Time-delay Plants Research Articles

Analytical design of modified Smith predictor for second-order stable time delay plants incorporating a zero

Simplified control tuning not only enhances engineers' proficiency in control theory and its application but also contributes to their skill development. This study focuses on the control of stable second-order plus time delay (SOPTD) plants incorporating a zero, by employing a modified Smith predictor structure. A forward path PID controller and a PID controller with a lead/lag filter in the feedback path contribute to the proposed control system. The PID controller determines the set-point tracking. The load disturbance rejection is influenced by both the PID and lead/lag filter. Each controller is simply designed using pole placement, while considering a tuning parameter to make a balance between performance and robustness. Filtering of the set-point signal is implemented to enhance its response. To assess the effectiveness of the proposed technique, the study involves examining a SOPTD plant and either a negative or a positive zero. Simulation and comparison analysis show that the proposed controller is appropriate for industrial usage since it quickly tracks the set-point and efficiently rejects disturbances, resulting in a smooth control signal. Furthermore, robustness tests reveal its satisfactory degree of robustness against model parameter uncertainties. In summary, the proposed approach is straightforward and outperforms recently published design methodologies in terms of both performance and robustness.

Enhanced control of double integrating plus time delay systems using a two‐degree‐of‐freedom Smith predictor

AbstractThis article presents a novel control approach using a two‐degree‐of‐freedom (2‐DOF) Smith predictor structure for double integrating plus time delay plants. The PD and PID controllers, integral components of the Smith predictor scheme, serve distinct roles in the control process. The PD controller is responsible for set‐point tracking, while both PD and PID controllers contribute to the rejection of load disturbances. Each controller is designed using the pole placement technique, with an appropriate tuning parameter established to balance performance and robustness effectively. A low‐pass filter is incorporated to improve the response of the set‐point signal by attenuating high‐frequency noise. The proposed method's effectiveness is compared with Skogestad internal model control, a well‐known PID tuning method, to benchmark performance improvements and demonstrate the advantages of the 2‐DOF Smith predictor approach. Simulation and comparison analysis demonstrates that the proposed controller setting is suitable for industrial applications due to its quick set‐point tracking, effective load disturbance rejection, and smooth control signal. The study highlights the practical benefits of the 2‐DOF Smith predictor in enhancing industrial control system performance and suggests directions for future research, including experimental validation and robustness analysis under varying system parameters.

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.

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.

Non-Integer Order Proportional Integral Control for Time Delay Plant with Single Fractional Order

This paper studies the tuning of non-integer order proportional integral controller for time delay plants having one fractional order in its denominator polynomial. The well-known first order plus time delay plant is reorganized to have the order of the operator s to be an arbitrary real number. The main aim is to tune the parameters of the fractional order proportional integral controller to make the mentioned plant behavior to be stable and robust against unexpected changes in the gain of the system. The approach here is a graphical point of view on the Bode diagram. The two crossover points in the Bode diagram, the gain crossover frequency and the phase crossover frequency are tuned towards the desire of the researcher. This brought us to extend or to restrict the distance between these two crossover frequencies and thus, to provide the stability and robustness of the system. The design process is an analytical way from beginning to the end. Hence, the method is more reliable when compared with the methods based on optimization. This paper presents the findings of the first step in the research. The formulas to design the controller are found and the results are shown on an illustrative example.

On robust stability of second order plus interval time delay plants using Fractional-Order Proportional Integral Derivative controllers

The robust stability assessment of the second order plus interval time delay (SOPITD) plant controlled by Fractional-Order Proportional Integral Derivative (FOPID) controllers is the focus of this research. A simple graphical procedure for analyzing the robust stability of the interval system is presented based on the zero exclusion condition and the value set concept. The incorporation of an auxiliary function, derived through a judicious application of fundamental geometric principles intrinsic to convex polygons, serves to significantly alleviate the complexity and facilitate the application of the robust stability analysis approach, thereby affording a more streamlined and efficient means of designing robust control systems. Moreover, the computational burden for the robust stability analysis is also reduced by novel bounds. Moreover, a novel robust performance checking function is provided to improve the performance system. Three illustrative examples are then given to support the findings and show their applicability.

Distributed Filtering for Semi-Markov-Type Sensor Networks With Hybrid Sojourn-Time Distributions—A Nonmonotonic Approach

This article examines the distributed filtering problem for a general class of filtering systems consisting of distributed time-delayed plant and filtering networks with semi-Markov-type topology switching (SMTTS). The SMTTS implies the topology sojourn time can be a hybrid function of different types of probabilistic distributions, typically, binomial distribution used to model unreliable communication links between the filtering nodes and Weibull distribution employed to depict the cumulative abrasion failure. First, by properly constructing a sojourn-time-dependent Lyapunov-Krasovski function (STDLKF), both time-varying topology-dependent filter and topology-dependent filter are designed. Second, a novel nonmonotonic approach with less design conservatism is developed by relaxing the monotonic requirement of STDLKF within each topology sojourn time. Moreover, an algorithm with less computational effort is proposed to generate a semi-Markov chain from a given Markov renewal chain. Simulation examples, including a microgrid islanded system, are presented to testify the generality and elucidate the practical potential of the nonmonotonic approach.

Enhanced design of PI controller with lead-lag filter for unstable and integrating plus time delay processes

Abstract In this work, a proportional–integral (PI) controller with a set point filter is designed using the direct synthesis method for unstable plus time delay process. The Suggested method involves design parameters whose suitable values are recommended based on robust stability and robust performance constraints. The absence of derivative term makes PI controllers less sensitive to noise and, therefore, PI controllers are more preferable than PID in industrial applications. Despite a simple control architecture, the proposed method gives improved or comparable performance to previously presented approaches, which are comparatively complex. Four case studies are considered to evaluate the suitability and superiority of the suggested control technique. Proposed controller may be applied to the integrating plus time delay plants after some elementary transformations in the process model.

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.

A Time-delay Approach for Extremum Seeking of Nonlinear Static Maps:

This paper develops a constructive time-delay approach to averaging for gradient-based extremum seeking (ES) control of nonlinear static maps of non-quadratic form. Under the assumption that some prior knowledge of the nonlinear map with its derivatives is available, for the first time, we derive a quantitative analysis for ES close-loop systems with upper bounds on the tuning parameter that preserves the exponential stability and on the convergence error of extremum seeking. By transforming the ES system into a time-delay neutral type system with distributed delays, the developed method gives an accurate perturbed system of ES without employing any approximate calculation, and suggests a direct Lyapunov-Krasovskii approach in the form of linear matrix inequalities (LMIs), for the transformed time-delay plant to derive efficient stability conditions.

Cascade PID Control Systems Based on DNA Strand Displacement With Application in Polarization of Tumor-Associated Macrophages

Disturbances are widespread in biochemical systems. Nowadays, prevalent single-loop control strategies only take external disturbances into account. However, internal perturbations that threaten the stability of biochemical systems are invariably ignored. In this paper, a DNA strand displacement (DSD)-based cascade PID control system is designed. In addition to traditionally realizing the tracking of reference input and the attenuation of primary disturbance, the presented control approach also innovatively completes the rejection of secondary disturbance. Specifically, the dynamics of the reference input signal are first governed by a first-order low-pass filter integrated with cascade PID control systems, which efficiently avoids the excessive response of the cascaded primary and secondary controllers to the reference signal. Then, cascade PID controllers and second-order time-delay plants are constructed by utilizing the chemical reaction network (CRN) and the DSD. In terms of secondary perturbation suppression, the obtained control scheme significantly outperforms the single-loop PID control scheme with a smaller overshoot and faster settling time. Finally, the DSD-based cascade PID control method is applied to regulate gene expressions of interferon regulatory factor 4 (IRF4) and interferon regulatory factor 5 (IRF5) that affect the polarization of tumor-associated macrophages (TAMs). Compared with the single-loop PID control strategy, the control strategy exhibits a better inhibitory effect on IRF5 gene overexpression (internal disturbance) and TAMs endogenous gene expression (external disturbance).

An optimal robust design method for fractional‐order reset controller

AbstractIn this paper, a novel design method for the reset controller structure (i.e., fractional‐order proportional and integral plus Clegg integrator (PI + CI )), is proposed for a second‐order plus time delay plant. To this end, the designer can get an optimal fractional reset controller that gives the control system more phase margin over the base linear PI controller and robust to loop gain variation. The describing function method is used to investigate the capability of phase lead and the frequency domain properties of PI + CI . The gain crossover frequency and phase margin specifications ensure the stability of the control system, and the flat phase constraint makes the control system robust to loop gain variations. Meanwhile, the integral of time and absolute error (ITAE) value is applied to achieve the optimal dynamic performance as the cost function. PI + CI is compared with its integer‐order counterpart (i.e., proportional and integral plus Clegg integrator (PI + CI) controller) and their base controllers (i.e., integer‐order PI and fractional‐order PI controllers) in terms of the step response and robustness to loop gain variations. The simulation results illustrate that the PI + CI control system obtains lower overshoot and oscillation and better robustness to loop gain variations than others. The experiments are performed on the speed control of an air bearing stage. Experimental results show that the designed PI + CI control system behaves better than others. The proposed PI + CI design method can be applied to other general control plants easily.

Robust Stability Analysis of Unstable Second Order Plus Time-Delay (SOPTD) Plant by Fractional-Order Proportional Integral (FOPI) Controllers

This study investigates the robust stability analysis of an unstable second order plus time-delay (SOPTD) plant by using Fractional-Order Proportional Integral (FOPI) controllers. We assume that there are simultaneous uncertainties in gain, time-constants, and time-delay of the plant. At first, a graphical method is provided for a robust stability analysis of the closed-loop system. Then, a robust stability checking function is introduced to facilitate the robust stability analysis. Additionally, new bounds are presented to reduce the computational burden for the robust stability analysis. Finally, two examples are provided to show the correctness of the proposed method.

Frequency frame approach on tuning FOPI controller for TOPTD thermal processes

The frequency frame is used to tune fractional order proportional–integral​ controllers for stability, performance and robustness of third order plus time delay plants. Such plants are frequently used in describing thermal processes such as an air heater or a fired boiler. The aim is to tune the controller to meet some frequency domain properties. As robustness is an indispensable issue for thermal processes, main inspiration of the paper comes from flattening the phase curve in the Bode plot to provide improved robustness for the system. In spite of some existing studies, flattening is not realized by equalizing the phase derivative to zero at a given frequency value. Firstly, gain and phase crossover frequency points are enclosed with a rectangular frame. Then, lengths of the edges of this frame are changed to tune phase and gain margins. Curves inside the frame can be flattened by proper tuning of the edges. This will enhance the robustness and also ensure the iso-damping property. Equations to obtain the controller are given with two theorems. Demonstrations are made on two different thermal plants which are a novel electrical air heater and a bagasse fired boiler and the results are given on detailed illustrations. The results proved that preferred gain and phase properties are successfully obtained and improved performance and robustness are provided for related systems.

Fractional order proportional derivative control for time delay plant of the second order: The frequency frame

This paper intends to tune fractional order proportional derivative controller for the performance, stability and robustness of second order plus time delay plant. The tuning method is based on the previously proposed “frequency frame” which is a rectangular frame enclosing gain and phase margins limited with gain and phase crossover frequencies in the Bode plot. Edges of the frame are tuned to achieve desired crossover frequencies and margins. By shaping the curves of the Bode plot, improvements are observed in the performance and robustness of the second order plus time delay system controlled by a fractional order proportional derivative controller. Generalized equations to obtain the parameters of the fractional order proportional derivative controller for second order plus time delay plant are given. In contrast to existing studies, this method reduces mathematical complexity when providing desired properties. Three examples are considered and effectiveness of the frequency frame is shown.

Termal Sistemler için Oransal-Integral Denetleyici Tasarımı

This study proposes to tune proportional integral (PI) controllers for the stability and performance of thermal processes described by first order plus time delay (FOPTD) and second order plus time delay (SOPTD) plants. In addition to stability, parameters of the controllers are tuned to meet the desired gain crossover frequency and phase margin for each system. Design schemes of the controllers are clearly given and the results are applied on some plants provided from the literature. Illustrative examples are given to prove the method.

Smith predictor based fractional-order integral controller for robust temperature control in a steel slab reheating furnace

In this paper, a new strategy for robust control of temperature in a steel slab reheating furnace with large time delay uncertainty based on fractional-order controllers combined with a Smith predictor is proposed. A time delay model of the preheating zone of this process is used, obtained from an identification procedure applied in a real industrial furnace. It is shown that this process experiences very large time delay changes. A fractional-order integral controller embedded in a Smith predictor structure (FI-SP) is designed, which is robust to changes in such time delay. Simulated results of a standard Proportinal Integral Derivative (PID) controller, a PID controller embedded in a Smith predictor and the proposed FI-SP controller are compared. Six performance indexes have been used in this comparison. The analysis of these indexes shows that the designed FI-SP controller exhibits the most robust behavior (lowest indexes averaged in all the range of time delay variation) for ranges that include large time delays. Then the robustness features of the FI-SP controller outperform the other integer order controllers in the time responses both to set-point changes and to step disturbances. Therefore, this controller guarantees the best accuracy of temperature control. The designed FI-SP guarantees system stability and robust performance for a high range of plant time delay uncertainties.

Fractional order proportional derivative control for first order plus time delay plants: achieving phase and gain specifications simultaneously

The aim of the method in this paper is to achieve desired gain and phase specifications for robustness and performance of first order plus time delay plants. The previously proposed method “frequency frame”, implemented for tuning fractional order proportional integral controllers, is applied on such plants controlled with a fractional order proportional derivative controller. Four specifications of gain and phase are considered in the Bode plot inspired from an ideal system. The frame is drawn enclosing the magnitude and phase curves limited by gain and phase crossover frequencies. Then, the size of the frame is tuned to provide loop-shaping of the curves to meet desired properties. The iso-damping property is achieved by shaping the phase curve. Similarly, numerous studies in the literature work on robustness achievement by loop shaping the phase curve of the Bode plot. However, the “frequency frame” approach is a new perspective in controller tuning. Two examples are illustratively given to prove the proposed method. Plants in the examples are also considered to be due to load disturbances. Simulation results and effects of the method are clearly explained.

On robustness of an AMB suspended energy storage flywheel platform under characteristic model based all-coefficient adaptive control laws

A characteristic model based all-coefficient adaptive control law was recently implemented on an experimental test rig for high-speed energy storage flywheels suspended on magnetic bearings. Such a control law is an intelligent control law, as its design does not rely on a pre-established mathematical model of a plant but identifies its characteristic model while the plant is being controlled. Extensive numerical simulations and experimental results indicated that this intelligent control law outperforms a μ-synthesis control law, originally designed when the experimental platform was built in terms of their ability to suppress vibration on the high-speed test rig. We further establish, through an extensive simulation, that this intelligent control law possesses considerable robustness with respect to plant uncertainties, external disturbances, and time delay.

Synthesis of PI Controller with a Simple Set-Point Filter for Unstable First-Order Time Delay Processes and Integral plus Time Delay Plant

The paper describes PI controllers tuning for unstable first order time delay processes and integral plus time delay plant. The suggested method for designing a PI controller is based on the pole assignment method. Conditions for selecting the PI controller parameters in the function of the desired poles and parameters of the plant are met by using the features of the Lambert W function. The system stability in feedback is guaranteed by selecting the desired poles of the pre-defined range. The determined scope for pole selection includes the condition that this controller operates without integral gain, merely as proportional. The overshoot is reduced by using the simple first-order set-point filter. The manner of selecting the initial matrix which is used in a LambertW_DDE toolbox has been proposed. The illustrations of the simulation have been provided. Performances of the system regulated with a suggested PI controller are compared with the results received from other methods wherefrom it may be seen that this method yields better results in terms of the system settling time, rise time and IAE, ISE for set-point and good results in term of IAE, ISE for load disturbance and for the robustness on the uncertain changes expressed by the process parameter change of 10 %.DOI: http://dx.doi.org/10.5755/j01.eie.24.2.20629