First Order Plus Dead Time Research Articles

Relay feedback identification and PI-PD control of asymmetrical heating and cooling processes

A common type of nonlinear system in the field of process industry is asymmetrical heating and cooling processes. These systems have two operating modes, heating and cooling, each with a particular dynamic feature. This study deals with identifying and controlling such processes. The relay feedback identification method based on the state-space approach, which results in exact estimates, is used in the identification procedure to achieve two first-order plus dead time (FOPDT) process models. Following process identification, two sets of PI-PD controller parameters are acquired in line with the user-defined gain and phase margin specifications, and the system is controlled using a gain-scheduled PI-PD control method. Some simulation examples are provided to demonstrate the use and profitability of the suggested identification and control approaches. Comparisons with a similar study are provided for both identification and control approaches to clearly demonstrate the benefits of the suggested procedures.

Tuning a PI/PID Controller with Direct Synthesis to Obtain a Non-Oscillatory Response of Time-Delayed Systems

The article presents a method for tuning PI/PID regulators controlling inertial time-delayed plants. The method was formulated on the basis of direct synthesis using the FOPDT (First-Order Plus Dead-Time) and the SOPDT (Second-Order Plus Dead-Time) models to represent the dynamics of the object. The performance objective is to achieve the non-oscillatory response of the system in the shortest time possible while set-point tracking. By employing a novel approach to the synthesis of the control systems with a time delay based on a root-locus analysis, the method eliminates errors resulting from the omission of high-order terms in the Taylor series expansion or the Padé approximation in simplified mathematical descriptions of the process. Consequently, the proposed method makes it possible to precisely determine controller settings to achieve the set control objective. The method was tested with a computer simulation, and the results obtained were compared with those of other methods designed to ensure specific system responses in the designed control systems. The comparisons confirm the proposed method’s ability to achieve the desired reference response and demonstrate its effectiveness in overcoming the limitation of permissible time delays present in other similar methods.

Identification of heat exchanger process through Hammerstein and polynomial models

Process industries extensively use heat exchangers in their operations, playing a crucial role in various sectors by facilitating efficient heat transfer, conserving energy, and reducing operational costs. This paper focuses on identifying and validating the system model, with the primary task of designing the controller involving the determination of the mathematical representation of the system. The First Order Plus Dead Time (FODT) model, derived from basic principles, is used to represent the system. To analyze the system’s behavior and construct a suitable controller, model development is essential, achieved by constructing principles models using energy balance equations to identify the heat exchanger process. Data collected from the model are utilized in the identification process, with the temperature at the outlet of the hot air blower being the controlled variable in this investigation. The research aims to determine the mathematical model based on time versus temperature data acquired from the Heat Exchanger. Various system identification methods, such as Hammerstein Wiener (HW), Auto Regressive with Exogenous Input (ARX), Box-Jenkins (BJ), Output-Error (OE), and Auto Regressive Moving Average with Exogenous Input (ARMAX) models, are implemented for the heat exchanger. The models obtained undergo validation, and the best-fit model closest to the physical system is considered for controller design. After conducting the analysis, it was found that the Output-Error (OE) model outperforms other models in terms of achieving the best fit.

Reaction Curve-Assisted Rule-Based PID Control Design for Islanded Microgrid

In a renewable energy-based islanded microgrid system, frequency control is one of the major challenges. In general, frequency oscillations occur in islanded microgrids due to the stochastic nature of load and variable output power of distributed generating units (DGUs). In the presented research proposal, frequency oscillations are suppressed by implementing the proportional integral derivative (PID) controller-based control design strategy for an islanded microgrid. The modeling of the islanded microgrid is firstly presented in the form of a linearized transfer function. Further, the derived transfer function is approximated into its equivalent first-order plus dead time (FOPDT) form. The approximated FOPDT transfer function is obtained by employing the reaction curve method to calculate the parameters of the FOPDT transfer function. Furthermore, the desired frequency regulation is achieved for the manifested FOPDT transfer function by incorporating PID control design. For PID controller tuning, different rule-based methods are implemented. Additionally, comparative analysis is also performed to ensure the applicability of the comparatively better rule-based tuning method. The Wang–Chan–Juang (WCJ) method is found effective over other rule-based tuning methods. The efficacy of the WCJ method is proved in terms of transient response and frequency deviation. The tabulated data of tuning parameters, time domain specifications, and error indices along with responses are provided in support of the presented control strategy.

Fractional PID with Genetic Algorithm Approach for Industrial Tank Level Control Process

Process control is used in various types of industries to boost production while using current resources, product quality, and safety, with level control being one of the most important schemes. It is suggested that study be conducted on nonlinear continuous processes, particularly in process control applications such as conical tank level control. Initially, each process receives one set of Proportional-Integral (PI) controller settings and a First Order Plus Dead-Time (FOPDT) model using the Ziegler Nicholas (ZN) step response tuning method. The numerous FOPDT models and parameter sets are also obtained. Responses obtained with a single set of parameters and responses obtained with many sets of parameters are compared. By creating a Fractional PID Controller (FPID) with Genetic Algorithm (GA), a simulation-based tuning strategy is proposed. The step responses are acquired through experimental research using fine-tuned settings. At most operational points, the Fractional PID Controller with Genetic Algorithm-based tuning approach outperforms, with lowest oscillation, extremely tiny overshoot, minimum average ISE, and minimum average IAE. The proposed FPID with GA method provides better setpoint and regulatory tracking performance compared to ZN-PID.

Design of a decentralized control law for variable area coupled tank systems using H∞complimentary sensitivity function

AbstractThis paper proposes a novel graphical approach to control the liquid levels of the different variable area coupled tank systems using a decentralized controller. The coupled tank systems are common benchmark systems that consist of two tanks interconnected with each other. The primary goal is to maintain the liquid level in the tank at the desired set point by controlling the flow rate. This is attained with a decentralized method wherein the controller values are obtained from the plane. Besides, the robust criteria is enforced to guarantee the robustness. The proposed controller design approach aims to improve the performance of the system in terms of disturbance rejection and tracking. The decentralized control structure uses a distributed control strategy, thereby reducing the computational load which leads to improving the control performance. The loop interactions are minimized with decouplers. Furthermore, first‐order plus dead‐time (FOPDT) models are derived for each of the decoupled subsystems. Besides, the servo and regulatory responses of the controller are verified with input and output disturbances. Additionally, the response of the controller to system uncertainties and parameter variations is also studied. The simulation results demonstrate the effectiveness and robustness of the proposed approach.

Optimal analytical cascade control for FOPDT systems

This paper proposes a novel control strategy based on optimal Linear Quadratic Regulator (LQR) design applied to cascade systems with stable, integrative, and unstable First Order plus Dead-Time (FOPDT) outer loop models. The secondary (inner) and primary (outer) loop controller designs are performed using the Simplified Filtered Smith Predictor (SFSP). The optimal analytical design is derived from a novel strategy where the pole of the internal loop is placed so that the LQR criterion can be achieved with a simple tuning of the external loop. In contrast to related work, the secondary controller is designed using an SFSP control structure to nominally achieve optimal LQR performance and accelerated rejection of disturbances acting on the inner-loop process. To illustrate the usefulness of the proposed design, we evaluated the strategy in different scenarios, showing the optimality and performance of the analytical design.

RelaxC controller and PID for time delay systems: Experimental test results on Boiler pilot plant

In this paper a novel method of RelaxC controller design is introduced for time delay systems, offering significant implications for process industry. RelaxC’s new technology involves the use of two significant concepts: generating functions and reactivity time. The designed RelaxC controller is applied to First Order Plus Dead Time (FOPDT), Second Order Plus Dead Time (SOPDT), second order integrating, multivariable and nonlinear systems using MATLAB simulations. The key parameters of RelaxC are set, by the designer’s expertise. Proportional Integral Derivative (PID) control is utilized to compare results in particular cases. This method addresses inherent limitations of traditional PID. The RelaxC controller effectively mitigates the adverse effects of time delays, providing more precise setpoint tracking, enhanced disturbance rejection and reduced control effort. The findings emphasize potential of adopting the RelaxC controller for many industrial applications. The experimental results of a real-time boiler pilot plant for temperature and drum level control are presented to demonstrate the efficacy of the proposed method.

An improved anti‐interference predictive PI for first order plus dead time processes

AbstractThe predictive PI control algorithm can handle time delay systems well, but still suffers from poor control and weak anti‐interference ability when facing large inertia and large lag links. This paper starts from the principle of predictive PI controller, equates it to Smith predictive controller, then combines Smith anti‐disturbance structure and proposes an improved predictive PI (IPPI). For the first‐order plus dead time (FOPDT) system simulation experiment, the experimental results show that the proposed controller has significantly improved the response speed and anti‐interference ability.

Model predictive control with exogenous auto-regressive model to improve performance in the CO2 removal

Model predictive control (MPC) is used in the CO2 removal process in the Subang field to improve its control performance. MPC is used to maintain the CO2 concentration at the sweet gas output by controlling the feed gas pressure (PIC-1101), makeup water flow rate (FIC-1102), and amine flow rate (FIC-1103). The empirical model applied to MPC to represent the process model is the auto-regressive exogenous (ARX) model. The ARX model is compared with the first order plus dead time (FOPDT) model based on the root mean square error (RMSE) between the model and the actual process, then MPC parameters are tuned which include sampling time (T), prediction horizon (P) and control horizon (M) to control for the three variables. Improved control performance is measured based on the integral square error (ISE). The results show that the ARX model is the best model for the CO2 removal process with an RMSE value of 35%-91% smaller than the FOPDT model. The optimal control parameters Prediction Horizon (P), Control Horizon (M) and Sampling Time (T) in the CO2 removal process are 75, 25 and 1 on PIC-1101, 25, 10 and 1 on FIC-1102, and 30, 25 and 1 on FIC-1103. The MPC-ARX (MPC using ARX model) can improve the control performance of 33% in the servo control and 6-56% on the regulatory control. However, not all of them showed an increase in control performance improvement from previous studies even though they had used the best model (ARX). This is due to the MPC parameter setting that is not yet appropriate, so it needs to be retuning.

Estimation of First Order Plus Dead Time and Second Order Plus Dead Time models from noisy step response data

SummaryThis paper proposes the estimation of first‐order‐plus‐dead‐time (FOPDT) and second‐order‐plus‐dead‐time (SOPDT) models from noisy step response data. The model parameters are estimated by computation of areas, which makes it robust in the presence of stochastic disturbances in the step response data. The efficiency of the methodology is extensively tested in various numerical examples as well as in real‐life experimental tests. The results—comparing our proposed estimation method with some other methods—suggest that the novel algorithm can be used with noisy step response data and adequately approximates high‐order systems. Moreover, it does not require any system identification expertise, making it readily accessible for the nonexperienced user in industrial practice. The method is successfully validated for overdamped, reasonably underdamped, as well as highly oscillatory processes, hence offering a comprehensive estimation method.

Frequency Domain Specifications Based Robust Decentralized PI/PID Control Algorithm for Benchmark Variable-Area Coupled Tank Systems.

A decentralized PI/PID controller based on the frequency domain analysis for two input two output (TITO) coupled tank systems is exploited in this paper. The fundamentals of the gain margin and phase margin are used to design the proposed PI/PID controller. The basic objective is to keep the tank at the predetermined level. To satisfy the design specifications, the control algorithm is implemented for decoupled subsystems by employing a decoupler. First-order plus dead time (FOPDT) models are obtained for the decoupled subsystems using the model-reduction technique. In addition, the control law is realized by considering the frequency domain analysis. Further, the robustness of the controller is verified by considering multiplicative input and output uncertainties. The proposed method is briefly contrasted with existing techniques. It is envisaged that the proposed control algorithm exhibits better servo and regulatory responses compared to the existing techniques.

Temperature Control using PI Controller

Indonesia is a large archipelago with a tropical climate consisting of dry and wet seasons. Indonesia has had high rainfall and temperature over the year because this country lies on the equator lines. Moreover, severe global warming occurs because of the depletion of the ozone which affects the inclement weather, air, and temperature over the years. Therefore, special equipment is required to obtain appropriate thermal conditions by controlling the temperature. This paper proposed the PI controller to maintain the temperature in their nominal values and its temperature stability is analyzed using pole placement. In this study, the system model is 1st order, called first order plus dead time (FOPDT). Pole placement is utilized to improve the output signal to obtain the gain of the PI controller. The gain of the PI controller obtained is Kp as 0.36095 and Ki as I as of 0.00072231. The percentages of overshoot and steady-state error are 29.98% and 1.5% for the Ziegler Nichols method while 1.28% and 0.26% for the PI Tunner, respectively. PI controller is robust for this system where the pole's position is on the left side of the real axis and has small values of overshoot and steady-state error.

Steady-state and transient dynamics for sweetening of LPG process

Amine treating is the most common system for gas sweetening that is used in petroleum, gas and petrochemical industries. Steady-state analysis of the process is conducted on the developed simulation-model using Aspen Hysys. For obtaining more accurate results, absorber internal specifications and feed gas conditions are taken from real industrial plant data. The effect of the system controlling parameters on concentrations of H2S and CO2 in sweet gas is inspected. The manipulated variables for the amine unit are Di-ethanolamine (DEA) solution circulation rate and temperature. Sour gas flow rate and H2S/CO2 mole ratio in feed become disturbance or load; whereas, the control variables are concentration and throughput of sour gas in exit sweet gas. The outcome of the sensitivity study is used to develop MIMO transient models with a first-order plus dead-time (FOPDT)structure for the control studies. Based on the developed model the model predictive control (MPC) and PID controls are implemented for 2 by 2 systems.

First Order Plus Dead Time Model Approximation and Proportional-Integral-Derivative Controllers Tuning for Multi-Volume Process

Analysis and controller design for the FOPDT model is widely used because of its simpleness and convenience. In this paper, the problem of the multi-volume process (MVP) being approximated to first order plus dead time (FOPDT) model, as well as its proportional-integral-derivative (PID) controller arguments tuning is studied. These have been heavily studied in recent years and the methods developed for its optimal design rely on the idea of including several robust performance specifications in the objective function the method presents fast convergence and consists of mentioning a desired closed-loop transfer function. Particle swarm optimization (PSO) algorithm and performance index of the integral of the time-weighted absolute error (ITAE) minimum is presented to determine the approximate FOPDT model coefficients of MVP processes, where the order is from two to fifteen. In addition, the approximate FOPDT model is used to design the PID controller, which is used to control MVP. A large number of tuning methods are provided to analyze and compare the closed-loop control performances. At the end of the paper, two simulation examples illustrate the superiority and effectiveness of the PID controller design based on the proposed model reduction method. The simulation results show that the reduced-order controller can control a high-order system well, but the process of order reduction is complicated and it needs a long computation time. The FOPID is a generalization of the conventional PID controller. This is based on an extension calculus. A new method for approximating MVP to the FOPDT model is presented in this paper with more effectiveness.

Design and Analysis of Decentralized Dynamic Sliding Mode Controller for TITO Process

In this paper, a decentralized dynamic sliding mode control (DySMC) strategy is applied to a multivariable level control system. The time derivative of the control input of the DySMC is considered a new control variable for an augmented system which is composed of the original system and the integrator. This DySMC can transfer discontinuous terms to the first-order derivative of the control input and effectively reduce the chattering. The interactions between input/output variables are a common phenomenon and a challenging task in the design of multi-loop controllers for interacting multivariable processes. For reducing the interaction among variables, ideal decouplers are used. Independent diagonal controllers are designed for each decoupled subsystem, which is reduced to the first-order plus dead-time (FOPDT) model. A numerical simulation test has been carried out on a reactor system of the Industrial-Scale Polymerization (ISP). Experimental tests are performed to check the efficacy of the proposed controller using a laboratory-level coupled tank system. A comparison of the proposed approach and sliding mode controller (SMC) is presented. Simulation and experiment results show that the DySMC approach reduces the chattering, and compensates for the effect of the external disturbances, and parametric uncertainties.

First Order Plus Dead Time (FOPDT) Model Approximation and Proportional-Integral-Derivative Controllers Tuning for Multi-Volume Process

Analysis and controller design for the FOPDT model is widely used because of its simpleness and convenience. In this paper, the problem of the multi-volume process (MVP) being approximated to first order plus dead time (FOPDT) model, as well as its proportional-integral-derivative (PID) controller arguments tuning is studied. These have been heavily studied in recent years and the methods developed for its optimal design rely on the idea of including several robust performance specifications in the objective function the method presents fast convergence and consists of mentioning a desired closed-loop transfer function. Particle swarm optimization (PSO) algorithm and performance index of the integral of the time-weighted absolute error (ITAE) minimum is presented to determine the approximate FOPDT model coefficients of MVP processes, where the order is from two to fifteen. In addition, the approximate FOPDT model is used to design the PID controller, which is used to control MVP. A large number of tuning methods are provided to analyze and compare the closed-loop control performances. At the end of the paper, two simulation examples illustrate the superiority and effectiveness of the PID controller design based on the proposed model reduction method. The simulation results show that the reduced-order controller can control a high-order system well, but the process of order reduction is complicated and it needs a long computation time. The FOPID is a generalization of the conventional PID controller. This is based on an extension calculus. A new method for approximating MVP to the FOPDT model is presented in this paper with more effectiveness.

Model-Independent Approach for Minimum Variance Performance Assessment of a Multivariate Process

In general, a plant model or its equivalent information, such as interactor matrix or the first several leading Markov matrices, is indispensable to the minimum variance (MV) performance assessment of a multivariate process. In this paper, a model-independent approach for performance assessment is developed to eliminate the requirement of a plant model. Without relying on any prior plant knowledge, the practical solutions are presented, in which the MV benchmark is obtained directly or is estimated in terms of the upper and lower bounds for the following different levels of available knowledge of the multivariate plant: (1) no knowledge available; (2) a known range of each entry in the pseudo first-Markov-matrix; (3) the available knowledge of the steady gain matrix for a first-order plus dead time (FOPDT) plant. The effectiveness of the proposed algorithm is verified through a classic numerical example and a practical example, namely, a “Shell” oil fractionator.

Simple and efficient PID algorithm design method for controlling first order systems with a time delay

Many processes in industry are characterized by delay time or by slow aperiodic dynamics called lag behavior. In addition, many plants in the industry are described mathematically by higher order systems that are approximated with the lower order systems, most frequently such processes and systems are described mathematically as first-order-systems-with time-delay (FOSTD), also called first-order-plus-dead-time (FOPDT). The presence of time delays causes degradation and limitation of achieving desired performance, moreover, it can induce instability. In such cases, design of feedback control algorithm becomes difficult and tedious task. The present work suggests an efficient, simple, linear, and easy to apply design expressions for designing continuous PID (proportional-integral-derivative) control algorithm modes to control the behavior of FOPDT systems. The design expressions are intended to overcome negative effects of time delay presence, as well as, to simplify the control algorithm design process and help designer, in easy and simple way, to get system under control with acceptable system stability, medium fastness of response and without or with minimum possible overshoot, oscillation and error. For testing and evaluating the correctness, applicability and efficiency of the derived expressions, MATLAB/Simulink software was applied to develop refined software simulation model that simulates real life values and returns maximum needed numerical and graphical data for assessment process. In addition, various FOSTD systems’ types and forms were used in the simulation model, in particular, systems with small, medium and large time constants, DC gains, and time delay, unstable systems, systems with variable delay. Furthermore, to assess the efficiency of suggested design expressions, the resulted overall system response were compared with resulted responses when two design methods were applied; worldwide known Ziegler Nichols method and MATLAB/Simulink auto-tuned PID block. Analysis of numerical and graphical testing results, show that, The designed control algorithm applying the suggested expressions can, not only simplify the design process, but also, efficient for successful in getting system under control and improving controlling system performance, speeding up response, reduce overshoot, and minimize error, but also stabilize an unstable plants.

Comparison of closed loop performance of consistency process dynamics for various PID controller algorithms

In this work, various algorithms of PID (Proportional-Integral-Derivative) controllers such as series, parallel, series together with derivative filter and parallel together with derivative filter form are implemented for the comparative analysis of the closed loop responses of an important parameter in head box of a paper machine in a paper making process industry called consistency, which has FOPDT (First Order Plus Dead Time) dynamics. Also the comparison is made between the closed loop responses achieved from different values of derivative filter factor for non-ideal situations. The steady state and dynamic characteristics are analyzed and compared and important inferences are derived.