First Order Plus Dead Time Research Articles

Improved linear quadratic and proportional control system for improved liquid level system regulation in a coke fractionation tower

A new linear quadratic regulation (LQ) control plus a proportional (P) control system is proposed for the level regulation in an industrial coke fractionation tower. The process is first stabilized using a P controller and then a subsequent LQ controller is designed for the P control system. The P control system is modeled as a generalized first order plus dead time (FOPDT) process using step-response test and the LQ-P controller is designed through a new state space structure. Performance in terms of regulatory and servo issues were investigated. Simulation results showed that the proposed method is more robust and improves performance than traditional model predictive control.

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.

Robust tuning for machine-directional predictive control of MIMO paper-making processes

This paper solves the controller tuning problem of machine-directional predictive control for multiple-input–multiple-output (MIMO) paper-making processes represented as superposition of first-order-plus-dead-time (FOPDT) components with uncertain model parameters. A user-friendly multi-variable tuning problem is formulated based on user-specified time domain specifications and then simplified based on the structure of the closed-loop system. Based on the simplified tuning problem and a proposed performance evaluation technique, a fast multi-variable tuning technique is developed by ignoring the constraints of the MPC. In addition, a technique to predict the computation time of the tuning algorithm is proposed. The efficiency of the proposed method is verified through Honeywell real time simulator platform with a MIMO paper-making process obtained from real data from an industrial site.

Optimal disturbance rejection for PI controller with constraints on relative delay margin

Performance optimization with robustness constraints is frequently encountered in process control. Motivated by the analytical difficulties in dealing with the conventional robustness index, e.g., maximum sensitivity, we introduce the relative delay margin as a good alternative, which gives much simpler robust analysis. This point is illustrated by designing an optimal PI controller for the first-order-plus-dead-time (FOPDT) model. It is first shown that the PI controller parameters can be analytically derived in terms of a new pair of parameters, i.e., the phase margin and gain crossover frequency. The stability region of PI controller is subsequently obtained with a much simpler procedure than the existing approaches. It is further shown that a certain relative delay margin can represent the robustness level well and the contour can be sketched with a simpler procedure than the one using maximum sensitivity index. With constraints on the relative delay margin, an optimal disturbance rejection problem is then formulated and analytically solved. Simulation results show that the performance of the proposed methodology is better than that of other PI tuning rules. In this paper, the relative delay margin is shown as a promising robustness measure to the analysis and design of other advanced controllers.

Soft Computing Technique and Conventional Controller for Conical Tank Level Control

In many process industries the control of liquid level is mandatory. But the control of nonlinear process is difficult. Many process industries use conical tanks because of its non linear shape contributes better drainage for solid mixtures, slurries and viscous liquids. So, control of conical tank level is a challenging task due to its non-linearity and continually varying cross-section. This is due to relationship between controlled variable level and manipulated variable flow rate, which has a square root relationship. The main objective is to execute the suitable controller for conical tank system to maintain the desired level. System identification of the non-linear process is done using black box modelling and found to be first order plus dead time (FOPDT) model. In this paper it is proposed to obtain the mathematical modelling of a conical tank system and to study the system using block diagram after that soft computing technique like fuzzy and conventional controller is also used for the comparison.

A Model Identification Method for Tuning of PID Controller in a Smith Predictor Structure

In this paper, a model identification method is presented for tuning of PID parameters in Smith predictor structure based on internal model control. The purposed method fits stability boundary locus (SBL) of a plant model with SBL of a FOPDT (First Order Plus Dead Time) or a SOPDT (Second Order Plus Dead Time) model to determine the controller parameters. Two examples are employed to illustrate the applicability and simplicity of the purposed method in both tuning of controller parameters and identification of model parameters for an integer order plant and a fractional order plant.

HS 알고리즘을 이용한 계단응답으로부터 FOPDT 모델 인식

This paper presents an application of heuristic harmony search (HS) optimization algorithm for the identification of linear continuous time-delay system from step response. Identification model is first-order plus dead time (FOPDT), which describes a linear monotonic process quite well in most chemical processes and HAVC process and is often sufficient for PID controller tuning. This recently developed HS algorithm is conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. The effectiveness of the identification method has been demonstrated through a number of simulation examples.

Decentralized PID controller for TITO systems using characteristic ratio assignment with an experimental application

This paper presents a decentralized PID controller design method for two input two output (TITO) systems with time delay using characteristic ratio assignment (CRA) method. The ability of CRA method to design controller for desired transient response has been explored for TITO systems. The design methodology uses an ideal decoupler to reduce the interaction. Each decoupled subsystem is reduced to first order plus dead time (FOPDT) model to design independent diagonal controllers. Based on specified overshoot and settling time, the controller parameters are computed using CRA method. To verify performance of the proposed controller, two benchmark simulation examples are presented. To demonstrate applicability of the proposed controller, experimentation is performed on real life interacting coupled tank level system.

Experimental Validation of a Multi Model PI Controller for a Non Linear Hybrid System in LabVIEW

In this paper a real time Single Spherical Tank Liquid Level System (SSTLLS) has been chosen for investigation. This paper describes the design and development of a Multi Model PI Controller (MMPIC) using classical controller tuning techniques for a single spherical nonlinear tank system. System identification of these different regions of nonlinear process are done using black box modeling, which is identified to be nonlinear and approximated to be a First Order Plus Dead Time (FOPDT) model. A proportional and integral controller is designed using LabVIEW and Chen-Hrones-Reswick (CHR), Zhuang-Atherton (ZA), and Skogestad’s Internal Model Controller (SIMC) tuning methods are implemented in real time. The paper provides the details about the data acquisition unit, shows the implementation of the controller, and comparision of the results of PI tuning methods used for an MMPI Controller.

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.

Gradient-based step response identification of overdamped processes with time delay

In this paper, a step response identification method is proposed for overdamped industrial processes with time delay from sampled data by developing a gradient searching approach to minimize the output prediction error. Based on establishing a least-squares fitting of the time domain expression of a low-order process model, i.e. first-order-plus-dead-time (FOPDT) or second-order-plus-dead-time (SOPDT), with respect to a step change, the rational model parameters together with the delay parameter can be simultaneously estimated, while the computation effort can be significantly reduced compared to the existing step identification methods based on using the time integral approach for model fitting. Both cases of repetitive poles and distinct poles are considered for the identification of an SOPDT model, along with a guideline for a suitable choice of the model structure for practical applications. The convergence and accuracy of the proposed algorithms are analysed with a strict proof. Four illustrative examples from recent references are used to show the effectiveness of the proposed method.

Relative Time scale analysis for pressure propagation during ignition process of a scramjet

The supersonic combustion ramjet (scramjet) engine is expected to become the most efficient air breathing propulsion system in the hypersonic flight regime. The behavior of wall pressures propagation was examined using a direct-connect model scramjet experiment along with high-frequency pressure measurements. High-frequency pressure transducers are employed to record the history of pressure response during ignition process. A first order plus dead time (FOPDT) model is employed to model the S-shape step response curve. The time scale distributions of pressure propagation are reported in this paper. The characteristics of pressure propagation are closely related to the combustion mode of the scramjet.

SET POINT TRACKING CAPABILITY ANALYSIS FOR AN INDUSTRIAL IPDT PROCESS MODEL

In this paper the Proportional integral controllers based on Internal Model Control principles tuning technique for a pure integrating process with dead time is designed. The performance of these controllers with different closed loop time constants is analyzed and compared for its set point tracking capability. The controller with best performance for the selected time constant is decided. Every tuning procedure is centered on process model. The understanding of the operator who knows how the plant responds to the different inputs is the simplest model. Neglecting model uncertainty leads controllers unstable in the real world operations. The input is to be decided according to their importance. Finally the design specifications are given for good performance(1). A process model is a set of equations including the necessary input data to solve the equations that allows us to predict the behaviour of a chemical process system(2).The process whose model to be prepared may be with time delay or without time delay. The processes with time delay are the complex processes which are difficult to analyze .The delay time in the process is due to the transportation lag i.e. delay is always present with movement and due to the location of the sensors. The delay in the process may also be caused due to the delay in any part of the system. The delay in the process creates a serious problem in the designing process control system. The system with time delay are difficult to analyze and can be classified as first order plus dead time (FOPDT),second order plus dead time (SOPDT) and integral plus dead time (IPDT). The time delay present in the process can be approximated by different approximating techniques like Taylor's approximation, Pade's approximation etc. �

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.

Analytical Design of Fractional Order Proportional Integral Controller for Spherical Tank <sup></sup>

This paper presents an analytical design method for fractional order proportional integral (FOPI) controller for the spherical tank which is modelled as a first order plus dead time (FOPDT) process. The design is based on the Bode’s ideal transfer function and fractional calculus. By using frequency domain, the proposed FOPI tuning rules are directly derived for a generalized first order plus dead time process and then applied to the transfer functions obtained at various operating points of the spherical tank. The performance of the designed FOPI controller is compared with the conventional integer order proportional integral derivative (IOPID) controller in simulation.

Proportional stabilization and closed-loop identification of an unstable fractional order process

This paper deals with proportional stabilization and closed-loop step response identification of the fractional order counterparts of the unstable first order plus dead time (FOPDT) processes. At first, the necessary and sufficient condition for stabilizability of such processes by proportional controllers is found. Then, by assuming that a process of this kind has been stabilized by a proportional controller and the step response data of the closed-loop system is available, an algorithm is proposed for estimating the order and the parameters of an unstable fractional order model by using the mentioned data.

Comparing 2DOF PI and predictive disturbance observer based filtered PI control

This paper analyses the optimal nominal tuning of a new modification of predictive disturbance observer (PDO) based filtered PI control (PDO FPI) applied to a first order plus dead time (FOPDT) plant with exactly known parameters.The impacts of applied filters on optimal controller tuning and on achievable closed loop performance are evaluated first of all. The limits of achievable performance are compared with those of traditional two degree of freedom (2DOF) PI control, with both controllers tuned by the multiple real dominant pole method. This comparison shows the potential of PDO FPI control to improve tracking and regulatory dynamics significantly, permitting the Pareto-like servo/regulator trade-off of 2DOF PI control to be removed.Two PDO FPI tuning approaches are proposed, allowing optimal filter degree and time constants to be evaluated.The first tuning scenario considers optimization of closed loop performance expressed in terms of the Integral of the Absolute Error (IAE) weighted alternatively by the relative total variance TV1 of the control signal. This is carried out by changing the filter order n under the constraint that a constant position of the dominant closed loop pole is maintained. This keeps the dynamics of the setpoint step responses almost unchanged. In the second tuning scenario the optimization is carried out under a constraint on constant speed of disturbance step responses.All the main results are then numerically checked for the integral first order plant with dead time by the performance portrait (PP) method.The analysis presented here shows that the new PDO FPI structure substantially enriches the spectrum of controllers applicable to simple control tasks.

IMC–PID Design: Analytical Optimization for Performance/Robustness Tradeoff Tuning for Servo/Regulation Mode

ABSTRACTThis paper addresses the analytical design of a one‐degree‐of‐freedom (1‐DoF) robust proportional–integral–derivative (PID) controller for the servo/regulation mode in line with the enhanced internal model control (IMC) principle based on a first order plus dead time (FOPDT) model. The proposed enhanced IMC–PID can provide acceptable performance both for set‐point tracking and for load disturbance rejection. The design procedure is formulated as a constrained optimization problem, in which the robustness of the system is adequately considered. Therefore, the resulting PID controller gives optimal performance with an exact selected robustness degree. Illustrative examples are given to show the effectiveness and merits of the analytical tuning rules for a wide range of plants.

On tuning FO[PI] controllers for FOPDT processes

A method recently proposed for tuning fractional order [proportional integral] (FO[PI]) controllers is investigated. This tuning method, when applied in control of first-order plus dead time (FOPDT) processes, can ensure the desired phase margin, the desired gain crossover frequency and the flatness of the phase Bode plot at such a frequency. The necessary and sufficient condition for the applicability of the aforementioned tuning method is derived. Also, it is shown that this condition can be used in obtaining the achievable performance region of the tuning method in the gain crossover frequency-phase margin plane.