First Order Plus Dead Time Model Research Articles

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.

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.

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.

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.

Control of TITO processes using sliding mode controller tuned by ITAE minimizing criterion based Nelder-Mead algorithm

Abstract Control of multi input and multi output (MIMO) process with interaction is often encountered in process industry. Such MIMO processes are controlled using conventional sliding mode controller (SMC) and tuned by integral square error (ISE) minimizing criterion based Nelder-Mead algorithm. SMC tuned by integral time absolute error (ITAE) minimization criterion based Nelder-Mead algorithm is proposed in this work. Three categories of two inputs and two outputs (TITO) process models are represented in the matrix form, with each of the matrix element representing a first order plus dead time (FOPDT) process. These TITO models are categorized based on the ratio ε, between dead time and time constant of the FOPDT model which forms the matrix element of the TITO model. The performance of conventional SMC is evaluated for these three categories of TITO models, in which the TITO process models with the ratio ε greater than the one, exhibited by poor closed loop performance, whereas the proposed SMC when applied to the these process models delivered superior closed loop performance.

Comparison of Model Predictive Controller and Neural Network Controller on Nonconventional Distillation Demethanizer/Deethanizer Rectifier/Column System

Nonconventional distillation demethanizer/deethanizer rectifier/column offers an economic advantage compared to conventional configurations by using sidestream from second column to remove the use of reboiler. However, this configuration brings a complex system that needs attention in its process control to ensure its operability. This work explores the use of neural network model predictive control (NNMPC) for this system. Aspen HYSYS was used to simulate the process, generate input-output data to develop the plant model and to conduct performance tests. MATLAB was used to conduct model identification, design the MPC and implement the multivariable control action. Sufficient time series data, where reflux valve positions and distillate compositions from each column act as input and output respectively, can be obtained from simulation and then utilized to train a nonlinear autoregressive exogenous (NARX) neural network which will be used as a predictive model. Model predictive Control based on this neural network model is designed to control distillate compositions for each column by the changes of reflux valve positions for each column as control signal. Least square algorithm from MATLAB function wass employed to optimize the cost function. A comparison has been made between NNMPC and conventional MPC configurations with first order plus dead time (FOPDT) model to test the performance of the controller based on disturbance rejection and set-point tracking test. Quantitative calculation was done using integral absolute error (IAE) with trapezoidal rule used as numerical integral method. NNMPC shows better performance than MPC with FOPDT model in set-point tracking test. However, NNMPC has a disadvantage on the cost function calculation algorithm, which did not account for the difference between plant and model value thus cause the MPC with FOPDT model to give better performance on disturbance rejection. Bias addition on NNMPC cost function algorithm made the controller has better responses to disturbance rejection compared to MPC.

Generalization of the FOPDT Model for Identification and Control Purposes

This paper proposes a theoretical framework for generalization of the well established first order plus dead time (FOPDT) model for linear systems. The FOPDT model has been broadly used in practice to capture essential dynamic response of real life processes for the purpose of control design systems. Recently, the model has been revisited towards a generalization of its orders, i.e., non-integer Laplace order and fractional order delay. This paper investigates the stability margins as they vary with each generalization step. The relevance of this generalization has great implications in both the identification of dynamic processes as well as in the controller parameter design of dynamic feedback closed loops. The discussion section addresses in detail each of this aspect and points the reader towards the potential unlocked by this contribution.

Pre‐computed GPC of a DC–DC buck converter

This study presents the control mechanism of a DC-DC buck converter using generalised predictive control by approximating the plant model to a stable first-order plus dead time (FOPDT) model. As most of the higher order plant dynamics can be represented by an FOPDT model, this study is limited only to a stable FOPDT dynamics system. In this work, a relation between FOPDT model parameters and weights of the cost function is derived. The controller design procedure is then verified by implementing voltage mode control of the DC-DC buck converter in the case of inactive constraints. Jury's stability criteria are used to analyse the stability of the closed-loop system. The implemented algorithm is then verified using simulation in MATLAB/Simulink, as well as the hardware implementation of the pre-computed control algorithm.

Model Reference Based Tuning for Fractional-Order 2DoF PI Controllers with a Robustness Consideration

Abstract The paper proposes the tuning of a two-degree-of-freedom (2-DoF) fractional-order PI (FOPI2) controller based on the Model Reference Robust Tuning (MoReRT) methodology presented by Alfaro and Vilanova (2012, 2016). The tuning rules are optimized for a first order plus dead time (FOPDT) model and for an over-damped servo and regulatory closed-loop target responses. Moreover, the design takes into account a robustness consideration, expressed as a maximum sensitivity target value of 2.0, dealing with the performance/robustness trade-off of the closed-loop control system. A set of controller tuning equations (four parameters) is provided for FOPDT models with normalized dead-times from 0.1 to 2.0. Also, an evaluation of the control system performance and robustness is presented, in order to show the effectiveness of the proposed tuning method, that is compared with other tuning rules.

L2–Optimal Fopdt Models of High–Order Transfer Functions

AbstractNecessary conditions for the L2 optimality of a first order plus dead time (FOPDT) model of a high‐order plant are derived using classic analytic function theory. They are expressed as a set of three nonlinear equations that partly resemble the interpolation conditions valid for rational approximation. From these conditions a simple procedure to find the optimal FOPDT model is obtained. Examples taken from the relevant literature are worked out to show the performance of the method in comparison with alternative techniques.

Dynamic modeling of friction stir welding for model predictive control

Controlling temperature in Friction Stir Welding (FSW) is important for consistent post-weld properties. PID temperature control of FSW has been previously implemented once the process is at a quasi-steady state, but has not worked well during either starting transients or during process changes that significantly alter the system dynamics. This work develops models and theories for the application of Model Predictive Control (MPC) to FSW and assesses temperature predication capabilities in simulation.Two different model forms are developed for MPC and are evaluated in simulation. The first model is a first-order plus dead time (FOPDT) model. The second is the Hybrid Heat Source model that combines the heat source method and a 1D discretized thermal model of the FSW tool. Model parameters are determined by fitting model predictions to weld data. This is done both manually and via optimization-based curve fitting. The models’ fits are compared quantitatively by calculating the mean-subtracted SSE (MSSSE) and average absolute derivative error. The manually tuned parameter sets result in a better fit by both metrics for both models. The FOPDT model matches the post-startup-transient data better than the Hybrid Heat Source, and is expected to have superior control in this region of the weld. The Hybrid Heat Source model is expected to have superior temperature control during the startup transient.

PIPIMC: Computational Tool for Teaching FOPDT Model Identification and PI-IMC Tuning

Modeling, PID controller tuning and advanced control design are necessary theoretical contents and of fundamental importance in the academic formation of electrical, chemical, automation and control engineers. Given the complexity and abstraction of control conceptions, several educational tools have been developed, with different characteristics and functionalities, trying to lessen the hardships in the teaching/learning relationship and offering students a larger set of options to understand these theoretical contents. This paper presents a new computational tool as an alternative for training, teaching and learning in First-Order Plus Dead-Time (FOPDT) plant identification and PI control tuning with Internal Model Controller (IMC), both using simplified models from the FOPDT representation. This educational software, called PIPIMC, has an interface which is pleasant, motivational and intuitive for the user, produces interesting dynamic results and was developed in Matlab® environment.

English

In process industries, the level of the liquid must be controlled and it is a mandatory process. But controlling a non-linear process is a highly complicated and complex process. Many process industries employs conical tank because of its non-linear shape, because of its constantly changing cross section, with respect to height controlling. For each operating region, the linear portion of the nonlinear process is determined as first order plus dead time model (FOPD). Different controller scheme such as conventional PID controllers based on Ziegler-Nicholas (ZN-PID) method, Chien, Hrones and Reswich (CHR-PID) method, Tyres-Luyben (T-L-PID) method, Internal Model Control (IMC-PID) and Model Predictive Controller (MPC) method were proposed and their responses was compared. The main objective of the controller is to provide a minimum settling time, peak overshoot and rise time and to provide a minimum performance error. Among the various controllers, Model Predictive Control (MPC) satisfies the above criteria. The controller will be simulated using MATLAB SIMULINK

Stability region analysis in Smith predictor configurations using a PI controller

This paper deals with the stabilization problem of Smith predictor structures using a PI controller. Stability regions that include all stabilizing parameters of a PI controller for the case of perfect matching between the plant and model and for mismatched case are obtained. The models of the plant are assumed to be FOPDT (first-order plus dead time) and SOPDT (second-order plus dead time) transfer functions. Thus, the aim of this study is to determine all stabilizing PI controllers for the Smith predictor scheme and to compare the stability regions obtained for perfectly matched and mismatched models. It is observed that the stability regions obtained for both cases are quite different and the stability regions for FOPDT and SOPDT models are broader than the stability region of the actual model. Furthermore, an approach is presented to find different models of an actual system using the stability region and it is shown that the stability region of these models can fit the stability region of actual system. A simulation example is provided to illustrate the results.

Application of Optimization Technique to Tune PID Controller for a Level Process

In any processes industry, process variables that need to be controlled are temperature, level, pressure and flow. This paper deals with an application of genetic algorithm to find the PID controller values to control the liquid level in the cylindrical tank. A process is identified as first order plus dead time model (FOPTD) and is validated. The intension of this paper is to obtain a minimum rise time, minimum setting time, and stable controlled system by obtaining the PID controller using conventional tuning method and Genetic Algorithm optimization technique. The simulation analysis was carried out for the mentioned PID controller settings. From the results based on time domain analysis, it is proved that the PID values are obtained using GA optimization technique yield a better perform than the conventional tuning method. General Terms Control System.

Analytical approach to tuning of model predictive control for first‐order plus dead time models

Model predictive control (MPC) is an effective control strategy in the presence of system constraints. The successful implementation of MPC in practical applications requires appropriate tuning of the controller parameters. An analytical tuning strategy for MPC of first-order plus dead time (FOPDT) systems is presented when the constraints are inactive. The available tuning methods are generally based on the user's experience and experimental results. Some tuning methods lead to a complex optimisation problem that provides numerical results for the controller parameters. On the other hand, many industrial plants can be effectively described by FOPDT models, and this model is therefore used to derive analytical results for the MPC tuning in a pole placement framework. Then, the issues of closed-loop stability and possible achievable performance are addressed. In the case of no active constraints, it is shown that for the FOPDT models, control horizons subsequent to two do not improve the achievable performance and control horizon of two provides the maximum achievable performance. Then, MPC tuning for higher order plants approximated by FOPDT models is considered. Finally, simulation results are employed to show the effectiveness of the proposed tuning formulas.

Air-Fuel Ratio Control of Spark Ignition Engines Using a Switching LPV Controller

The three way catalytic converter (TWC) is a critical component for the mitigation of tailpipe emissions of modern spark ignition internal combustion (IC) engines. Because the TWC operates effectively only when the air-fuel ratio is very close to stoichiometric, accurate control of the air-fuel ratio is required. This paper uses a switching linear parameter varying (LPV) controller to regulate the air-fuel ratio. For controller design purposes, the dynamics of the fuel path is modeled as a time-varying first-order plus dead time (FOPDT) model, varying with the engine operating point, i.e., engine speed and air flow. Large variation of the FOPDT model across the engine operating range leads to a conservative LPV controller. Therefore, the operating range is divided into smaller subregions, an individual LPV controller is designed for each, and the LPV controllers are then switched based on the operating point. The LPV controllers are found by solving a convex optimization problem with linear matrix inequalities (LMIs) which can be efficiently solved using available LMI techniques. The resulting closed-loop system has guaranteed performance over the operating range of the engine. Simulations show the improved air-fuel ratio regulation of the switching LPV controller over the engine's operating range compared to that of an H∞ controller which is scheduled based on air flow only as well as a non-switching LPV controller.

Physical parameter estimation in spatial heat transport models with an application to food storage

Parameter estimation plays an important role in physical modelling, but can be problematic due to the complexity of spatiotemporal models that are used for analysis, control and design in industry. In this paper we aim to circumvent these problems by using a methodology that approximates a model, or a part of a model, by a first-order plus dead time (FOPDT) approximation, explicit in the physical parameters. The FOPDT model with its physical parameters can be calibrated and validated to experimental data via an Output Error identification. The methodology is illustrated by a model of a temperature-controlled food storage room using experimental data. The complex part of the model is reduced to an accurate first-order model that has predictive power with respect to physical parameter variations. Moreover, this methodology allows one to test model adjustments for phenomena that were not considered in the physical model, in a relatively easy way.

A New Predictive PI Controller with Additonal Filtering

A new predictive PI controller is proposed and applied to the benchmark MIMO PID 2012. Estimate of disturbance, obtained from the Disturbance Observer (DO), is introduced in the loop to obtain the offset free control. First-Order Plus Dead-time (FOPDT) model of stable, integrating and unstable plants is used to design DO, by applying inverse modeling technique. Tuning rules are proposed, and analyzed by simulation of stable, integrating and unstable processes. The high performance of the proposed predictive PI controller with additional filtering is demonstrated by simulation and on the benchmark MIMO PID 2012 plant, with the open-loop dynamics approximated by FOPDT models for the pressure and the water level.

Tuning of Dynamic Matrix Controller for FOPDT Models Using Analysis of Variance

AbstractDynamic Matrix Control (DMC) is well known in the MPC family and has been implemented in many industrial processes. In all the MPC methods, tuning of controller parameters is a key step in successful control system performance. An analytical tuning expression for DMC is derived using the analysis of variance (ANOVA) methodology and nonlinear regression. It is assumed that the plants under consideration can be modeled by a First Order plus Dead Time (FOPDT) linear model. This facilitates the derivation of a closed form formulae for the tuning procedure. The proposed method is tested via simulations and experimental work. The plant chosen for practical implementation of the proposed tuning strategy is a nonlinear laboratory scale pH plant. Also, comparison results are provided to show the effectiveness of this method.