenging job. This manuscript is objectively focused on the temperature control of the reactor. In the presented methodology, the temporary reaction of a plant is superior by scheming an appropriate PID controller. Multi-objective PSO MOPSO-PID optimization algorithm is recovering rise time tr, settling time ts, and maximum overshoot Mp. The remaining of the manuscript is organized as below. Section 2 discusses the mathematical modeling of the reactor in elaborated form. Section 3 shows the regulator of the reactor based on the traditional PID controller. Section 4 shows the Design of an Adaptive PSO-based PID controller and Proposed MOPSO-PID Controller, and Section 5 is based on the comparative study of results obtained by diverse control systems. Lastly, a summarized inference is discussed in Section 6.

The conventional approaches to deal with constraints suffer severe limitations and hence are the motivation of researchers to seek more flexible and powerful algorithms. A recent approach was Bio-inspired intelligent computing that from its starting was continuously installed in various applications. Fuzzy logic has come as a powerful tool to mitigate the issues mentioned. The global interest in fuzzy logic demonstrates the academic and industrial performances of approximate reasoning over crisp assumption models in real environment applications. The fuzzy controllers in their industrial implementation are employed as intelligent controllers in real controlling applications. With low computational cost, fuzzy logic is highly flexible in dealing with complex non-linear problems. The performances are strictly according to the expertise of a developer that generates rules basis and hence is a subject of interest for most researchers [

The adaptive approaches for controlling the non-linear CSTR system depend on its parameters according to the system's actual state during control. The polynomial approaches are confronted for controller design, and the satisfaction of initial control requirements is considered. Moreover, the systems with negative properties (for example, non-minimum phase behavior or process that consumes additional time) provide more accurate outputs. The subsidiary pole placement method also furnishes the requirements such as stability, asymptotic tracking of reference signals, and compensation of disturbances [_{r}, t_{s}, and overshoot.

Utmost commonly employed chemical reactors in the industry are the entirely agitated and irreversible exothermic with CSTR. The system comprises a reactor with a cooling cover. The dissolution process of a manufactured item ‘A’ into another manufactured item ‘B’ arises in the CSTR and is shown in

The progress of the preliminary model is founded on some assumptions: This is entirely restless; the mass density of the input module is denoted by

By Arrhenius law:

The dynamic performance of the device is depicted through generalized nonlinear differential

The second-order transfer function of the CSTR plant, commonly used for simulation studies for standard data specification, is obtained below [

The schematic design of the control scheme for CSTR is presented in _{s}, rise time t_{r} and maximum overshoot M_{p}.

This section first describes the working of conventional PID controllers and mentions the parameters to be tuned by PSO. Finally, the proposed Multi-objective PSO (MOPSO) based adaptive PID controller design is presented in detail. The control signal generated by the controller is the function of these tuning parameters

t: Time

These PID parameters are chosen to meet prescribed performance criteria for system response. This paper emphasizes the applications of PSO for tuning the controller. This algorithm (inherently) calculates PID parameters’ values based on their prior states [_{r}, t_{s}, M_{p}, and steady-state error E_{ss}. The system's step response can be improved by optimizing the time domain specification, which depends on the designing suitable controller. Two significant factors can express the transient response of the CSTR; firs, t the speed of response (characterized by the t_{r} and t_{p}), and second is the nearness of the response to the reference input (represented by the M_{p} and t_{s}) [_{s} but prominent M_{p} or vice versa. Thus, ITAE and ITSE conquer the drawback of the IAE and ISE. Further, ITSE and ITAE are trying to reduce the squared error signals and weighted absolute, respectively. However, it is not necessary to minimize all the response specifications such as E_{ss}, M_{p}, t_{r}, and t_{s} at the same time. Therefore, the multi minimum problem can be overcome by using a weighted sum of frequency and time response specifications objective functions. M. R. Haque et al. [

This fitness function is optimized to tune the PID parameters for getting the minimum values of time response specifications. To get the appropriate values of

In 1995, the heuristic method PSO was proposed by James Kennedy. As shown in

PSO is initialized with the first position and velocity using random solutions, which is named the swarm. PSO algorithm has three steps. Which following three steps are iterated until the criterion of termination is done:

The best solution (fitness) achieved so far is named pbest.

The best value obtained so far by any particle in the population named as gbest.

_{p}, K_{i},_{d}

_{p} K_{i}K_{d}

This work proposes a MOPSO-PID controller for probing the optimized values of PID controller parameters _{p}, K_{i} _{d} _{p}, K_{i} _{d}

_{p}_{ss}_{r}_{s}

if

if

This segment shows outcomes by MATLAB programming, and a comparative investigation is completed to express the supremacy of the projected MOPSO control system. MATLAB programming is done for the parameters of CSTR given in the appendix. Initial parameters of the PID controller and PSO algorithm for visual examination are shown in

Size of unit (particle) | 30 |
---|---|

Number of repetition | 200 |

Weight function | Arithmetic |

Constants for acceleration C_{1}& C_{2} |
1.2 and 0.012 |

Dimension for search-space | 03 |

Constraints | Control methods | |
---|---|---|

Conventional PID | MOPSO-PID | |

5 | 7.8395 | |

50 | 41.3427 | |

0.5 | 0.0295 |

The time response curve of ^{o}F. The desired temperature is set to 80^{o}F. It can be observed that without any controller, the reactor temperature is not reaching its desired value. With the application of a conventional PID controller, the desired temperature is achieved, but there is an overshoot of 14.46%, while with the proposed MOPSO-PID controller, this overshoot is reduced to 2.14%. The minimization of error takes a response time of 0.42 sec by MOPSO-PID for achieving the required temperature of 80^{°}F.

The CSTR system's response for without controller, conventional PID, and the MOPSO-PID controller have been depicted in _{r}, t_{p}, t_{s}, _{p}

Performance index | Control methods | ||
---|---|---|---|

Without controller | Conventional PID | MOPSO-PID | |

MSE | 267.6768 | 26.7112 | 10.0934 |

ITAE | 15428.3682 | 1642.1107 | 518.2681 |

This paper projected a temperature control technique due to the abrupt change in flow rate and temperature. The controller wants to be precisely adjusted to maintain the response temperature of the reactor at reference value. A novel approach is employed for calculating the PID controller parameters with the usage of the swarm algorithm. The proposed technique MOPSO-PID controller, integrates the new time-response specification with the PSO algorithm. The results graphically and analytically are analyzed using the reactor transfer function time response subjected to a unit step function. There is a remarkable improvement in more petite t_{r}, t_{p}, t_{s}, and a lower M_{p} overshoot. Simulation results justify that the proposed MOPSO-PID controller can highly improvise the PID tuning optimization in comparison with a conventional PID controller.

The authors would like to thank the editors of CMC and anonymous reviewers for their time and review of this manuscript and Professor Dr. Yong-Jin Park (IEEE Life member and former Director IEEE Region 10) valuable comments and suggestions on improving the paper.