First Order Plus Time Delay Research Articles

FOPDT model and CHR method based control of flywheel energy storage integrated microgrid

The main causes of frequency instability or oscillations in islanded microgrids are unstable load and varying power output from distributed generating units (DGUs). An important challenge for islanded microgrid systems powered by renewable energy is maintaining frequency stability. To address this issue, a proportional integral derivative (PID) controller is designed in this article. Firstly, islanded microgrid model is constructed by incorporating various DGUs and flywheel energy storage system (FESS). Further, considering first order transfer function of FESS and DGUs, a linearized transfer function is obtained. This transfer function is further approximated into first order plus time delay (FOPTD) form to design PID control strategy, which is efficient and easy to analyze. PID parameters are evaluated using the Chien-Hrones-Reswick (CHR) method for set point tracking and load disturbance rejection for 0% and 20% overshoot. The CHR method for load disturbance rejection for 20% overshoot emerges as the preferred choice over other discussed tuning methods. The effectiveness of the discussed method is demonstrated through frequency analysis and transient responses and also validated through real time simulations. Moreover, tabulated data presenting tuning parameters, time domain specifications and comparative frequency plots, support the validity of the proposed tuning method for PID control design of the presented islanded model.

Robust fractional-order PID controller assisted by active disturbance rejection control for the first-order plus time-delay systems

Time-delay characteristics of various industrial processes may degrade the stability and dynamic performance of the control systems. Aiming at the problems of the existing methods in dealing with the time delay plant, a modified fractional-order proportional–integral–derivative (FOPID) controller for the first-order plus time-delay (FOPTD) system is developed. Assisted by a modified active disturbance rejection control (ADRC) scheme with increased observer bandwidth, the proposed FOPID controller inherently obtains good robustness to time-delay uncertainties and external disturbances. In addition, taking advantage of the fractional-order operator, the proposed controller can provide larger stability margin over the proportional–integral–derivative (PID) controller. By suitably establishing the relation between ADRC and FOPID controller parameters, the proposed controller can be analytically tuned based on the common design indices. A practical tuning guideline is developed according to frequency-domain characteristic analysis, making the proposed controller more acceptable to industrial application. The performance of the ADRC-based FOPID controller is tested by the control simulation of some typical FOPTD systems and a diesel engine speed regulation system. The efficiency of the ADRC-based FOPID controller is demonstrated by the comparisons with some existing controllers.

Trajectory tracking for non-holonomic mobile robots: A comparison of sliding mode control approaches

This paper implements and compares the performance of three controllers based on Sliding Mode Control (SMC) applied to the motion control of mobile robots. The controllers include a standard SMC controller and two variations, namely Dynamic Sliding Mode Control (D-SMC) and Dual Sliding Mode Control (DM-SMC). The three controllers differ from conventional SMC approaches since they are designed based on a generic reduced-order empirical model that can represent any system that exhibits behavior akin to a First-Order Plus Delay Time (FOPDT) system. In this study, the comparison of controllers focuses on the Trajectory Tracking Problem (TTP) of a Nonholonomic Mobile Robot (NMR). Performance indices are employed to quantify the controllers' results across three trajectory types. Simulation results evidence that if a smooth curvature trajectory is tracked, the best performance (in terms of minimizing trajectory tracking error and controller effort) can be obtained by using a DM-SMC. On the other hand, if there are discontinuities in the curvature, the results suggest that a better alternative is the D-SMC since it compensates for abrupt changes as in the case of tracking a square trajectory. Overall, the findings from this work demonstrated that the use of simplified empirical models to design SMC-based motion controllers can be successfully applied to solve the TTP of NMR.

Zero/low overshoot conditions based on maximally‐flatness for PID‐type controller design for uncertain systems with time‐delay or zeros

AbstractThis paper extends the characteristic ratio approach using novel inequalities to ensure zero/low overshoot for linear‐time‐invariant systems with zeros. The extension provided by this paper is based on the maximally‐flatness property of a transfer function, where the square‐magnitude of the transfer function is ensured to be a low‐pass filter. In order to be able to design low‐order/fixed structure controllers, a partial pole‐assignment approach is used instead of the full pole‐assignment used in the Characteristic Ratio Assignment (CRA) method. The developed inequalities and additional stability conditions are combined into an optimization problem using time domain restrictions when necessary. Although the method given in the paper is general, particular inequalities are developed for PI and PI‐PD controller cases, due to their frequent use in industrial applications. Similarly, First‐Order‐Plus‐Delay‐Time (FOPDT) and Second‐Order‐Plus‐Delay‐Time (SOPDT) systems are considered specifically, since most of the practical systems can be approximated by one of these types. The study is extended to plants with uncertainties where a theorem is developed to decrease computation time dramatically. The benefits of the proposed methods are demonstrated by several examples.

Will Fractional Order Model Based MPC Save Control Energy?

In real-world situations, many complex processes exhibit fractional order dynamic characteristics. In this context, the common integer order modeling methods may not appropriately capture the physics of these processes, leading to a less satisfactory controller design. This paper conducts a comparative analysis between the First order plus time delay (FOPTD) model and the Time Delay with Single Fractional Pole (TDWFP) model. These two modeling methods are employed to characterize a one-dimensional heat propagation process and two model predictive controllers are developed based on the models. The results demonstrate a better fitting performance in both time and frequency response with the TDWFP model. Furthermore, the TDWFP model-based Model Predictive Control exhibits reduced sensitivity to the prediction horizon and requires low control input energy. This indicates the potential of using fractional order model in MPC for improved control energy efficiency in practical applications.

Automatic Tuning of Level Controllers in a Flotation Bank using Bayesian Optimisation

A flotation bank consisting of 6 cells in series under Single-Input-Single-Output (SISO) Proportional Integral (PI) level control is automatically tuned using Bayesian Optimisation (BO). Open loop step tests from the valve position to the level are used to identify first-order plus time-delay (FOPTD) models for each flotation cell. The PI controller settings are tuned according to the Skogestad Internal Model Control (SIMC) tuning rules. Stability bounds derived from µ-analysis are defined using these SIMC settings. As the optimum achieved by the Bayesian optimiser is largely dependent on the parameter space provided to the tuning algorithm, this space is selected first to ensure stability and secondly for performance. The BO framework is able to tune each of the six SISO PI controllers to provide significantly improved level control over the original SIMC controllers with regards to different forms of the integrated error when the plant is subjected to step changes in the level setpoints and disturbances to the feed flow. This improvement comes at the cost of an increased number of tests to conduct.

A Particle Swarm Optimization tuned nonlinear PID controller with improved performance and robustness for First Order Plus Time Delay systems

The Proportional, Integral, and Derivative (PID) controller is a ubiquitous controller within industry. The conventional PID controller can struggle to provide a satisfactory response for the nonlinear systems faced by industry. In addition, conventional PID controllers have a trade-off between performance and robustness, where they cannot compensate for both without compromising stability or speed. In this paper, a novel Nonlinear gains Proportional, Integral, and Derivative (NLPID) control algorithm is proposed as a practical control strategy that shows improvements in the simultaneous set-point tracking and disturbance rejection, to control nonlinear systems. The paper shows the performance and robustness of the proposed controller for the case of a First Order Plus Time Delay (FOPTD) system, which heavily exists in industry. The Particle Swarm Optimization (PSO) algorithm is used to tune the proposed NLPID controller. The performance of the proposed NLPID controller is simulated and compared against established controllers in literature such as conventional PID, two degree of freedom PID, and Smith Predictor PID controllers in MATLAB/Simulink for an FOPTD system, with various uncertainties and disturbances. This study shows that the proposed NLPID controller maintains faster settling and rise time, with no overshoot and excellent disturbance rejection, without compromising stability or speed, and is robust against parametric, additive, and multiplicative uncertainties.

Robust tuning of uncertainty and disturbance estimator-based control for stable processes with time delay

To expand the potential of uncertainty and disturbance estimator (UDE)-based control in practical application to most industrial stable processes, this paper proposes a convenient yet robust tuning rule according to the widely used first-order plus time delay (FOPTD) plant. The Smith predictor is first introduced to anticipate the delay-free output, which guarantees signal synchronizations in three control modules and enables remarkable restorations of nominal stability and performance. Then a second-order filter is employed in UDE to decouple the trade-off between disturbance rejection and noise attenuation. Based on this improvement and fixing both tracking speed and feedback gain to suggested patterns, the exhaustive evaluations for robustness against model distortion are executed through scanning the dimensionless filter bandwidth. The boundary demarcation triggered by the plunge of the continuous range of tolerable mismatched delays subsequently facilitates the formulation of an intuitive tuning rule with prescribed robustness. Its inherent model-based scaling property largely enables this rule to be implemented readily in industrial processes just like the proportional-integral-derivative (PID) controller. Several representative simulations are performed to demonstrate the merits of the proposed method over the related control strategies. And the promising prospect of the UDE-based control in the practical application is further illustrated by conducting a water level control experiment.

Online Tuning Diagnosis of Proportional Integral Derivative Controller based on IEC 61499 Function Blocks

Controller performance is a crucial aspect of industrial processes; hence, it is critical to maintaining optimal controller performance conditions. Bad controller performance can be caused by poor proportional integral derivative (PID) controller tuning those results in aggressive and sluggish controllers’ behavior. Correct diagnosis of poor controller tuning becomes vital so that it can adequately handle the controller. This study designs several function blocks for online diagnosis of poor PID controller tuning based on the IEC 61499 standard. The design of the function blocks began with design the method used for diagnosing a poor controller tuning. The procedure was based on autocorrelation function (ACF), comparison of signal to noise ratio (SNR) estimation, and idle index. The function blocks were validated with first order plus delay time (FOPDT) processes, which had aggressive, sluggish, or well-tuned behavior. The function blocks were implemented on a Fluid Catalytic Cracking (FCC) plant and industrial data with various process faults to evaluate its capability to diagnose a poor controller tuning. The developed function block can precisely analyze a poor controller tuning on FCC plant and 8 of 10 industrial data. It showed that the function blocks could diagnose a poor controller tuning correctly if the oscillation were regular.

Data-driven iterative tuning based active disturbance rejection control for FOPTD model

Active Disturbance Rejection Control (ADRC) emerges as a promising control method that can effectively handle uncertainties and disturbances. However, many model-based ADRC tuning methods turn laborious to achieve satisfactory control performance, when the critical process parameters are difficult to accurately obtain, especially the time delay information. To this end, this paper aims to propose a data-driven iterative tuning method for time-delayed ADRC (TD-ADRC). Based on parameter scaling technique, the quantitative correlation among control performance, robustness and normalized controller parameters are investigated. It is then used to design robust nominal controller. Then, based on the TD-ADRC inner-loop equivalent structure, an iterative feedback tuning (IFT) method is proposed to optimally obtain the nominal first order plus time delay (FOPTD) process model. Its unbiasedness and convergence are also described. With the empirical relations and the IFT stochastic approximation algorithm, a data-driven iterative tuning method for TA-ADRC is proposed, which allows a reasonable trade-off between system performance and robustness. Simulation results validate the efficacy of the proposed method, and a water-tank control experiment depicts a promising prospect in control practice.

Simple model reduction technique for transfer function models

AbstractIn this work, a novel model reduction method is proposed for transfer function models. The method is based on equating the ratio of the coefficients of the ‘s’, powers of ‘s’ in the numerator to the corresponding coefficients of the s, powers of ‘s’ in the denominator of the closed‐loop transfer function of the higher order process to the closed‐loop transfer function of the reduced order model with PI controlling settings. Using this method, a stable higher order process is reduced to a first‐order plus time delay (FOPTD) model. The step response of the closed loop of the reduced order model is compared with the corresponding higher order process. The efficiency of the proposed method is shown for several examples and for the experimental temperature control process. By the proposed reduction method for higher order processes without zero, the reduced model time constant is simply written with the addition of the all time constants of the higher order process.

Tuning Generalized Predictive PI controllers for process control applications

Predictive PI (PPI) controllers have demonstrated to exceed traditional PID controllers when they are applied to systems with long delays. This work proposes a new controller structure and tuning that we call Generalized Predictive PI (GPPI) controller which provides greater design flexibility than PI and PPI strategies. To realize a fair comparison, the design and tuning rules for discrete PI and PPI controllers were developed using optimal arguments based on the root-locus, for critically damped response before a step change in the reference. Experimental results, using industrial equipment, have illustrated the tuning methodology and the performance of the proposed controller under real conditions. Flow and water level process in a laboratory flume were considered. For these processes, First Order Plus Time Delay (FOPTD) models are used. The GPPI control results are encouraging, reducing the settling time plus a very small overshoot before step change in the reference regarding the PI and PPI strategies, up to 41.03% for the flow control loop and up to 54.21% for the level control loop. The discrete analysis of the strategies in the Z plane was performed, allowing for a direct translation to recursive equations that can then be programmed into a Programmable Logic Controller (PLC), other industrial controllers such as Distributed Control Systems (DSC), or microcontrollers, such as Arduino, Raspberry or FPGA. This is an important result, since it demonstrates that the increased complexity of the proposed controller does not hamper its implementation in industrial controller systems. In this work, we used a Rockwell ControlLogix \\protect \\relax \\special {t4ht=®} PLC with Structured Text programming language.

Quantitative Tuning of Active Disturbance Rejection Controller for FOPTD Model With Application to Power Plant Control

Active disturbance rejection controller (ADRC) has achieved soaring success in motion controls featured by rapid dynamics. However, it turns obstreperous to implement it in the power plant process with considerable time-delay, largely because of the tuning difficulty. To this end, this article proposes a quantitative tuning rule for the time-delayed ADRC (TD-ADRC) structure based on the typical first order plus time delay (FOPTD) model. By compensating the FOPTD process as an integrator plus time delay in low frequencies, the gain parameter of TD-ADRC can be related to a scaled time constant which shapes the closed-loop tracking performance. Bandwidth parameter of extended state observer is scaled as a dimensionless parameter. A sufficient stability condition of TD-ADRC is theoretically derived in terms of the scaled parameter pair, the range of which falls within the practical interest. Relative delay margin is revealed as a critical robustness metric among others, a default pair of scaled parameter setting is recommended as well as an explicit retuning guideline according to the user's preference for performance or robustness. Simulation and laboratory water tank experiment validate the tuning efficacy and a coal mill temperature control test depicts a promising prospective of the proposed method in process control practice.

Optimal robust fractional order PI[formula omitted]D controller synthesis for first order plus time delay systems

In this paper, a practical and systematic tuning procedure combining both frequency-domain (FD) and time-domain (TD) specifications is proposed to obtain an optimal robust fractional order (FO) PIλD (FOPIλD) controller for the first order plus time delay (FOPTD) processes. The FD specifications (i.e. phase margin (PM), gain crossover frequency (ωgc) and flat phase constrain (FPC)) guarantee the systemic stability and robustness to plant gain variations. Meanwhile, the TD specification (i.e. the smallest JITAE) achieves optimal dynamic performance. Furthermore, the entire feasible regions of two frequency-domain specifications ωgc and PM have been obtained with a synthesis scheme and visualized in three-dimensional plots which can be used as prior knowledge before the controller design. The comparisons of feasible region with FOPI and integer order PID (IOPID) controllers clearly present the superiority of proposed FOPIλD controller. Simulation illustration for delay dominant systems, lag dominant systems and high order system with one zero, using the proposed optimal robust FOPIλD controller is presented to demonstrate the significant performance improvement over FOPI controller, three-parameter FOPID controller, Ziegler–Nichols FOPID controller, fractional filter-FOPID controller and SIMC-PI controller.

Shape factor for the relay feedback autotuning

ABSTRACT Relay in the feedback loop produces a stable oscillation whose cyclic steady state response contains process information of ultimate gain and ultimate period. By measuring these process data and Ziegler-Nichols type tuning rules, PID controllers can be designed. Due to its simplicity and performances, this earlier relay feedback method becomes one of the standard methods for autotuning of PID controllers. Later the first-order plus time delay (FOPTD) models are used for the relay feedback method with additional process data such as the process steady-state gain, improving autotuning performances. Like other FOPTD model-based methods, this FOPTD model-based relay feedback method is very popular in the field. However, for some high-order processes, the FOPTD model-based method shows oscillatory closed-loop responses that are not acceptable. For such processes, the critically damped second-order plus time delay (C2PTD) identifiable with the same three process information of steady state gain, ultimate gain and ultimate period can be used. Unfortunately, the C2PTD model-based relay feedback method cannot cover the whole range of processes. One solution is the selective use of FOPTD and C2PTD models. For this purpose of selection, a shape factor that uses the process measurement of average residence time is proposed here.

First‐order plus time‐delay systems under the effects of actuator rate limit

Actuator rate limit phenomenon is ubiquitous in control systems, but it has always been neglected in practical engineering. Especially, few papers are published to investigate the system identification while considering the rate limit. Step function is commonly used in parameter estimation and its first-order derivative at the step time goes to infinity, which is not affordable by real actuators. As a result, the rate limit slows down the system response speed, misleads the parameter identification, and subsequently affects the controller design and deteriorates the control performance. This study proposes both graphical method and curve fitting method to identify the first-order plus time-delay (FOPTD) systems with consideration of the actuator rate limit effect whose limit value is unknown. Quantitative analyses of the parameter mismatch in the traditional FOPTD model and parameter sensitivity analyses are also carried out. Both simulation results and experimental results have shown the necessity and feasibility of defining a new model structure which includes the rate limit value.

Robust internal model controller with increased closed‐loop bandwidth for process control systems

This study proposes a modified internal model control (IMC) structure in which an additional controller is added to the standard IMC structure to improve the closed-loop system bandwidth. The resulting structure is evaluated to satisfy standard IMC objectives of nominal performance and robust stability. The novelty of the work is to design a fractional order (FO) filter in the IMC structure so that gain margin ( A m ) and phase margin ( ϕ m ) specifications could be independently satisfied for a first-order plus time delay (FOPTD) process control plant. The proposed modified IMC (m-IMC) is simulated for three different FOPTD systems to validate and substantiate the theoretical analysis. The proposed m-IMC is compared with different integer order as well as FO controllers. The transient performance are compared in terms of rise time ( T r ), settling time ( T s ), maximum overshoot (% M p ) and the effectiveness is measured in terms of integral square error. To validate the viability of the proposed control scheme, it is implemented on a laboratory DC servo-system.

Assessment of spatial-temporal characteristics for disturbance propagation with combined FOPDT and Padé Approximant in large-scale power system

In large-scale power system, the frequency response for disturbance exhibits spatial and temporal characteristics, of which a proper model for the propagation mechanism is not clear. In this paper, the disturbance power propagates along the transmission line and is treated as external excitations for the distributed generators. The dispersion of disturbance power causes the spatial-temporal features of frequency dynamics. The propagation is mainly divided into electro-magnetic and electro-mechanical stages. The process is modulated by the Kirchhoff laws and swing equation with the temporal and spatial distribution. The disturbance power, generators’ inertia and line parameter determine the propagation model. A combination of First Order Plus Delay Time (FOPDT) and Padé Approximant are proposed to extract the propagation delay. The mathematical solution of propagation delay is obtained for a one-dimensional ring system and a two-dimensional system. Numerical results are presented to verify the proposed models on a one-dimensional 32-machine ring system, two-area four-machine system and WECC-179 bus system.

Robust decentralized proportional–integral controller design for an activated sludge process

AbstractThis paper presents the design of a decentralized proportional–integral (PI) controller for a wastewater treatment plant (WWTP). The aeration rate and the return recycle sludge rate are manipulated inputs to the WWTP process, while substrate and biomass concentration are considered as the output variables. The study is divided into two segments: A decentralized controller is designed based on the best pairing in the first segment, and in the second segment, a decoupler is developed to reduce the interactions. Decouplers are generally used to create independent loops in the multivariable control loops. Each decoupled subsystem is converted to first order plus time delay (FOPTD) model using a system identification toolbox to design independent diagonal controllers. The numerical simulations have been performed to evaluate the effectiveness of the presented methods. Furthermore, a robustness study has also been carried out by taking into account multiplicative input and output uncertainties, and it is found that the controller designed based on minimizing the integral of absolute error (IAE) criteria shows more robust.

The influence of rate limit on proportional–integral controller for first-order plus time-delay systems

The control performance can be worsened by actuator rate limit, which can result in amplitude attenuation and phase delay in process control. In some extreme situations, actuator rate limit may bring about the system non-convergence. This paper focuses on the control difficulties and solutions of first-order plus time-delay (FOPTD) systems caused by rate limit. The influence of rate limit on stability regions of proportional–integral (PI) controller is analysed. Results show that a small rate limit value can reduce stability regions of PI parameters greatly. The negative correlation between the integral gain and the onset frequency, and the positive correlation between the proportional gain and the onset frequency are conducted. Moreover, the control performance of different PI tuning rules such as Skogestad internal model control, integral gain maximization, delay robustness-constrained optimization and Tyreus–Luyben​ tuning rules is evidently affected by rate limit. Simulation and experiment results verify that the PI controller tuned by Skogestad internal model control (SIMC) method is less sensitive to the rate limit variation and is more suitable for processes (the normalized dead-time is from 0.03 to 1) which have severe actuator rate limit. Tyreus–Luyben tuning rule is another optional method. In addition, the reasons why SIMC is not sensitive to rate limit variation are analysed. These analytical results can offer a guideline for practical applications.