Predictive two-loop fractional-order control law for industry-oriented integrating type chemical processes and reactors

Fractional-order controllers are recognized for their enhanced tuning flexibility, while the Smith predictor (SP) is a widely used approach for compensating time delays in control systems. This study explores a hybrid approach that integrates the advantages of both fractional-order control and SP structure to address challenges in time-delay process control. In this study, a predictive modified fractional-order internal model control (MFOIMC) strategy is proposed, wherein the fractional-order controller C FOC ( s ) is designed based on maximum sensitivity and phase margin specifications to achieve desired robustness and performance. The proposed controller is tested in four benchmark case studies: a proton exchange membrane fuel cell (PEMFC), a bioreactor, a continuous stirred tank reactor (CSTR), and a cryogenic distillation process. Simulation results demonstrate the superior performance of the proposed MFOIMC approach in terms of tracking, disturbance rejection, and robustness, compared to existing methods. The effectiveness is quantitatively validated using error indices and the integral square of control input (ISU). Robust stability under parametric uncertainties is also verified. Practical viability is confirmed through real-time implementation on a two-tank level control setup, showcasing the industrial applicability of the proposed method.

This paper proposes an optimal Active Disturbance Rejection Control (ADRC) based on using Asexual Reproduction Optimization (ARO) to control the temperature of a nonlinear CSTR. The parameters of non-isothermal continuous stirred tank reactor (CSTR) are varying with time caused by fouling and the deactivation and regeneration of the catalyst. Furthermore, in the exothermal region, dynamic behavior of this reactor is unstable. Therefore, designing an efficient controller in this complicated situation is difficult and challenging. ADRC is used as a robust method to control the temperature of CSTR in the situation that the CSTR parameters are varying with time. The parameters of ADRC are difficult to adjust and if these parameters tuned properly, it performs more efficiently in setpoint tracking and disturbance rejection. In this paper Controller design is represented as an optimization problem. The parameters of ADRC are tuned by ARO and then by Particle Swarm Optimization (PSO). The performance of ADRC tuned by ARO (ADRC-ARO) is compared with the performance of ADRC tuned by PSO (ADRC-PSO) and PID controller. The simulation results that the proposed ADRC-ARO method reveals robustness and better performance in both setpoint tracking and disturbance rejection with faster response time and less settling time.

This paper proposes a fractional-order PD controller to suppress the vibration of the typical pipeline system of a nuclear power plant. In view of the characteristics of typical pipeline systems of nuclear power plants, mathematical models are established and dynamic equations are derived to make complex systems digitized for analysis and research. A piping system vibration damping controller based on fractional-order PD control is designed. The fractional-order PD controller introduces a differential order on the basis of the traditional integer-order PD controller to improve the matching degree of the model. Under this system structure, the quadratic performance index is designed, and the particle swarm optimization algorithm is used to optimize the controller parameters to optimize the effect of suppressing vibration. The simulation results show that in the typical pipeline system of nuclear power plant, the fractional-order PD controller designed by this method can suppress the vibration of the system better than the traditional integer-order PD controller.

This paper focuses on the design, analysis and implementation of Integer-order (IO) and Fractional-order (FO) controllers for systems characterized by lag-dominant time delays. The existing literature has been examined to analyze the methodology employed in tuning IO and FO controllers for first-order time delay system for perturbations in process parameters. It is observed that there is scope to investigate better controllers for lag-dominant time delay systems. The five different structures of controllers are chosen. The paper proposes IO and FO controllers tailored for a test group comprising 16 first-order systems with time delays. These IO and FO controllers are designed to fulfil design specifications: phase margin, peak overshoot, IAE, ITAE and ISE using Modified Bode’s Ideal Loop Transfer Function with delay method. For comparison conventional IO tuning method, Gain-Phase Margin Tester (GPMT) and Fractional Ms Constrained Integral Gain Optimization Method (F-MIGO) is used. The simulation results and performance evaluation for both IO and FO controllers are obtained for a range of values of relative dead time of the system represented by τ. The τ value is obtained by varying conditions of delay (L) and time constant (T). Two scenarios are taken into account: the first involves varying L while keeping T constant, and the second involves keeping L constant while varying T. The main objective of the paper is to analyze IO and FO controllers based on time and frequency domain parameters, performance error indices, disturbance rejection, gain variations, Total Variation (TV) and control efforts for perturbations in process parameters. The simulation results indicate that FO controllers show superior tolerance to perturbations in L and T when compared to IO counterparts. This observation was noted during the analysis of the control system by varying values of L and T to obtain a consistent value of τ . Thus, the extensive simulation studies demonstrate that the FO controller tailored for lag-dominant time delay systems outperforms its IO counterpart in terms of robustness, closed-loop stability and error performance metrics.

Vibrations in airplane wings have a negative impact on the quality and safety of a flight. For this reason, active vibration suppression techniques are of extreme importance. In this paper, a smart beam is used as a simulator for the airplane wings and a fractional order PD controller is designed for active vibration mitigation. To implement the ideal fractional order controller on the smart beam unit, its digital approximation is required. In this paper, a new continuous-to-discrete-time operator is used to obtain the discrete-time approximation of the ideal fractional order PD controller. The efficiency and flexibility, as well as some guidelines for using this new operator, are given. The numerical examples show that high accuracy of approximation is obtained and that the proposed method can be considered as a suitable solution for obtaining the digital approximation of fractional order controllers. The experimental results demonstrate that the designed controller can significantly improve the vibration suppression in smart beams.

In most of the industrial process plants, PI/PID controllers have been widely used because of its simple design, easy tuning, and operational advantages. However, the performance of these controllers degrades for the processes with long dead-time and variation in set-point. Up next, a PPI controller is designed based on the Smith predictor to handle dead-time processes by compensation technique, but it failed to achieve adequate performance in the presence of external noise, large disturbances, and higher-order systems. Furthermore, the model-based controllers structure is complex in nature and requires the exact model of the process with more tunable parameters. Therefore, in this research, a fractional-order predictive PI controller has been proposed for dead-time processes with added filtering abilities. The controller uses the dead-time compensation characteristics of the Smith predictor and the fractional-order controller's robustness nature. For the high peak overshoot, external noise, and disturbance problems, a new set-point and noise filtering technique is proposed, and later it is compared with different conventional methods. In servo and regulatory operations, the proposed controller and filtering techniques produced optimal performance. Multiple real-time industrial process models are simulated with long dead-time to evaluate the proposed technique's flexibility, set-point tracking, disturbance rejection, signal smoothing, and dead-time compensation capabilities.

To control unstable and stable plants a new series cascade control structure (SCCS) is proposed. The proposed SCCS incorporates two or three controllers (setpoint tracking controller, secondary disturbance rejection controller and stabilising controller for only unstable plants). Internal model control scheme (IMCS) augmented with integration of square error (ISE) minimisation along with robustness considerations are applied to design the secondary loop disturbance rejection controller. In contrast, relocated IMCS augmented with ISE minimisation is applied for the outer loop or setpoint tracking controller. Routh Hurwitz stability criteria and maximum sensitivity considerations are used to design the proportional-derivative (PD) controller, which stabilises the unstable plant. It is important to note that the suggested SCCS only needs four controller parameters to be tuned, which is less than the recently reported techniques. Robust stability analysis of the proposed SCCS is performed in the presence of uncertainty. The simulation results depict that the suggested approach imparts pre-eminent improvement in closed-loop performance such as faster setpoint tracking and better disturbance rejection for nominal and perturbed plants.

In this paper, a fractional-order PD controller based on Laguerre orthonormal functions is constructed for commensurate fractional order systems. The main idea is to expand the transfer functions of the fractional order plant, the desired open loop gain, and the fractional order PD controller in terms of their Laguerre basis functions. The fractional order PD controller coefficients are obtained by matching the first two coefficients of the open loop gain Laguerre series with the desired one. The optimum value of the Laguerre basis function pole is appropriately selected to minimize an integral square error performance index. The numerical simulations demonstrate the performance of the proposed Laguerre based fractional order PD controller, as well.

In this paper, based on the extended state observer (ESO) and on a fractional order controller (FOC), composed of an integer order PID cascaded with a fractional order filter (FOF), a new control scheme for an n th order integer plant is proposed. The ESO is used to estimate and cancel the unknown internal dynamics and the external disturbance. Afterwards, an FOC is designed to resolve the set-point tracking problem. An analytical and systematic method is proposed to design the FOC. This method is based on the Internal Model Control (IMC) and the Bode’s Ideal Transfer Function (BITF). Therefore, the proposed control structure improves the robustness and performance of the traditional linear active disturbance rejection control (LADRC), especially for the open-loop gain variation. In addition, since the system be controlled is an n th order, a general form of the BITF is also proposed. Numerical simulations on a nonlinear model and experimental results on a cart-pendulum system design illustrate the effectiveness of the suggested ESO-PID-FOF scheme for the disturbance rejection, the set-point tracking and robustness. A comparison with the results obtained using the standard LADRC is also presented.

Parallel cascade control of dead time processes via fractional order controllers based on Smith predictor

This article examines the performance of the proposed complex-order, conventional and fractional-order controllers for process automation and control in process plants. The controllers are compared regarding disturbance rejection and set-point tracking, considering variables such as response time, robustness to uncertainty, and steady-state error. The study shows that a complex PI-PD controller has better accuracy, faster response time, and better noise rejection. Still, implementation is challenging due to increased complexity and processing requirements. In contrast, a standard PI-PD controller is a known solution but may have problems with accuracy and robustness. Fractional-order controllers based on fractional computations have the potential to improve control accuracy and robustness of non-linear and time-varying systems. Experimental insights and real-world case studies are used to highlight the strengths and weaknesses of each controller. The findings provide valuable insights into the strengths and weaknesses of complex-order and fractional-order controllers and help to select the appropriate controller for specific process plant requirements. Future perspectives on controller design and performance optimization are detailed, identifying the potential benefits of using complex and fractional-order controllers in process plants.

A maximum sensitivity constrained modified Smith predictor consisting of two PD controllers is developed for integrating type continuously stirred tank reactors (CSTRs) model. This CSTR type model approximated as integrating first order plus time delay with and without inverse response processes is challenging to control as it contains integrating term, process time delay and a zero lying in the right half of s-plane. The inner and outer loop PD blocks are tuned to achieve the desired set-point tracking and load disturbance rejection responses using direct synthesis approach. The proposed control is free from integrating action and therefore, smooth setpoint tracking response with no overshoot is obtained which is highly desirable in the process industries. Two design parameters λ and τ are involved in the suggested control whose suitable values are recommended to achieve the desired robustness level by specifying the maximum sensitivities of the inner and outer loop transfer functions. Various illustrative models are considered to show the effectiveness and superiority of the proposed control structure. The system robustness towards process parameter perturbations and load disturbances are investigated in all the examples. Performance of the suggested modified Smith predictor is found superior as compared to the other recently published works.

<p>IMC-PID controllers supply exceptional set point tracking but slow<br />disturbance refutation, because of introduction of slow process pole<br />introduced by the conventional filter. Disturbance rejection is important in<br />many industrial applications over set point tracking. An enhanced IMC filter<br />cascaded with PID controller with Internal Model Control Tuning System<br />(IMC-PID) is presented right now for efficient disruption rejection and<br />reliable first order process operation with time delay (FOPTD). The optional<br />filter does away with the sluggish dominant pole. The present learning shows<br />that the recommended IMC filter provide excellent trouble rejection<br />irrespective of where the trouble enters the procedure and provide high-<br />quality robustness to duplicate deviation in surroundings of accepting in<br />difference with other method cited in the text. Reenactment study was led to<br />show the feasibility of the suggested approach on processes with different 0/r ratios by measuring the controller parameters while retaining the same<br />robustness as regards maximal sensitivity. His efficiency of the closed loops<br />was assessed utilizing integral error parameters. Viz. ISE, ITAE, IAE. The<br />recommended filter provides excellent response pro lag dominant processes.</p>

This study analyzes with the technology of auto tuning using relay feedback test for non-square MIMO system through process modeling, identification, input-output pairing and control strategies. However, the control configuration selection based on conventional steady-state Relative Gain Array (RGA) matrix sometimes degrades the loop performance and it needs attention. This study also deals with the real challenges in time domain modeling and appropriate pairing of loops for non-linear chemical processes. The choice of input-output pairing for square system has been extended to non-linear chemical processes. This ensures the system’s stability by selecting an appropriate manipulated-controlled variable pairing in non-linear chemical processes and the same is also tested for benchmark of non-linear chemical processes. In this study, two types of non-square systems are considered: one is systems with excess input than output variables and the other is systems with excess output than input variables. Some benchmark non-linear chemical processes, such as processes with mild nonlinearity, moderate to high nonlinearity and highly nonlinearity, are also taken for this study. Three standard benchmark processes are used in analysis of nonlinear chemical processes, namely: (1) Continuous Stirred Tank Reactor (CSTR) process; (2) hydrogen-ion- concentration (pH) process and (3) distillation column and this procedure is illustrated via simulation of 3-by-2 and 2-by-3 non-linear chemical processes.

This paper presents a systematic and robust design methodology for Proportional-Integral-Derivative (PID) and Proportional-Integral-Derivative-Acceleration (PIDA) controllers for second-order and third-order systems with time delay, respectively. The proposed approach is rooted in the Internal Model Control (IMC) framework, providing a transparent structure and analytical tuning rules. A key contribution is the development of a systematic tuning methodology that establishes a direct numerical-empirical relationship between the desired closed-loop robustness, specified by the maximum sensitivity ( S max ), and the single controller tuning parameter (ϵ), replacing heuristic trial-and-error procedures with a specification-driven approach. The controller gains are derived directly from the process model parameters, and the design incorporates lead-lag compensators to manage time delays effectively, as well as derivative filters to ensure practical implementability and noise attenuation. The efficacy of this approach is validated through comprehensive simulations on three distinct benchmarks: a SOPTD process, a nonlinear continuous stirred-tank reactor, and an industrial TOPTD boiler model. The results demonstrate quantifiable superiority in setpoint tracking, disturbance rejection, and robustness to parametric uncertainty when compared against a range of classical, optimization-based, and advanced fractional-order control strategies.