Dead Time Model Research Articles

Control of continuous digester kappa number using generalized model predictive control

Kappa number variability at the digester impacts pulp yield, physical strength properties, and lignin content for downstream delignification processing. Regulation of the digester kappa number is therefore of great importance to the pulp and paper industry. In this work, an industrial application of model-based predictive control (MPC), based on generalized prediction control, was developed for kappa number feedback control and applied to a dual vessel continuous digester located in Western Canada. The problem was complicated by the need to apply heat at multiple locations in the cook. In this study, the problem was reduced from a multiple to a single input system by identifying three potential single variable permutations for temperature adjustment. In the end, a coordinated approach to the heaters was adopted. The process was perturbed and modeled as a simple first order plus dead time model and implemented in generalized predictive control (GPC). The GPC was then configured to be equivalent to Dahlin’s controller, which reduced tuning parameterization to a single closed loop time constant. The controller was then tuned based on robustness towards a worst-case dead time mismatch of 50%. The control held the mean value of the kappa number close to the setpoint, and a 40% reduction in the kappa number’s standard deviation was achieved. Different kappa number trials were run, and the average fiberline yield for each period was evaluated. Trial results suggested yield gains of 0.3%–0.5% were possible for each 1 kappa number target increase.

Determination of Variable Humidity Profile for Lactic Acid Maximization in Fungal Solid-State Fermentation

Solid-state fermentation (SSF) is the bioprocess where microorganisms are cultivated in the absence of free water under controlled conditions. Lactic acid can be produced by Rhizopus oryzae SSF of grape stalks. During the microorganism’s growth, the temperature and water content of the solid bed fluctuate, leading to areas of either dry or excessive moisture in the solid substrate. Therefore, it is crucial to control the water supply to the matrix. In this work, we obtain lactic acid through SSF of grape stalks using Rhizopus oryzae NCIM 1299. The SSF was conducted at a fixed temperature of 35 °C, with five constant relative humidity (RH) levels: 50, 57, 65, 72, and 80%RH. Mathematical models, including the Logistic and First-Order Plus Dead-Time models for fungal biomass growth and the Luedeking and Piret with Delay Time model for lactic acid production, were adjusted to kinetic curves. Growth kinetic parameters (Xmax, μmax, Tp, T0, Yp/x, and td) were determined for all conditions. These kinetic parameters were then correlated with relative humidity using a second-degree polynomial relationship. We observed a decrease in Xmax with an increasing %RH, while the value of Yp/x increased at a higher %RH. Finally, the optimal variable relative humidity profile was obtained by applying the dynamic optimization technique, resulting in a 16.63% increase in lactic acid production.

A decentralized optimal PID controller with disk margin-based robust stability analysis for higher-order industrial systems

ABSTRACT Decentralized control systems are frequently employed to tackle control challenges in multi-input multi-output (MIMO) systems. Hence, this paper proposes a decentralized PID controller that relies on frequency domain specifications. This controller is designed to minimize the loop interactions and fulfill the design criteria of the MIMO system. The PID parameters are calculated based on gain and phase margin specifications. Additionally, a first-order plus dead time model is derived for each of the decoupled subsystems. Furthermore, robust stability is analysed using disc margin analysis, which overcomes the constraints of traditional margins. Moreover, the paper determines a secure range of uncertainty for various levels of gain and phase uncertainties. The findings suggest that the proposed controller achieves robust stability over a broader range of margins when compared to alternative control methods.

Identification of heat exchanger process through Hammerstein and polynomial models

Process industries extensively use heat exchangers in their operations, playing a crucial role in various sectors by facilitating efficient heat transfer, conserving energy, and reducing operational costs. This paper focuses on identifying and validating the system model, with the primary task of designing the controller involving the determination of the mathematical representation of the system. The First Order Plus Dead Time (FODT) model, derived from basic principles, is used to represent the system. To analyze the system’s behavior and construct a suitable controller, model development is essential, achieved by constructing principles models using energy balance equations to identify the heat exchanger process. Data collected from the model are utilized in the identification process, with the temperature at the outlet of the hot air blower being the controlled variable in this investigation. The research aims to determine the mathematical model based on time versus temperature data acquired from the Heat Exchanger. Various system identification methods, such as Hammerstein Wiener (HW), Auto Regressive with Exogenous Input (ARX), Box-Jenkins (BJ), Output-Error (OE), and Auto Regressive Moving Average with Exogenous Input (ARMAX) models, are implemented for the heat exchanger. The models obtained undergo validation, and the best-fit model closest to the physical system is considered for controller design. After conducting the analysis, it was found that the Output-Error (OE) model outperforms other models in terms of achieving the best fit.

A hybrid dynamics modeling method for micro-turbine engine thrust vectoring

Thrust vector control technology is widely used in modern advanced aircrafts, space shuttles and unmanned aerial vehicles, etc. An accurate thrust vector mathematical model is of great significance to enhance the thrust vector control effect. In this paper, the P200 micro-turbine engine with an axisymmetric thrust vector nozzle placed at the rear is taken as an example, A hybrid thrust vectoring dynamics modeling method consisting of engine speed model, engine thrust model, actuator dynamics model, airflow angle model and thrust loss coefficients is proposed. The engine speed model is of Linear Parameter Varying (LPV) model with each segment is characterized by a First Oder Plus Dead Time (FOPDT) model. The engine thrust model is characterized as a cubic polynomial function of engine speed. The actuator’s dynamic model is a FOPDT model. The nozzle airflow deflection angle is proportional to the airflow deflection angle. the thrust loss coefficient is approximated by a cosine relationship with the airflow deflection angle. The experimental results show that the established model can well characterize the dynamics of the thrust vector system.

Analytically derived disturbance rejection‐based PID controller tuning for second‐order plus dead time plants

AbstractThis letter proposes a proportional‐integral‐derivative (PID) design method for second‐order plus dead time models based on a desired closed‐loop transfer function for load disturbance changes. Also, tuning rules for single integrating first‐order plus dead time models are provided. Using a two‐degree‐of‐freedom control scheme, the design problem considers load disturbance rejection, robustness to model uncertainties, and setpoint tracking. Three examples are used to assess the performance of the proposed method. Finally, the results are compared to two popular PID control design methodologies, skogestad internal model control or skogestad IMC (SIMC) and improved SIMC (iSIMC).

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.

Fractional PID with Genetic Algorithm Approach for Industrial Tank Level Control Process

Process control is used in various types of industries to boost production while using current resources, product quality, and safety, with level control being one of the most important schemes. It is suggested that study be conducted on nonlinear continuous processes, particularly in process control applications such as conical tank level control. Initially, each process receives one set of Proportional-Integral (PI) controller settings and a First Order Plus Dead-Time (FOPDT) model using the Ziegler Nicholas (ZN) step response tuning method. The numerous FOPDT models and parameter sets are also obtained. Responses obtained with a single set of parameters and responses obtained with many sets of parameters are compared. By creating a Fractional PID Controller (FPID) with Genetic Algorithm (GA), a simulation-based tuning strategy is proposed. The step responses are acquired through experimental research using fine-tuned settings. At most operational points, the Fractional PID Controller with Genetic Algorithm-based tuning approach outperforms, with lowest oscillation, extremely tiny overshoot, minimum average ISE, and minimum average IAE. The proposed FPID with GA method provides better setpoint and regulatory tracking performance compared to ZN-PID.

Dynamic Optimization of Lactic Acid Production from Grape Stalk Solid-State Fermentation with Rhizopus oryzae Applying a Variable Temperature Profile

Lactic acid is widely used in the food industry. It can be produced via chemical synthesis or biotechnological pathways by using renewable resources as substrates. The main challenge of sustainable production lies in reaching productivities and yields that allow for their industrial production. In this case, the application of process engineering becomes a crucial tool to improve the performance of bioprocesses. In this work, we performed the solid-state fermentation of grape stalk using Rhizopus oryzae NCIM 1299 to obtain lactic acid, employing three different temperatures (22, 35, and 40 °C) and a relative humidity of 50%. The Logistic and First-Order Plus Dead Time models were adjusted for fungal biomass growth, and the Luedeking and Piret with Delay Time model was used for lactic acid production, obtaining higher R2 values in all cases. At 40 °C, it was observed that Rhizopus oryzae grew in pellet form, resulting in an increase in lactic acid productivity. In this context, the effect of temperature on the kinetic parameters was evaluated with a polynomial correlation. Finally, using this correlation, a smooth and continuous optimal temperature profile was obtained by a dynamic optimization method, improving the final lactic acid concentration by 53%.

First experimental evaluation of count-rate performance for micrometre resolution deep silicon detector

Objective. An ultra-fine-pitch deep silicon detector has been developed for clinical photon-counting computed tomography (CT). With a small pixel size of 14 × 650 μm2, it has shown potential to reach micrometre spatial resolution in previous simulation studies. A detector prototype with such geometry has been manufactured, and we report on the first experimental evaluation of its count-rate performance. Approach. The measurement was carried out at MAX IV synchrotron laboratory with 35 keV monochromatic x-rays. By inserting tungsten attenuators of 50, 75, 100, 150, 200, 225, 325 μ m-thicknesses into the beam, the response of the detector to fluence rates from 3.3 × 107 to 1.3 × 1011 mm−2 s−1 was characterized. Main results. The measurement result showed that the detector exhibited count rate linearity up to 6.66 × 108 mm−2 s−1 with 13% count loss and was still functional at count rate up to 2.9 × 1010 mm−2 s−1. A semi-nonparalyzable dead-time model was fitted to the count-rate behaviour of the detector, showing great agreement with the measured data, with an estimated nonparalyzable dead time of 2.9 ns. Significance. This is the first experimental evaluation of the count-rate performance for a deep silicon detector with such small pixel geometry. The results suggest that this type of detector shows the potential to be used at fluence rates encountered in clinical CT with little count loss due to pile-up.

Fractional-order model identification based on the process reaction curve: A unified framework for chemical processes

This study introduces a novel method for identifying dynamic systems aimed at deriving reduced-fractional-order models. Applicable to processes exhibiting an S-shaped step response, the method effectively characterizes fractional behavior within the range of fractional orders (α∈[0.5,1.0]). The uniqueness of this approach lies in its hybrid nature, combining one-variable optimization techniques for estimating the model fractional order α with analytical expressions to estimate parameters T and L. This hybrid approach leverages information from the reaction curve obtained through an open-loop step-test experiment. The proposed method demonstrates its efficacy and simplicity through several illustrative examples, showcasing its advantages over established analytical and optimization-based techniques. Notably, the hybrid approach proves particularly advantageous compared to methods relying on the process reaction curve. To highlight its practical applicability, the identification algorithm based on this hybrid approach is implemented on hardware using a microprocessor. The experimental prototype successfully identifies the First-Order Plus Dead Time (FFOPDT) model of a thermal-based process, validating the proposed method's real-world utility.

Auto-Tuning Software Tool for Inverse Response Model Robust Tuning of 1-DoF PID and FOPID Controllers

The main objective of this work is to present a software tool that allows to perform the tuning process of PID and Fractional Order PID controllers in an automated method. The tool tunes 1DoF PID and FOPID controllers for a controlled process with a inverse response second-order plus dead time model. This tuning is based on the Inverse Response Model Robust Tuning (IRM-RoT) rule, which aims to achieve optimal control system performance while ensuring a target robustness. Additionally, the tool measures the performance obtained from the control system, as well as the robustness achieved, and displays the control signal obtained by implementing the tuned controller. The examples used show the main characteristics of the tool and conclude that it can be a very useful contribution for educational purposes in fields such as electrical engineering.

A practical approach for transfer function estimation using short, transient process data

Increased productivity in the industrial sector requires optimal closed loop performance. This can be solely achieved through optimal tuning of the controller parameters, which requires reliable and efficient process data, further employed in process estimations or high quality models. Most of the classical identification methods require long input-output data sets. In this paper we propose a technique to extract process information from short transient process data. The method is based on short sine test which can be superimposed on nominal process inputs, and estimates the process impulse response, consequently providing a band limited, but highly accurate, frequency response. This in turn is used to accurately estimate a high order plus dead time model. The method is reliable and requires less effort compared to classical step based methods. The main features of the proposed method are: 1) it uses a short duration test based on a sine input; 2) it produces accurate models in the presence of stochastic disturbances; and 3) it can be executed in open or closed loop. Numerical examples are provided to validate the theoretical approach and demonstrate the accuracy of the estimation.

Analytical fractional reduced-order model identification method for processes with overdamped and underdamped response

In this paper, an analytical procedure to identify a fractional-first order plus dead time (FFOPDT) model is presented. This procedure is applied to processes with overdamped or underdamped step response, i.e., fractional order values in the range 0.5 ≤ α ≤ 2.0 can be estimated. The required process information is obtained through a simple open-loop step experiment and is based on fitting three arbitrary points (x1-x2-x3%) on the process reaction curve. Some numerical examples are proposed to show the effectiveness and applicability of this procedure for the identification of fractional-order models. The main feature of this approach is that it estimates the FFOPDT model of overdamped and underdamped processes.

Fractional-Order PID Optimal Tuning Rule based on a FOPDT Process Model with Robustness Constraints

This paper introduces a tuning rule design for fractional order PID controllers. The design is based on a first order plus dead time model for the controlled process. The control problem presented, requires minimizing the integrated absolute error for each control mode, then making a different set of rules for set-point and load-disturbance response. For the proposed optimization, a robustness constraint based on the maximum value of the sensitivity function has been considered so that the tuned controllers have an optimal performance and guarantee the stability of the control system at the time of implementation. By performing a curve fitting process towards the optimal controller parameters, the Model based Robust Tuning rule was designed and its improvement over other tuning methods is validated through examples.

Sliding mode controller design for unstable processes with dead time with a case study on continuous stirred tank reactor

Unstable processes are difficult to control because one or more poles lie on the right-hand side of the s-plane. Control becomes further complicated by the presence of dead time in such systems. In this study, a sliding mode control (SMC) design is proposed for the control of unstable processes with dead time. To apply the SMC, a second order plus dead time (SOPDT) model of the unstable process is used, and a proportional-integral-derivative-acceleration type sliding surface is considered. The parameters of continuous and discontinuous control laws are obtained using the differential evolution optimization technique. The optimal control problem is solved by satisfying a new weighted bi-objective function constituting the performance index integral absolute error and control input total variation. The proposed control scheme has been satisfactorily extended to control unstable integrating and higher-order unstable processes with dead time by approximating them into the unstable SOPDT model. The efficacy of the suggested scheme has been evaluated on several benchmark unstable industrial chemical processes, including the continuous stirred tank reactor (CSTR). Further, this scheme has been compared with recently reported work, and the obtained results clearly demonstrate the effectiveness of the suggested controller.

Model predictive control with exogenous auto-regressive model to improve performance in the CO2 removal

Model predictive control (MPC) is used in the CO2 removal process in the Subang field to improve its control performance. MPC is used to maintain the CO2 concentration at the sweet gas output by controlling the feed gas pressure (PIC-1101), makeup water flow rate (FIC-1102), and amine flow rate (FIC-1103). The empirical model applied to MPC to represent the process model is the auto-regressive exogenous (ARX) model. The ARX model is compared with the first order plus dead time (FOPDT) model based on the root mean square error (RMSE) between the model and the actual process, then MPC parameters are tuned which include sampling time (T), prediction horizon (P) and control horizon (M) to control for the three variables. Improved control performance is measured based on the integral square error (ISE). The results show that the ARX model is the best model for the CO2 removal process with an RMSE value of 35%-91% smaller than the FOPDT model. The optimal control parameters Prediction Horizon (P), Control Horizon (M) and Sampling Time (T) in the CO2 removal process are 75, 25 and 1 on PIC-1101, 25, 10 and 1 on FIC-1102, and 30, 25 and 1 on FIC-1103. The MPC-ARX (MPC using ARX model) can improve the control performance of 33% in the servo control and 6-56% on the regulatory control. However, not all of them showed an increase in control performance improvement from previous studies even though they had used the best model (ARX). This is due to the MPC parameter setting that is not yet appropriate, so it needs to be retuning.

Dynamic response of the performance and emissions of an LPG diesel dual-fuel engine with water injection

This paper evaluated the dynamic response of the compression ignition engine's performance parameters and emissions when water was injected into the intake manifold at different water ratios. This technique effectively decreased NOx emissions and mitigated knock intensity when the engine ran at dual fuel mode. With a WR = 143 %, NOx emissions were reduced by 52 % at 100 % diesel operation, whereas with a WR = 132 %, NOx emissions were reduced by 57 % at dual fuel mode operation. The knock intensity decreased from 1.52 V to 1.12 V using a water ratio of 133 % when the engine operated with a substitution of diesel by LPG of 50 % on a mass basis. The results also revealed that water injection increased HC emissions from 220 ± 1 ppm to 430 ± 1 ppm, whereas the Particle Matter (PM2.5) increased from 42.4 μg/kWh to 127.3 μg/kWh at 100 % diesel operation. When the engine operated at dual fuel mode PM2.5 increased from 42.4 μg/kWh to 84.3 μg/kWh. Finally, two First Order plus Dead Time models were deduced through the system identification technique to simulate the dynamic response of Knock Intensity when a step change of water ratio was made. These models play a key role in tuning system controllers for knock suppression.

Improved response model of a superconducting nanowire array for high photon count rate communication

In high-speed photon-counting communication where the slot duration is close to the scale of detector reset time, the detection efficiency recovery characteristics of superconducting nanowire single photon detector (SNSPD) become the key factors affecting counting and communication performance. We introduced the nonlinear detection efficiency recovery model derived from the kinetic inductance model combined with the nonlinear efficiency-current relationship into the pulse position modulation (PPM) optical communication system based on the SNSPD array, and studied the impact of the recovery characteristics on the counting and communication performance of the system. On this basis, we introduce the efficiency recovery model into the correction of the channel logarithmic likelihood ratio (LLR) to estimate the SNR of each slot more accurately. Relevant results show that compared with the existing Poisson channel model, fixed deadtime model and detection efficiency exponential recovery model, this modification combined with FEC can provide the best decoding performance, especially in scenarios with high PPM order, small array pixel number and strong noise level. Besides, the nonlinear detection efficiency recovery model also reflects the best consistency with the experimental measurements of the SNSPD array in terms of response count rates near saturation.

Counting-loss correction method based on window pulse shaping

In order to obtain a precise X-ray counting rate, a window shaping algorithm is proposed and is applied. The proposed algorithm shapes original pulses into window pulses with sharp edge and stable width. In the experiment, the measured counting rate at 3.9uA tube current is used to estimate the incoming counting rate. The dead time and corrected counting rate are estimated by the paralyzable dead-time model. The experimental results show that the mean dead time of radiation events is 260ns and the relative mean deviation is 3.44% in the newly designed counting system. While the incoming counting rate is in the range of 100kcps to 2Mcps, the relative error of the corrected counting rate compared with the incoming counting rate is less than 1.78%. The proposed algorithm suppresses the dead time swing and improves the accuracy of the total counting rate of X-ray fluorescence spectrum.