Fractional Order Internal Model Control Research Articles

Modified fractional order PID structure for non‐integer model bioreactor control

AbstractTemperature control for fermentation is crucial as it directly affects microorganism growth, productivity, and metabolic activity. This work proposes a modified fractional order proportional‐integral‐derivative (FOPID‐DF) controller that incorporates the system model in the control loop configuration utilizing a differential filter for precise temperature control within a narrow operating range. PID, fractional order PID (FOPID), modified fractional order PID (MFOPID), and fractional order internal model control (IMC) controllers were also designed for comparative analysis. The simulation results demonstrated that the proposed FOPID‐DF controller outperforms the other designed controllers, shown by a 22.33% reduction in integral absolute error (IAE) and a 29.06% decrease in integral square error (ISE) compared to the FOPID controller and various other improved performance indicators. Parameter variation and noise analysis highlighted the ability of the controller to maintain stability and performance under changing conditions. The simulation outcomes suggested that the FOPID‐DF controller excels in temperature control, ensuring optimal microorganism growth and metabolic activity.

Design of Two-Degree-of-Freedom Fractional-Order Internal Model Control Algorithm for Pneumatic Control Valves

In response to the problems of the inaccurate pneumatic control valve model, the slow valve position control, and the low precision in the industrial control process, some improvement methods are proposed. Firstly, the fractional-order concept is introduced based on the first-order inertia model and IBBO (improved biogeography-based optimization) is used for iteration to obtain a specific transfer function model. Secondly, a fractional-order and two-degree-of-freedom combined internal model control algorithm is proposed. Finally, semi-physical experiments are carried out on a semi-physical experimental platform. The results show that in the field of pneumatic regulating valves, the fractional-order model has good adaptability and effectiveness, and the two-degree-of-freedom fractional-order internal model control algorithm also effectively improves the accuracy, speed, and robustness of the valve position control.

Improved control of integrating cascade processes with time delays using fractional-order internal model controller with the Smith predictor

This article proposes an enhanced control of integrating cascade processes. The importance of the scheme shows by controlling a double integrating process with time delay under significant parametric uncertainties and load disturbances. A novel design is proposed based on the Smith predictor principle and uses a fractional-order internal model controller in the outer loop. The required fractional-order tuning parameter follows the desired gain and phase margins. At the same time, another tuning parameter, such as the fractional filter’s time constant, is calculated from the desired performance constraint. Numerical analysis and comparison are performed to showcase the feature of the hybrid structure. The simulation results show that the fractional-order internal model controller–based scheme provides enhanced tracking and faster regulation capabilities and works well under nominal and parameter uncertainty conditions.

Fractional Order Internal Model PID Control for Pulp Batch Cooking Process

Pulp batch cooking is performed in a sealed high-temperature and high-pressure digester and is a complex black-box process. Based on the analysis of the mechanism of batch cooking, a model with nonlinear characteristics was established. To optimize the nonlinear part of the model, function fitting and numerical approximation were used for the simple cooking process. A novel fractional-order model is proposed to solve the problems of model inaccuracy and uncertain system parameters during batch cooking. For fractional-order systems, a two-degree-of-freedom fractional-order PID (FO-PID) controller based on internal model control is designed. The internal model control simplifies the number of parameter settings of the fractional-order controller and allows accurate adjustment of the adjustable parameters of the FO-PID controller based on the maximum sensitivity and stability margin. The simulation results show that the fractional-order internal model control in the batch cooking process is superior to the integer-order control in terms of overshoot, response speed, and robustness. Compared to internal model control, it provides better setpoint tracking dynamics and better robustness to system parameter disturbances. The practical application results in paper mills are given to illustrate the effectiveness of the method.

Multi-Drug Scheduling for Chemotherapy Using Fractional Order Internal Model Controller

Chemotherapy is a widely used cancer treatment method globally. However, cancer cells can develop resistance towards single-drug-based chemotherapy if it is infused for extended periods, resulting in treatment failure in many cases. To address this issue, oncologists have progressed towards using multi-drug chemotherapy (MDC). This method considers different drug concentrations for cancer treatment, but choosing incorrect drug concentrations can adversely affect the patient’s body. Therefore, it is crucial to recognize the trade-off between drug concentrations and their adverse effects. To address this issue, a closed-loop multi-drug scheduling based on Fractional Order Internal-Model-Control Proportional Integral (IMC-FOPI) Control is proposed. The proposed scheme combines the benefits of fractional PI and internal model controllers. Additionally, the parameters of IMC-FOPI are optimally tuned using a random walk-based Moth-flame optimization. The performance of the proposed controller is compared with PI and Two degrees of freedom PI (2PI) controllers for drug concentration control at the tumor site. The results reveal that the proposed control scheme improves the settling time by 43% and 21% for VX, 54% and 48 % for VY, and 48% and 40% for VZ, respectively, compared to PI and 2PI. Therefore, it can be concluded that the proposed control scheme is more efficient in scheduling multi-drug than conventional controllers.

Fractional order internal model control of non‐minimum phase and time‐delayed plants

AbstractSeveral applications on fractional order (FO) control have gained considerable significance in the recent years, which led to the evolution of novel tuning strategies of the generalized order FO controllers. Some of the methods in available literatures are based on constrained minimization optimization techniques or analytical method defined only for specific plants. They are valid only for some special model cases. On the contrary, in this technical note, a generalized non‐integer order internal model control (IMC) framework is realized for any order non‐minimum phase (NMP) plants with right half plane (RHP) zero as well as time delayed plants having any finite relative order. Its parameters are graphically interpreted satisfying the frequency domain design stipulations for single input and single output (SISO) higher order linear time invariant (LTI) plants. The performance of the same on a bioreactor fermentation process for its temperature control is found to have outperformed in contrast to its integer order (IO)‐IMC. It is therefore inferred here that this new approach pledges to impart unique solution of the controller parameters, formulating a highly efficient tool outperforming the existing paradigms. Simulation and real time experimentation are presented to validate the method put forward providing satisfactory performance in reference tracking, disturbance rejection, and robustness to various plant parameter perturbations.

Fractional-order model identification and indirect internal model controller design for higher-order processes

Several studies have shown that fractional-order models with dead-time can be used to capture the dynamics of a wide range of processes. Also, there is more scope to improve the existing identification and control strategies. Hence, this work revisits the identification of fractional-order models (IDFOM) approach to augment the same with a robust indirect fractional-order internal model control (IFOIMC) method to formulate a new identification and control strategy. In this strategy, the fractional-order model obtained using the IDFOM approach is shifted in the frequency domain by a frequency-shifting parameter. With the help of IMC principles, the frequency-shifted model is used to design the IFOIMC controller with the frequency-shifting parameter as the only tuneable parameter. Thus, the frequency-shifting parameter/robustness parameter replaces the only tuning parameter of conventional IMC design. This frequency-shifting parameter is tuned based on maximum sensitivity considerations to ensure the robustness of the design. The resulting IFOIMC controller is further realized as a fractional-order proportional-integral controller in series with a fractional-order filter (FOPIFOF). The effectiveness of the proposed identification and control strategy is illustrated by comparing the closed-loop performance achieved by IFOIMC controllers designed using two widely used identification strategies.

Parameters’ Optimization in Compressed Air Pressure Process Using Hybrid F min–GA-Based PID and Fractional Order Internal Model Controller

The Compressed Air Pressure Process (CAPP) is very important in an industrial environment. Because compressed air is used in many applications such as pneumatic-based actuation such as pneumatics valves, pneumatic-based tools, etc. In this process, the minute linkages are very difficult to arrest and also nonlinear behavior of conversion elements such as pressure (3–15) psi to current (4–20) mA (P/I) as well as current (4–20) mA to voltage (0–5) v (I/V) converters are making the process highly nonlinear. To maintain the process variable at a certain prescribed value and to design a good and effective controller, the non-linear process must be controlled, and the best model is needed. In this research work optimized integer with non-integer designs are gained and based on the models the PID controller with optimized controller parameters is selected depending on the model using optimized methods such as F min–GA and also Internal Model controllers (IMC) are designed, the Investigations are done by comparing the dynamic behaviors. The performance of the proposed technique is implemented in the MATLAB platform and the experimental prototype is also presented.

Unified fractional indirect IMC-based hybrid dual-loop strategy for unstable and integrating type CSTRs

Abstract Controlling unstable and integrating type continuously stirred tank reactors (CSTRs) are more difficult due to the presence of poles in the right half and at the origin of the s-plane respectively. The existence of dead-time needs more efficient control requirements for CSTRs. In this work, a modified indirect fractional-order internal model control proportional-derivative (MIFOIMC-PD) decoupled dual-loop control strategy is suggested for unstable and integrating plants with dead time. The external-loop controller is designed using the MIFOIMC strategy for obtaining adequate servo performance. PD controller is designed such that it stabilizes the plant while disturbances occur. Decoupled nature of the suggested strategy allows this PD controller to be designed without considering the external-loop dynamics. Reference tracking and disturbance elimination capabilities of the suggested method are also quantitatively compared with reported methods. It is established that the suggested MIFOIMC-PD control architecture controls CSTRs more effectively than some lately reported schemes.

Hybrid dual-loop control method for dead-time second-order unstable inverse response plants with a case study on CSTR

Abstract Unstable processes are hard to stabilize as they contain one or more positive poles which result in unbounded dynamic behavior. The occurrence of the delay and positive zeros often creates more difficulty in controlling such unstable plants. Most control strategies meant for first-order unstable processes fail to stabilize and control the higher-order unstable processes. Hence, a new dual-loop hybrid control structure is suggested for dead-time unbounded second-order processes with positive/negative zeros. Inner-loop has a stabilizing PID controller. The PID controller parameters are derived by comparing the numerator and characteristic polynomial coefficients in the transfer function for internal-loop servo action. A fractional-order internal model controller (FOIMC) is used in the external-loop. Methods for the selection of outer-loop tuning parameter and fractional-order are also discussed. By comparing the simulation results with a contemporary single-loop scheme, the usefulness of the suggested scheme is proved. The suggested scheme is capable of minimizing the overshoot and improving the overall dynamic performance. Finally, the usefulness of the suggested scheme is also demonstrated by a case study on temperature control of a continuous stirred tank reactor (CSTR) during a first-order irrevocable exothermic reaction.

Decoupled double‐loop FOIMC‐PD control architecture for double integral with dead time processes

AbstractA novel double‐loop control configuration with two controllers is suggested for double integrating processes with dead‐time. The stabilizing range of the inner‐loop proportional‐derivative (PD) controller is obtained using the Routh stability criteria. From this range, the exact PD settings are obtained by following a graphical approach where the integration of absolute error (IAE) is plotted for different PD settings. The PD settings resulting in the minimum IAE are chosen. In addition to stabilizing the plant, the inner‐loop also rejects the disturbances. A fractional‐order internal model controller (FOIMC) is designed for satisfactory set‐point tracking response in the outer‐loop. The suggested strategy has four adjustable parameters (proportional and derivative time constants, outer closed‐loop adjustment parameter, and fractional‐order of the FOIMC low‐pass filter). Based on extensive simulations, the tuning ranges for the above‐mentioned adjustable parameters are specified. The simulation study is done with the help of benchmark double integrating plant models with large dead‐time. Quantitative performance measures are also computed for comparing the suggested and previously reported schemes. The suggested FOIMC‐PD control architecture yields enhanced control performance than some recently reported techniques.

Closed loop fractional order drug delivery control scheme for chemotherapy

Chemotherapy is one of the most extensively utilized cancer treatment strategies worldwide. It is intended to eliminate fast-developing cancer cells in a patient’s body. The amount of chemotherapeutic drug that must be administered precisely into a patient’s body determines the efficacy of the treatment and governs the patient survival during chemotherapy. Therefore, controlling the chemotherapeutic drug dose delivered to the patient is essential. This research aims to propose a two-degree-of-freedom fractional order proportional–integral–derivative (2FOPID) controller with a set point filter for implementing an automatic drug delivery control scheme during chemotherapy. The Whale optimization algorithm (WOA) is used to tune the parameters of the 2FOPID controller, resulting in a WOA-tuned 2FOPID controller (W2FOPID). The performance of the proposed W2FOPID is compared with the Integral–Proportional–Derivative (IPD), Internal Model Control (IMC), and Fractional Order IMC (FOIMC) schemes. The experimental results demonstrate that the proposed W2FOPID controller is effective, accurate, and robust for drug concentration control during chemotherapy. W2FOPID outperforms IPD, IMC, and FOIMC schemes in terms of Integral Absolute Error by 79.9%, 25.3%, and 23.36%, respectively. In addition, W2FOPID exhibits excellent set-point tracking, noise suppression and uncertainty handling capabilities.

Design of a novel fractional‐order internal model controller‐based Smith predictor for integrating processes with large dead‐time

AbstractA novel multi‐loop control configuration with two controllers is suggested for integrating processes having large dead‐time. The inner‐loop consists of a Smith predictor having proportional (P)/proportional‐derivative (PD) controller for first/second‐order integrating processes, respectively. Once the dead‐time is compensated by the inner‐loop Smith predictor, a fractional‐order internal model controller (FOIMC) is designed in the outer‐loop. The P/PD controllers are tuned using direct synthesis methodology. The proposed control architecture has three adjustable parameters (inner and outer closed‐loop adjustment parameters, fractional‐order of the FOIMC low‐pass filter). Based on extensive simulations, the tuning ranges for the above‐mentioned adjustable parameters are specified. Suitable justification is also provided for the suggested range of tuning parameters. Several benchmark examples of plant models are used to study the set‐point following and disturbance elimination capabilities of the proposed control architecture. Quantitative performance measures are also computed for comparing the suggested and previously reported schemes. It is evident that the suggested FOIMC based Smith predictor yields enhanced control performance than some recently reported techniques.

Design and simulation of a novel FOIMC-PD/P double-loop control structure for CSTRs and bioreactors

Abstract The design of control methods for unstable plants is somewhat complex than that of stable plants. This is because unstable process models contain one or more poles lying on the right of the s-plane which yields unbounded closed-loop response. Further, the presence of the dead-time induces more complexity as it decreases the gain and phase margins which in turn deteriorates the closed-loop performance. The design of control strategies become more challenging for plants of unstable nature with positive zeros because they exhibit a phenomenon called inverse response. This paper suggests a method to design a double-loop scheme for unstable plants with/without inverse response. Accordingly, a proportional-derivative (PD)/proportional (P) controllers are used in the inner-loop for stabilizing the plant. A fractional order internal model controller (FOIMC) scheme is used to obtain the outer-loop controller using the stabilized plant model. The P/PD controller settings have been obtained by using the Routh-stability criteria and the maximum sensitivity approach. Procedure for selecting the outer-loop tuning parameter and fractional order is also given. Linear and nonlinear models of unstable plants including bioreactors and isothermal chemical reactors are used to demonstrate the merits of the suggested strategy. Robustness of the design and effect of measurement noise are also studied. Integrated absolute/squared error measures are also calculated. The suggested design is found to be more effective in controlling unstable processes than some reported works.

Order Diminution of LTI Systems Using Modified Big Bang Big Crunch Algorithm and Pade Approximation with Fractional Order Controller Design

In this paper, a novel approach is proposed for the reduced order modelling of linear time invariant (LTI) systems. The proposed approach is a combination of modified Big bang big crunch (BBBC) optimization algorithm and Pade approximation technique. The beauty of the proposed approach is that the selection of solution space for BBBC algorithm is not entirely random, but structured via the use of Pade approximation approach. Hence, two principal criticisms of soft computing algorithms, i.e., random choice of solution space and larger simulation time are averted in the proposed technique. The proposed technique is substantiated via four different numerical examples from literature and compared with existing model order reduction (MOR) techniques. The concept of controller design is introduced via application of fractional order internal model control technique for load frequency control of power systems. Further, BBBC algorithm is employed to tune a boiler loop in power station. The results convey the efficiency and powerfulness of the proposed technique.

Design of the fractional order internal model controller using the swarm intelligence techniques for the coupled tank system

Design of the fractional order internal model controller using the swarm intelligence techniques for the coupled tank system

Tuning of the two degrees of freedom FOIMC based on the Smith predictor

This paper proposes a novel two degrees of freedom (2-DOF) fractional order internal model controller (FOIMC) for the height control of a coupled tank system. Coupled tank systems find applications in the process control industries. The level control of the coupled tank system is a challenging problem in the control systems because of its nonlinearity and time delay involved. The level control of the coupled tank system has variable servo tracking and disturbance rejection requirements. 2-DOF controller achieves better servo tracking and disturbance rejection than a one degree of freedom (1-DOF) controller. The proposed servo tracking controller is designed using the Bode’s ideal loop transfer function and direct synthesis approach. The parameters of the Servo tracking controller are tuned using peak overshoot and settling time specifications. The disturbance rejection controller is designed analytically. A detailed study of the effect of the fractional order on the disturbance rejection property and stability. Robust stability of the proposed controller is analysed using $$H_{\infty }$$ norm of the uncertainty bound. Comparison of the simulation results of the proposed controller with the state of the art showed better performance of the proposed controller. Frequency domain analysis also indicates the superior performance of the proposed 2-DOF FOIMC.

Level control of a conical tank using the fractional order controller

This work proposes a fractional-order internal model controller (FOIMC), for the height control of a conical tank nonlinear system. The proposed controller has a fractional filter cascaded with an integer-order PID controller. The FOIMC combines the advantages of IMC such as few tuning parameters, and a stable controller with the advantages of fractional control such as robustness, flexibility in tuning parameters, and a wide stability margin. Linearising the nonlinear system includes the Lagrange remainder term to compensate for the higher-order derivatives. The PSO algorithm and WOA are used to optimise the FOIMC controller parameters. The servo and regulatory responses of the proposed controller are compared with those of state-of-the-art technique showing a 35% improvement in the rise time and 100% improvement in the peak overshoot of the step response. The proposed controller shows better robustness to gain variations and consumes less control energy than the other controller. The proposed controller rejects disturbances faster than the other controller.

Analytical design of fractional IMC filter – PID control strategy for performance enhancement of cascade control systems

The cascade control is widely used in chemical industries for disturbance attenuation as an alternative to a single feedback loop. This article presents an internal model control (IMC)-based series cascade control system for different time delay process models. The novelty of the work lies in the use of fractional order IMC filter of the first order and higher order for designing controller in the outer loop based on specific maximum sensitivity. The design also considers different approximations for the time delay term. The controller designed for the inner loop assumes the standard PID controller structure and the outer loop controller takes a fractional filter PID structure. The proposed method gives improved performance for set point tracking and disturbance rejection. Further, the proposed method gives robust performance for noise in the measured signal. Also, the robustness analysis is performed to know the insensitivity of the closed-loop system for process parameter variations. The fragility of the controller is investigated for perturbations in the controller parameters.

Experimental validation of fractional order internal model controller design on buck and boost converter

In this paper, fractional order internal model control technique is formulated for non-ideal dc–dc buck and boost converter. The fractional order internal model control approach integrates the concept of Commande Robuste d’Ordre Non Entier principle for tuning a fractional order filter with internal model control scheme. The final controller can be expressed as a series combination of proportional integral derivative controller and a fractional order low pass filter. To assess the robustness of the proposed fractional order internal model control scheme, both the servo response and regulatory response of the dc–dc converters are investigated in the presence of disturbances. The efficacy of fractional order internal model control technique is demonstrated via comparison with 2 degrees of freedom internal model control scheme. Furthermore, an experimental validation of fractional order internal model control is conducted on laboratory setup, and a dSPACE 1104 microcontroller is used for hardware implementation. The simulation results and the hardware validation are a testimony to the effectiveness of fractional order internal model control technique.