Process Transfer Function Research Articles

ПРЕОБРАЗОВАНИЕ ТЕПЛОВОЙ ЭНЕРГИИ В ЭЛЕКТРИЧЕСТВО: ПОТЕНЦИАЛ И ЭФФЕКТИВНОСТЬ ТЕРМОЭЛЕКТРИЧЕСКИХ ГЕНЕРАТОРОВ НА ОСНОВЕ ЭЛЕМЕНТОВ ПЕЛЬТЬЕ

Relevance Energy extraction using thermoelectric generators powered by Peltier elements through the application of both natural and engineered heat sources, aiming to create a new green method for clean energy production. Aim of research This study delves into the literature analysis to identify the factors that influence the accuracy of energy conversion, and aims to investigate the performance of Peltier elements while learning the principles of heat transfer, creating optimal conditions for the operation of a thermoelectric generator based on them. During the experiments, by adapting the process conditions, a process transfer function is formed, which aims to improve the energy generation efficiency. The aim of the study is to analyze the efficiency of thermoelectric generators based on Peltier cells. Research methods Physical foundations of thermoelectricity, development of a mathematical model. Results The study analyzed that the simulation revealed the presence of temperature gradients in regions with thermal waters of the mountain mass, and a mathematical model of the process was developed.

Performance comparison between PID, PIDD2 and PIDD2α

We evaluate the performance achievable with Proportional-Integral-Derivative fractional Double-Derivative controllers, denoted as PIDD2α, by comparing it with that achievable with standard PID controllers and with Proportional-Integral-Double-Derivative (PIDD or PIDD2) controllers, which are also called Proportional-Integral-Derivative-Acceleration (PIDA) controllers. The cost-effectiveness ratio improvement obtained when augmenting the control law with an element proportional to the fractional second derivative of the control error is assessed by considering different process transfer functions and by tuning the controllers minimizing the integrated absolute error with genetic algorithms. Further, a constraint on the maximum sensitivity is also posed so that the system robustness is taken into account. The set-point following and the load disturbance rejection tasks are evaluated separately.

Estimation of a SOPDT process transfer function for PID tuning

The paper deals with the estimation of a Second-Order-Plus-Dead-Time (SOPDT) process transfer function for the tuning of a Proportional-Integral-Derivative (PID) controller. In particular, different methodologies for the estimation of the transfer function parameters based on the open-loop process step response are proposed and compared to an existing one that has been recently presented in the literature. A pole-zero cancellation strategy is then employed to tune the PID controller. Advantages and disadvantages of the different methods are then discussed by considering the obtained results and implementation issues.

RNGA based Centralized PI Controller for Multivariable Non Square Systems using Direct Synthesis Method

Design of centralized PI controllers for multivariable non square systems is proposed in the present work. The centralized controller is designed based on the direct synthesis method. The method includes approximating the inverse of the process transfer matrix with the effective transfer function matrix. The effective transfer function for each element in the process transfer function matrix is derived by using the relative normalized gain array (RNGA), and relative average residence time array (RARTA) concepts proposed by Cai et al [1]. The transfer function models used in the present work include first order processes with time delay (FOPDT). Maclaurin series is applied to reduce the resulting controllers in to standard PI forms. The design method requires a single tuning parameter (filter time constant) to adjust the performance of the controller. Simulation study is carried out for various case studies and the results show the advantage of proposed method over the literature reported methods. The control algorithms are comparatively analyzed using standard robust stability measure. The designed controllers give a good performance with lesser interaction compared to the literature methods, Davison Method [2] and Tanttu and Lieslehto’s method [3].

Proportional–integral and proportional–derivative controller design based on analytically computed centroid point for controlling integrating processes

The proportional–integral and proportional–derivative controller is characterized by its capability to effectively control integrating processes compared with proportional–integral/proportional–integral–derivative controllers. Recently, several graphical methods have been proposed for tuning the PI-PD controller parameters by computing the centroid point of the stability boundary locus. However, these approaches are time-consuming because they entail plotting the stability boundary locus for finding the centroid point. Another disadvantage of those design methods is that the design procedure has to be redone as the transfer function changes. In this article, a generalized stability boundary locus is constructed in terms of the controller and assumed plant transfer function model parameters to enable the designer to avoid replotting the stability boundary locus as the process transfer function changes. More importantly, two analytical approaches, which simplify the design of the proportional–integral and proportional–derivative controller very much, are proposed to compute the centroid point of the generalized stability boundary locus. Analytical expressions for computing the performance measures of the designed closed-loop system have also been provided so that one can predict the performance of the designed closed-loop system. It has been shown by simulation examples that the analytical centroid of convex stability region method provides quicker responses with faster disturbance rejections compared to other reported design methods. Also, the simulation results have displayed that analytical weighted geometrical center gives more robust closed-loop responses in terms of gain margin, phase margins, and maximum sensitivity than analytical centroid of convex stability region. Finally, the feasibility of the proposed methods is tested using a real-time application based on an aerodynamical system. Real-time results have demonstrated that the analytical centroid of convex stability region and analytical weighted geometrical center methods give quicker responses with small overshoots compared to other reported methods.

SIMULATION OF THE SYSTEM OF MINERAL NUTRITION OF PLANTS IN CLOSED SOIL

One of the important factors in the high productivity of growing vegetable crops by the method of small volume of this system of vegetable production is the accurate and timely supply of mineral nutrition to their root system. During hydroponic cultivation, all mineral substances of plants are obtained from their aqueous solutions. In closed soil, the water regime should be regulated taking into account the biological characteristics of the culture, the growth phase and the intensity of light. To successfully implement the plant nutrition process, it is necessary to formulate a mathematical model of the process and equivalent transfer functions. This will make it possible to choose a rational way of management and determine the parameters of management systems. The analysis of the latest researches in the field of automation of processes of nutrition of plants grown in closed soil shows that for each specific case, a scheme of automation of this process was proposed, which led to different results of the implementation of the process of nutrition. To generalize the principles of regulating the supply of nutrient solutions to plants in closed soil, it is necessary to develop real mathematical models of processes and equivalent transfer functions that will allow choosing a rational method of management. The specificity of the object of research determines the need to use the analytical method of obtaining dynamic models as the main one. The mathematical description of the dynamics of mass transfer during drip irrigation includes the value of the evaporative capacity of plants. This value significantly depends on the parameters of the microclimate in the building. To determine the influence of these parameters on the dynamics of liquid transpiration, a mathematical model was obtained in the form of differential equations of heat and material balances. The obtained mathematical models and the structural schemes built on their basis will serve as the basis for creating a system of mineral nutrition of plants in closed soil.

Optimal integral–proportional derivative controller design for input load disturbance rejection of time delay integrating processes

One of the commonly encountered type of processes in industry is integrating systems. For this type of processes, tuning formulas to calculate optimally integral–proportional derivative controller parameters to reject input load disturbance, which is an important problem in process control, are presented here. Simple tuning formulas are provided to set the integral–proportional derivative controller parameters for rejection of input load disturbance of integrating plus first order plus dead time and double integrating plus first order plus dead time processes. Time-weighted integral performance indices are exploited to derive optimal formulas for input load disturbance rejection. Achieved formulas for integral–proportional derivative tuning contain only process transfer function parameters. To show benefits and usefulness of the suggested design approach, simulation examples are imparted. Furthermore, comparisons to some available design approaches are given to reveal the superior performance of the suggested design method. In addition, proposed design method is experimentally validated by controlling a cart position.

Maximum sensitivity (Ms)-based I-PD controller design for the control of integrating processes with time delay

Integrating processes, whose one or more poles are located at the origin, are common in the process industry. This paper focuses on maximum sensitivity (Ms)-based control of these types of processes. Integral–proportional derivative (I-PD) controllers are designed by exploiting the direct synthesis method for different forms of integrating processes. The suggested design approach is based on comparing the characteristic equation of the closed-loop system, which comprises the integrating system and I-PD controller with a lead/lag filter, with the desired characteristic equation. Simple and analytical adjusting rules are followed to determine the parameters of the I-PD controller and the lead/lag filter according to desired robustness specified by maximum sensitivity (Ms). The formulas provided contain process transfer function parameters and a tuning parameter that is used for setting the desired Ms. The benefits of the proposed technique are demonstrated by simulation examples and a real-time application of cart position control on an experimental set-up. Comparisons with some reported proportional–integral–derivative (PID) and I-PD design techniques are presented to demonstrate the advantages of the proposed design method more evidently.

RETRACTED: Cuckoo Search Optimization based PI Controller Tuning for Hopper Tank System

The paper work focuses on soft computing and Conventional controller tuning approach to design of PI controller, for a nonlinear hopper tank liquid level control system process Industries. The automation industries provide conventional techniques where it is impossible to maintain its settling time which motivates to do the research in this field. The system processes the combination of a conical and cylindrical tank for providing Multi-region based mathematical modelling to obtain the first order with delay time (FOPDT) process transfer function model. The Ziegler Nichols, Cohen-coon, Tyreus Luben, CHR (Chien, Hrones, and Reswick), IMC (Internal Model Control), Direct Synthesis, FOPI(Fractional Order PI) Conventional tuning formulae and Cuckoo Search Optimization (CSO) algorithm are used to optimize the servo regulatory responses of PI controller. The integral and proportional gain of the PI controller is said to produce the fastest settling time and reduces the error using performance indices and achieves Liquid Level control in hopper tank. Comparison is made for the various conventional controller tuning methods with Cuckoo Search Optimization tuning responses and identified to CSO-PI method offers enhanced Optimized Performance of settling time which was about 105.58 s which is relatively less while comparing to Conventional PI controller tuning methods for a different region based system.

High-Order Filtered PID Controller Tuning Based on Magnitude Optimum

The paper presents a tuning method for PID controllers with higher-order derivatives and higher-order controller filters (HO-PID), where the controller and filter orders can be arbitrarily chosen by the user. The controller and filter parameters are tuned according to the magnitude optimum criteria and the specified noise gain of the controller. The advantages of the proposed approach are twofold. First, all parameters can be obtained from the process transfer function or from the measured input and output time responses of the process as the steady-state changes. Second, the a priori defined controller noise gain limits the amount of HO-PID output noise. Therefore, the method can be successfully applied in practice. The work shows that the HO-PID controllers can significantly improve the control performance of various process models compared to the standard PID controllers. Of course, the increased efficiency is limited by the selected noise gain. The proposed tuning method is illustrated on several process models and compared with two other tuning methods for higher-order controllers.

System Identification and Design of Inverted Decoupling IMC PID Controller for Non-Minimum Phase Quadruple Tank Process

A systematic analytical and experimental method of identification of Two Input Two Output (TITO) Quadruple-Tank Process (QTP), operated at non-minimum phase condition has been presented. Parameters of the process transfer function matrix have been validated on an experimental laboratory-scale physical setup of the process. Appropriate input-output pairing and interaction among control loops have been studied based on the Relative Gain Array (RGA) analysis. Inverted Decoupling Internal Model Control (IMC) based Proportional Integral Derivative (PID) controller has been designed for the TITO process. The effect of changes in controller tuning parameters on the closed-loop response for servo problem has been reported in terms of quantitative performance indices such as Integral of Square of Error (ISE), Integral of Absolute Error (IAE), percentage overshoot and offset. The simulation results have been compared with the literature.

Extending the Model-Based Controller Design to Higher-Order Plant Models and Measurement Noise

The article extends a model-based controller design to higher-order systems, focusing on the speed and shapes of the closed loop responses, including the noise attenuation. It shows that, to obtain simple but reliable results, it is necessary to pay attention to the initial process identification and modelling and also to modify the target closed-loop transfer functions, which must remain causal. To attenuate high initial control signal peaks, appropriate pre-filters are introduced. In order to work with as few parameters as possible, all higher-order transfer functions (process models, target closed loops, pre-filters and noise-attenuation filters) are selected in the form of binomial filters with multiple time constants. Consequently, the so-called “half-rule”, used to reduce too complex process transfer functions, has been modified accordingly. Because derived controllers can lead to different transient dynamics depending on the context of use, the article recalls the need to introduce dynamic classes of control to clarify the mission of individual types of controllers. Consequently, also the performance evaluation using the total variation (TV) criterion had to be refined. Indeed, in its original version, TV is not suitable to distinguish between reasonable and excessive control effort due to improper tuning and noise. The modified TVs allow evaluating higher order systems with multiple changes in direction of their control signal increase without contributing to the excessive control increments. The advantages of the proposed modifications, compared to the traditional approaches, are made clear through simulation examples.

Model-based adaptive controller for personalized ventilation and thermal comfort in naturally ventilated spaces

This work develops a standalone autonomously controlled personalized ventilation (PV) unit in a naturally ventilated (NV) office space to maintain acceptable thermal comfort (TC) under steady and transient indoor conditions and activity levels. The NV-PV proportional integral derivative (PID) controller adjusts the PV supply temperature (TSPV) at the occupant set flow rate (QSPV) based on predicted TC using a regression model. The target TC level that the controller attains at all times is between 0 (neutral) and 1 (slightly comfortable). Process transfer functions were developed and then used to find the adaptive PID tuning coefficients using the Internal Model Control (IMC) method. The controller was tested in a case study at indoor temperature range of 25 to 33 °C with relative humidity range of 55% and 80%. It was shown that the NV-PV controller adjusted TSPV to maintain acceptable TC under transients of indoor conditions and metabolic rates.

Optimal PI–PD Controller Design for Pure Integrating Processes with Time Delay

Though Proportional-Integral-Derivative (PID) controllers are commonly being used for process control applications, it has been proven that they may give unacceptable closed loop responses for open loop unstable processes including integrating ones. Hence, this paper addresses to tuning of PI–PD controllers which is an extension of PID controllers and uses PD part in an inner feedback loop to convert the open loop unstable processes to a stable one so that PI controller in the forward path can be used to achieve a better closed loop response. PI–PD tuning parameters are determined from simple analytical rules which were obtained from minimization of the control system error based on IST3E criterion which is an integral performance index and has been proven to be resulting in very satisfactory closed loop responses. Derived tuning rules are in terms of the assumed process transfer function parameters, namely the gain and time delay. Effectiveness and superiority of obtained tuning rules have been shown by simulation examples.

A MULTILEVEL RESOURCE-SAVING BLAST FURNACE PROCESS CONTROL

A multilevel resource-saving blast furnace process control is considered. The resource-saving control is provided for operating, adaptation, technical and economic control in the automated systems of blast-furnace processes. It is proposed to form optimal operation modes of blast furnace heating, metal charge structures, natural gas and oxygen consumption. Decisions are made using Kohonen neural networks taking into account current and planned parameters of coke quality, iron ore, raw materials and blast. At the level of operating control, the work suggests a model predictive control to improve the resource conservation indicators. The method is based on decomposition of the general problem of the process dynamics identification on particular problems: dynamic synchronization and identification of process transfer functions. At the level of adaptive control, optimal operating modes of blast furnaces are expedient to be developed with respect to blast furnace heating, structure of metal charge, natural gas and oxygen rate considering the current and planned parameters of coke, blasting. The blast furnace operating modes are suggested to be determined based on Kohonen neural networks. In evaluating the efficiency of introducing the model predictive control, the existing actual statistics of scatter of BF mode parameters should be based upon. The fact is that the introduction of model predictive control assumes no radical change of the BF melt technology. Like in all the control systems, the BF process is considered as the set control object with all its characteristics. Changing process settings, raw material content does not introduce any cardinal variation in the scatter of process characteristics. However, in this case a transient process occurs which is necessary for the control system to identify the changing conditions. The transient process is inherent to all the control systems and the blast furnace process is not an exclusion. As a result of transient process, the control system is set to the optimal mode.

Centralized PI controller design method for MIMO processes based on frequency response approximation

A simple method of controller design for multi-input multi-output (MIMO) processes have been proposed in frequency domain. The intensive calculation for the inverse of the process transfer function matrix is simplified to a great extent by evaluating the process transfer function matrix at a low frequency point. The desired closed loop transfer functions are derived for the process using a single tuning parameter for each diagonal element of the process transfer function matrix which represents the desired closed loop time constant. Centralized PI controllers are then designed using a model matching technique by evaluating the transfer functions at a low frequency point. The PI controllers provide acceptable performances for lag dominated as well as time-delay dominated processes and is also applicable to high-dimensional processes. The proposed method is extended for the non-square MIMO processes using two approaches one of which squares up the process transfer function matrix to apply the proposed technique while the other is based on pseudo-inverse evaluation of the process transfer function matrix at a low frequency point.

Parametric and Nonparametric PID Controller Tuning Method for Integrating Processes Based on Magnitude Optimum

Integrating systems are frequently encountered in power plants, paper-production plants, storage tanks, distillation columns, chemical reactors, and the oil industry. Due to the open-loop instability that leads to an unbounded output from a bounded input, the efficient control of integrating systems remains a challenging task. Many researchers have addressed the control of integrating processes: Some solutions are based on a single closed-loop controller, while others employ more complex control structures. However, it is difficult to find one solution requiring only a simple tuning procedure for the process. This is the advantage of the magnitude optimum multiple integration (MOMI) tuning method. In this paper, we propose an extension of the MOMI tuning method for integrating processes, controlled with a two-degrees-of-freedom (2-DOF) proportional–integral–derivative (PID) controller. This extension allows for calculations of the controller parameters from either time domain measurements or from a process transfer function of an arbitrary order with a time-delay, when both approaches are exactly equivalent. The user has the option to emphasise disturbance-rejection or tracking with the reference weighting factor b or apply two different reference filters for the best overall response. The proposed extension was also compared to other tuning methods for the control of integrating processes and tested on a charge-amplifier drift-compensation system. All closed-loop responses were relatively fast and stable, all in accordance with the magnitude optimum criteria.

Comparative Performance of a Hybrid Renewable Energy Generation System with Dynamic Load Demand

This article presents the modeling and simulation of a hybrid generation system, which uses solar energy generation, wind energy, and the regulation of a proton exchange membrane (PEM) cell to raise the demanded load, empowering the use of these hydride systems worldwide. This generation system was simulated for different locations in Puerto Bolivar (Colombia), Bremen (Germany), Beijing (China), and Texas (USA), for two demand profiles. The data used for the simulation was calculated using the mathematical solar model proposed by Beistow and Campbell for solar radiation. In contrast, for the wind resource evaluation, the Weibull probability distribution was used to calculate the most probable wind speed for each day, according to the historical data for each of the studied locations. Considering these data, the process transfer functions were used for tuning the control parameters for the hydrogen and oxygen production system. For the evaluation of the performance of these controllers, the indices of the absolute value of the error (IAE), the integral of the square of the error (ISE), the integral of the absolute value of the error for time (ITAE), and the integral of the square of the error for time (ITSE) were used. It was found that in the second load profile studied, better performance of the ITSE performance parameter was obtained, with stabilization times lower than those of the first profile.

Enhanced performance of PID controllers for unstable time delay systems using direct synthesis method

ABSTRACT Design proportional–integral–derivative (PID) controllers for unstable first-order plus time delay (FOPTD) and unstable second-order plus time delay (SOPTD) systems with/without a zero is proposed by direct synthesis method. For unstable FOPTD system, a series PID controller is considered. The derivative time of series PID controller is made equal to 0.5 times time delay to cancel the numerator zero with the pole of the loop transfer function (product of process transfer function and controller transfer function). The reduced characteristic equation is compared with the desired characteristic equation to get PI settings. The conventional PID controller parameters are obtained from series PID controller. For unstable SOPTD systems, PID controller with a first-order lead/lag compensator is considered. The controllers designed by the proposed method are implemented on various transfer function models, nonlinear model equations of bioreactor and on inverted pendulum (IP) set-up to show the efficiency of the proposed method. The performance of the proposed controllers is compared with the controllers reported in the recent literature in terms of IAE. The robustness of the controller is determined by the maximum magnitude of sensitivity function, phase margin and gain margin.

Parametric and Nonparametric PI Controller Tuning Method for Integrating Processes Based on Magnitude Optimum

Integrating systems are frequently encountered in the oil industry (oil–water–gas separators, distillation columns), power plants, paper-production plants, polymerisation processes, and in storage tanks. Due to the non-self-regulating character of the processes, any disturbance can cause a drift of the process output signal. Therefore, efficient closed-loop control of such processes is required. There are many PI and PID controller tuning methods for integrating processes. However, it is hard to find one requiring only a simple tuning procedure on the process, while the tuning method is based either on time-domain measurements or on a process transfer function of arbitrary order, which are the advantages of the magnitude optimum multiple integration (MOMI) tuning method. In this paper, we propose the extension of the MOMI tuning method to integrating processes. Besides the mentioned advantages, the extension provides efficient closed-loop control, while PI controller parameters calculation is still based on simple algebraic expressions, making it suitable for less-demanding hardware, like simpler programmable logic controllers (PLC). Additionally, the proposed method incorporates reference weighting factor b that allows users to emphasize either the disturbance-rejection or reference-following response. The proposed extension of the MOMI method (time-domain approach) was also tested on a charge-amplifier drift-compensation system, a laboratory hydraulic plant, on an industrial autoclave, and on a solid-oxide fuel-cell temperature control. All closed-loop responses were relatively stable and fast, all in accordance with the magnitude optimum criteria.