System Dead Time Research Articles

Efficient parameter estimation for second order plus dead time systems in process plant control

AbstractDesigning a controller for a process plant typically modeled as a first or second‐order system with dead time involves an efficient and accurate estimation of its parameters. Since many process plants are characterized as second‐order plus dead time (SOPDT) overdamped or critically damped systems, this study presents a straightforward parameter estimation method using transient response data from a step input at three specific time instants. Two‐time domain performance indices (PIs), (= for system dead time = 0 and for system dead time ≠ 0; , and are respectively the times at which the response reaches 5%, 10% and 90% of the steady‐state response) and (reciprocal of rise time ) are proposed in this work. Correlations are established between these PIs and the parameters of the SOPDT system. The first correlation establishes that is a function of the damping ratio only and is independent of the undamped natural frequency which means that the evaluation of from the time response data is sufficient to estimate . The second correlation establishes that for a given , is a function of . Thus the evaluation of from the time response data and an estimate of from the first correlation is sufficient to estimate . The proposed algorithm estimates the parameters of the canonical transfer function of the plant by these correlations from the three specific time instants, as mentioned above, of the step response of the plant. Comparisons with four methods existing in the literature reveal that the method is also effective with higher order systems that may be approximated by SOPDT dynamics, and robust even with measurement noise, making it useful for implementing control strategies, not only in process plants but also in other systems having similar time responses.

High-rate Gamma Spectrometry Using a LaBr3(Ce) Scintillator with a Fast Pulse Shaping.

The performance of a LaBr3(Ce) gamma spectrometer at high count rates was investigated up to an input count rate of 1.3 Mcps. In order to make its pulse processing faster, a preamplifier provided by the detector manufacturer was eliminated, and the signal from the photomultiplier tube was fed directly to a digital pulse processing system. To accomplish both fast pulse processing and good energy resolution, the pulse-shaping parameters were optimized at a low count rate of 1.5 kcps, and then measurements were carried out at various count rates. Input count rates ranging from 1.5 kcps to 21 kcps were produced using a set of 137Cs resin sources, while higher rates between 45 kcps and 1.3 Mcps were produced using a 1.2-GBq 137Cs source. The spectrometer showed an excellent performance for the input rate up to 150 kcps, while the dead time increased rapidly for the input rates above 150 kcps. The system dead time has been improved greatly by eliminating the preamplifier.

Control of cascaded series dead-time processes with ideal achievable disturbance attenuation using a predictors-based structure

This paper proposes a cascade series control structure and design for two series processes represented by first-order plus dead-time FOPDT models. The proposed controller uses two series predictors, one for each process, and can deal with stable, unstable, or integrative processes. The design follows similar principles of the simplified filtered Smith Predictor (SFSP) for a single-loop dead-time system. Initially, the primary controller, composed of a set-point static gain and two feedback controllers, is tuned to achieve the desired set-point tracking. Then, the predictor filters are tuned to ensure stability, robustness, and disturbance attenuation. Different from standard cascaded SFSP, one of the feedback controllers, instead of only a static gain, includes a finite time integral. The main advantage of this approach is that disturbances generated in the primary or secondary process can be handled independently by the predictor filters, simplifying the tuning procedure and enhancing the overall control performance. Additionally, for the nominal case, the proposed cascaded controller allows obtaining an ideal set-point tracking and disturbance rejection. After the dead-time effect, the proposed cascade controller achieves the set point exponentially and rejects exponentially step-like disturbances where the user defines the time constants of the exponentials. Simulation results demonstrate the advantages of the proposed controller compared to other recently published approaches, mainly in the inner loop disturbance rejection, which is precisely what is expected from a series cascade controller.

Using Constrained Convex Optimization in Parameter Estimation of Process Dynamics with Dead Time

Abstract This paper proposes the usage of constrained convex optimization in improving the quality of the parameter estimates of a typical process plant with dead time from its time response data by incorporating system-specific constraints that are not considered in standard estimation methods. As the majority of the process plants are identified as second-order plus dead time (SOPDT) systems, the proposed method uses the same for establishing the optimization process. Traditional methods for parameter estimation in SOPDT systems have often relied on heuristic approaches or simplified assumptions, leading to suboptimal results. The proposed methodology augments the accuracy of the estimated values by leveraging the power of constrained convex optimization techniques, using Newton's Quadratic Model and Sequential Quadratic Programming, which provide a rigorous mathematical framework for parameter estimation. By incorporating system constraints, such as bounds on the parameters or stability requirements, it is ensured that the obtained parameter estimates adhere to physical and practical limitations. The proposed approach is demonstrated using simulations and on a real-time system, and the results show that it is effective not only in accurately estimating the parameters of the underdamped SOPDT systems but also works efficiently for parameter estimation of SOPDT systems in the presence of measurement noise. The efficacy of the proposed algorithm is verified by comparing it with similar published methods.

A PID Control Architecture Based on IEC 61499

This work presents an approach for PID control and optimization in a distributed system, using the IEC 61499 control standard. This standard enables communication among different PLCs, which are used to develop a three-layered event-driven control of a SISO loop. The lowest layer is in charge of cyclical data acquisition. The second layer carries out an event-based PID control. The highest layer runs a control optimization algorithm, specifically a simple tuning approach based on Ziegler-Nichols that is used to determine the PID parameters for different operating points. The proposed approach is assessed in a tank level SISO control problem, whose behavior can be modeled as a first-order plus dead time system in each operating point. For that purpose, it has been implemented using two PLCs and a software PLC running on an industrial computer. The experimental results on the SISO level control loop show the feasibility of the proposed approach for event-driven control in a distributed system and open interesting research questions in the intersection of controller design and distributed automation.

Application of Quasi-Fractional Order PI Controller to IPDT Plant Control

The paper focuses on the design of a fractional order PI controller (FO-PI) and the verification of the properties of the control loop with an integral plus dead time (IPDT) system. The fractional order integrator in the controller is approximated by the Oustaloup method. The multiple dominant pole method (MDPM) is used to tune the controller parameters. The input parameters for controller tuning are obtained by optimization using the algorithm presented in the paper. The properties of the control loop with the FO-PI controller tuned in this way have been verified by simulation and compared with the properties of the control loop using an integer order PI controller.

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

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

Tuning of PID controllers for unstable first-order plus dead time systems

Abstract In this paper, proportional-integral-derivative (PID) controllers are tuned for unstable first-order plus dead time (UFOPDT) systems. Genetic algorithm (GA) is used to find the parameters of the PID controller for UFOPDT systems under the constraint of robustness measure. By curve fitting, the controller parameters are expressed as the functions of the UFOPDT model parameters. Two tuning formulas which consider robustness and the tradeoff between disturbance rejection and robustness of the closed-loop system are proposed. The proposed tuning formulas extend the application range of the existing methods and simulation results show that the tuned PID controllers can achieve good performance for UFOPDT systems.

Residence Time Distribution-Based Smith Predictor: an Advanced Feedback Control for Dead Time–Dominated Continuous Powder Blending Process

PurposeIn continuous manufacturing (CM), the material traceability and process dynamics can be investigated by residence time distribution (RTD). Many of the unit operations used in the pharma industry were characterized by dead time–dominated RTD. Even though feasible and proper feedback control is one of the many advantages of CM, its application is challenging in these cases. This study aims to develop a feedback control, implementing the RTD in a Smith predictor control structure in a continuous powder blender line.MethodsContinuous powder blending was investigated with near-infrared spectroscopy (NIR), and the blending was controlled through a volumetric feeder. A MATLAB GUI was developed to calculate and control the concentration of the API based on the chemometric evaluation of the spectra. The programmed GUI changed the feeding rate based on the proportional integral derivative (PID) and the Smith predictor, which implemented the RTD of the system. The control structures were compared even on a system with amplified dead time.ResultsIn this work, the control structure of the Smith control was devised by utilizing the RTD of the system. The Smith control was compared to a classic PI control structure on the normal system and on an increased dead time system. The Smith predictor was able to reduce the response time for various disturbances by up to 50%, and the dead time had a lower effect on the control.ConclusionsImplementing the RTD models in the control structure improved the process design and further expanded the wide range of applications of the RTD models. Both control structures were able to reduce the effect of disturbances on the system; however, the Smith predictor presented more reliable and faster control, with a wider space for control tuning.

A predictor for square multivariable dead-time systems with multiple delays based on the Kalman filter

Dead-time is a phenomena that is present in many industrial processes and it presents a challenge for feedback control, especially for multivariable processes. To attenuate the dead-time effects, a common method is the use of predictor structures, which use input/output information of the process to predict the output (or states) of the system after the dead-time. In this paper, the Modified Kalman Predictor (MKP) is proposed, which is a novel predictor for linear multivariable square systems with multiple dead-time (or delays) based on the Kalman Filter that has disturbance estimation and can cope with systems of any order or dynamics, including unstable ones. It uses a specific state-space representation of the process which makes its implementation more straight-forward when compared to other methods. The MKP affects the disturbance rejection but not the closed-loop stability in the nominal case, and it can help to improve closed-loop robustness in the uncertain case. The impacts of the MKP tuning in the closed-loop response considering disturbance rejection and robustness are analyzed using standard frequency domain tools. To illustrate the benefits of the MKP, two examples are used that highlight the tuning guidelines for disturbance rejection and robustness improvements.

A Novel Toolbox for Automatic Design of Fractional Order PI Controllers Based on Automatic System Identification from Step Response Data

This paper describes a novel automatic control toolbox, designed for non-experienced practitioners. Fractional order (FO) controllers are easily tuned with the main purpose of easy practical implementation. Experimental step data are required for the automatic FO controller tuning. An embedded system identification algorithm uses the step data to obtain a process model as a second order plus dead-time (SOPDT) system. Finally, the FO controller is computed based on the previously estimated SOPDT model in order to fulfil a set of user-imposed frequency domain performance specifications: phase margin, gain crossover frequency and gain margin maximization. Experimental step response data from a strongly nonlinear vertical take-off and landing unit have been used to design an FO controller using the toolbox. The experimental closed loop results validate the proposed toolbox. The end result is a user-friendly automatic fractional order controller tuning with endless possibilities of real-world applicability.

An Interval Approach for Robust Parameterization of Controllers for Electric Drives

Uncertain models, e.g., due to component variations and measurement errors during system identification, in combination with the desire to be able to provide guarantees regarding system performances a priori, represent major challenges for users when designing controllers on the basis of models. The aim of this publication is to mitigate this obstacle in the design. For this purpose, criteria of classical control engineering are combined with interval arithmetic in general and the SIVIA algorithm in particular. Thereby, the approach is valid for linear dead time systems. The algorithm evaluates performance criteria for closed interval-bounded sets of parameter values in a single iteration. When overestimation prevents a definite result, the size of the parameter set is recursively reduced by bisecting the evaluated set. The application of the methodology to the controller design for an electromechanical linear actuator shows that the approach not only contributes to theory but can also simplify the practical controller design, especially in the area of electric drives.

FITEVT: A FORTRAN program for arrival-time analysis of nuclear-decay events

FITEVT is a FORTRAN program designed to analyze recorded arrival times of nuclear-decay events affected by dead-time. The primary goal of the program is precise and accurate determination of half-lives. Its method involves imposition of a known sufficiently long extending dead-time to the recorded event sequence, so that the original dead-time effects are completely obliterated and the remaining live-times of the survived events are known exactly. Upon completion of the analysis, the arrival-time spectrum and the live-time spectrum are predicted and compared to those constructed from the survived events. Program summaryProgram title: FITEVTLicensing provisions: MITCPC Library link to program files:https://doi.org/10.17632/scg6p9jxjk.1Programming language: FORTRAN (using double precision)Nature of problem: Accurate determination of the ideal event rate from the observed event rate in a nuclear decay can be a challenging task due to the inevitable presence of detection system's dead-time, whose nature and extent are typically unknown. Consequently, the results of nuclear half-life measurements may depend on the method used to correct for event losses due to dead-time. Therefore, there is a need for an exact method of data analysis and the means to apply it in order to ensure reproducibility, accuracy and optimized precision of the results.Solution method: FITEVT performs arrival-time analysis of the recorded events, in which a known, sufficiently large extending dead-time is imposed by means of software, so that in the resulting set of survived events the original dead-time effects are completely replaced by the effects of the imposed dead-time. As a result, the dead-time following each survived event and the remaining live-time preceding each surviving event are known exactly. This allows for application of the maximum-likelihood method of estimation, in which the half-lives as well as the other parameters of the ideal-decay-rate function can be accurately determined.Additional comments including restrictions and unusual features: In its original form the program can handle contributions from a constant event rate (i.e., a typical background) plus up to 4 different exponentially-decaying event rates. One of these 4 contributions is allowed to be negative, so that the program can be applied to the general case involving a single two-component decay chain. The employed method of analysis produces accurate results even when the product of the ideal event rate (ρ) and the extending dead-time parameter (τe) is as large as 51.2 [1]. Example used in the present paper involves simulated events having initial rate of 105 s−1, to which extending dead-time of 64 μs is imposed.Data analysis is based on maximum-likelihood principle, in which minimization of the deviance involves calculations in double precision and determination of its derivatives is based on analytical expressions. This is done in order to optimize precision and accuracy of the results as well as the program execution time.With the provided input data and a typical contemporary laptop computer, the program execution typically lasts about 5 minutes. Reducing the imposed dead-time to zero increases the number of survived events approximately by a factor of 6, but the program execution time increases by about a factor of 3.

A Fractional-Order On-Line Self Optimizing Control Framework and a Benchmark Control System Accelerated Using Fractional-Order Stochasticity

This paper presents a design and evaluation of a fractional-order self optimizing control (FOSOC) architecture for process control. It is based on a real-time derivative-free optimization layer that adjusts the parameters of a discrete-time fractional-order proportional integral (FOPI) controller according to an economic cost function. A simulation benchmark is designed to assess the performance of the FOSOC controller based on a first order plus dead time system. Similarly, an acceleration mechanism is proposed for the fractional-order self optimizing control framework employing fractional-order Gaussian noise with long-range dependence given by the Hurst exponent. The obtained results show that the FOSOC controller can improve the system closed-loop response under different operating conditions and reduce the convergence time of the real-time derivative-free optimization algorithm by using fractional-order stochasticity.

Implementation of a complex fractional order proportional-integral-derivative controller for a first order plus dead time system

<span lang="EN-US">This paper presents the implementation of a complex fractional order proportional integral derivative (CPID) and a real fractional order PID (RPID) controllers. The analysis and design of both controllers were carried out in a previous work done by the author, where the design specifications were classified into easy (case 1) and hard (case 2) design specifications. The main contribution of this paper is combining CRONE approximation and linear phase CRONE approximation to implement the CPID controller. The designed controllers-RPID and CPID-are implemented to control flowing water with low pressure circuit, which is a first order plus dead time system. Simulation results demonstrate that while the implemented RPID controller fails to stabilize the system in case 2, the implemented CPID controller stabilizes the system in both cases and achieves better transient response specifications.</span>

Two-channel combination methods for count-loss correction in radiation measurements at high rates and with pulsed sources

Pile-up effects due to the overlap of signals within the system dead-time (τ) influence the counting capability of radiation detection devices, necessitating the use of correction algorithms to compensate for the count-losses at high radiation rates. Count-rate linearity is especially critical for clinical applications like X-ray imaging or beam monitoring in particle therapy. In particular, in proton therapy the number of delivered particles must be measured online during the treatment session with a maximum error of 1 % up to an average input beam flux of about 1010cm−2s−1. For a segmented detector used to identify and count the single beam particles, assuming a channel area of 1 mm2 and a dead-time τ=2ns, a maximum counting inefficiency of 1 % is required up to τ.fin=0.2 for each detector channel, where fin represents the input rate. Moreover, the beam is often delivered in bunches with higher instantaneous particle rates, and the saturation model of the detector and electronic chain could not be easily determined. Similar considerations are applicable for pixelated detectors used for photon counting.Two methods are proposed to mitigate counting inefficiencies with radiation sources of variable time-structures. Both methods are based on the collection of logic signals provided by two independent detector channels exposed to the same radiation field after discriminating the detector analog outputs with a fixed threshold, assuming that the duration of the discriminator output signal corresponds to the system dead-time. The correction algorithms employ the measurements of the time durations, the number of signals from the two channels and of their AND/OR combinations. The methods provide count-loss corrections without the need to know the dead-time model.The performances of the proposed algorithms are evaluated by using simulations of ideal boxcar signals of fixed duration τ, distributed randomly in time to emulate the dead-time behavior of the system. Both methods provide an effective count-loss correction with a maximum deviation of 1% for different input rates up to τ.fin=1, assuming a uniform random time distribution of input events for both paralyzable and non-paralyzable systems. The simulations of pulsed radiation fluxes provide the same results as a function of the instantaneous input rates.These results are similar to those obtainable by the standard live-time correction algorithm. However, the latter algorithm can only be applied to continuous particle fluxes, while the proposed algorithms work also for pulsed beams, without any hypothesis on the bunch duration or frequency. The robustness of the algorithms with respect to the resolution of the time measurement is studied and the potential limitations in more realistic systems are discussed.The algorithms can be easily implemented in standard logical circuits with multiple input signals provided by segmented detectors. Even if the methods are intended for real-time correction in beam particle counting, they could be applied in a wider range of applications of radiation measurements.

Data Compression in the NEXT-100 Data Acquisition System.

NEXT collaboration detectors are based on energy measured by an array of photomultipliers (PMT) and topological event filtering based on an array of silicon photomultipliers (SiPMs). The readout of the PMT sensors for low-frequency noise effects and detector safety issues requires a grounded cathode connection that makes the readout AC-couple with variations in the signal baseline. Strict detector requirements of energy resolution better than 1% FWHM require a precise baseline reconstruction that is performed offline for data analysis and detector performance characterization. Baseline variations make it inefficient to apply traditional lossy data compression techniques, such as zero-suppression, that help to minimize data throughput and, therefore, the dead time of the system. However, for the readout of the SiPM sensors with less demanding requirements in terms of accuracy, a traditional zero-suppression is currently applied with a configuration that allows for a compression ratio of around 71%. The third stage in the NEXT detectors program, the NEXT-100 detector, is a 100 kg detector that instruments approximately five times more PMT sensors and twice the number of SiPM sensors than its predecessor, the NEXT-White detector, putting more pressure in the DAQ throughput, expected to be over 900 MB/s with the current configuration, which will worsen the dead time of the acquisition data system. This paper describes the data compression techniques applied to the sensor data in the NEXT-100 detector, which reduces data throughput and minimizes dead time while maintaining the event rate to the level of its predecessor, around 50 Hz.

Performance Improvement for Single-Photon LiDAR with Dead Time Selection

Compared with the impulse LiDAR, the single-photon LiDAR has higher measurement sensitivity in the prominent feature, especially for space-based long-distance imaging. The distance measurement and the detection probability are the critical performance for LiDAR. The ranging of single-photon LiDAR is mainly different from the photon ranging of pulsed LiDAR. Dead time has a significant effect on distance measurement accuracy and detection probability, which are key parameters for detectors when implementing sound control. Therefore, the model of detector dead time, measurement accuracy, and detection probability should be established, and simulation results that meet application requirements should be achieved. Based on the single-photon ranging theory, the dead time, measurement accuracy, and detection probability model of single-photon LiDAR are studied. Furthermore, the systematic simulation of different contrasts is carried out according to the model. The simulation results demonstrate that the model can accurately perform the relationship between dead time and single-photon LiDAR system parameters. The research results can prove the design and verification of single-photon LiDAR dead time.

Engine-in-the-Loop in practical application: A sensitivity study toward the influence of test bench parameters

The complexity of automobile powertrains continues to increase, leading to increased development time and effort. One method to address this challenge is to shift vehicle calibration and testing tasks to simulations with Engine-in-the-Loop (EiL) test setups. This increases the efficiency of the development process through high flexibility, low prototype costs, an early starting point, and a high degree of automation. EiL emulates the dynamic interactions between the internal combustion engine and other powertrain components by closed-loop coupling to real-time simulation models. The coupling quality strongly depends on the interface properties, the hardware layout, and the control functionality of the dynamometer test bench. This paper analyzes an existing test bench and presents the impact of altered test bench parameters on different EiL quality aspects. Thereto, the setup is analyzed and a Simulink based grey box test bench model is derived. The latter is parametrized with a full factorial approach in comparison to real test bench measurements. The test bench model is then used for simulative investigations considering different test bench parameters: Two different use cases of Model-in-the-Loop (MiL) supported EiL are investigated. First, a simulative improvement of the test bench control quality by altering the PI based dyno speed controller parameters is investigated. The virtually calibrated controller parameters are applied to the real EiL system and compared to vehicle measurements. Second, sensitivity studies are shown with respect to dynamometer inertia and system dead time in terms of control quality and energy. As a major outcome, a compromise of control accuracy and stability for different speed controller parameters, dyno inertia, and system dead time is shown. Furthermore, it is demonstrated that EiL has only a small deviation in terms of energy compared to a full vehicle, making it a valid approach when considering CO2 emissions.

Modification of the Luedeking and Piret model with a delay time parameter for biotechnological lactic acid production.

To obtain a mathematical model that adequately describes the time lag between biomass generation and lactic acid production of lactic fermentations. Seven experimental kinetics from other research works were studied to validate our proposal: four studies of Fungal Submerged Fermentation and three cases of Bacterial Submerged Fermentation, including the data recollected by Luedeking and Piret. We introduce a modification to the Luedeking and Piret model that consist in the introduction of a time delay parameter in the model, this parameter would account for the lag time that exists between the production of biomass and lactic acid. It is possible to determine this time delay in a simple way by approximating the biomass and product formation considering that they behave as a first order plus dead time system. The duration of this phenomenon, which is not described with the classical Luedeking and Piret model, is a function of microorganism physiology (ease of biomass growth), environment (nutrients) and type of inoculum. The Luedeking and Piret with delay model applications reveal an increase of the R2 in all cases, evidencing the quality of fit and the simplicity of the method proposed. These model would improve the accuracy of bioprocess scaling up.