The paper presents the methodology for the synthesis of a Fuzzy Multi-Regional Fractional Order PID controller (FMR-FOPID) used to control the average thermal power of a PWR nuclear reactor in the load following mode. The controller utilizes a set of FOPID controllers and the fuzzy logic Takagi-Sugeno reasoning system. The proposed methodology is based on two optimization parts. The first part is devoted to finding the optimal parameters of local FOPID controllers and in the second part, the optimal membership functions of the fuzzy reasoning system are designed. During the controller designing and comparison phase, the two validated nodal models of a nuclear reactor are used, simplified model and extended model respectively. The proposed approach has been verified by computer simulations that confirm its effectiveness.
District Heating (DH) systems are commonly supplied using local heat sources. Nowadays, modern insulation materials allow for effective and economically viable heat transportation over long distances (over 20 km). The paper proposes a Decision Support System (DSS) for optimized selection of design and operating parameters of a long distance Heat Transportation System (HTS). The method allows for evaluation of feasibility and effectiveness of heat transportation from the considered heat sources to the given DH area. The optimized selection is formulated as the multicriteria decision-making problem. The constraints for this problem include a static HTS model, allowing considerations of the system life cycle, as well as time variability and spatial topology. Thereby, the variation of heat demand and ground temperature within the DH area, the insulation and pipe aging, as well as the terrain elevation profile are taken into account in the decision-making process. The HTS construction costs, the operating costs (pumping power), and the heat loss are considered as objective functions, while such parameters as: inner pipeline diameter, insulation thickness, temperature and pressure profiles, as well as pumping station locations are optimized during the decision-making process. Moreover, variants of pipe laying e.g. one pipeline with a larger diameter, or two parallel pipelines with smaller diameters might be considered during the optimization. The analyzed optimization problem is multicriteria, hybrid and nonlinear. The genetic solver has been proposed to solve it.
In the paper authors describe proposition of design and verification procedures of the discrete Fractional Order PID (FOPID) algorithm for control of the Pressurized Water Reactor (PWR) thermal power near its nominal operating point. The FOPID algorithm synthesis consists of: off-line optimal tunning of its parameters in continuous time-domain with LQ (Linear Quadratic) performance index and simplified models of nuclear reactor and control rods drive; its transformation into equivalent integer order structure with Oustaloup filters; and finally its transformation into equivalent discrete form. Discrete FOPID algorithm is further implemented in the PLC controller and verified by real-time simulation in the Hardware In the Loop (HIL) structure with non-linear nuclear reactor model. Promising simulation results were obtained, which confirm improved flexibility of the discrete FOPID algorithm in comparison to its classical PID counterpart.
Model-based predictive control is an effective method for control the large scale systems –, , , . Method is based on on-line solution of the control task over the control horizon using current and past measurements, as well as the system model. Only a first element of calculated control sequence is applied to the plant. At the next sampling instant, based on new process output measurements, control procedure is repeated.
District Heating (DH) systems are commonly supplied using local heat sources. Nowadays, modern insulation materials allow for effective and economically viable heat transportation over long distances (over 20 km). In the paper a method for optimized selection of design and operating parameters of long distance Heat Transportation System (HTS) is proposed. The method allows for evaluation of feasibility and effectivity of heat transportation from the considered heat sources. The optimized selection is formulated as multicriteria decision-making problem. The constraints for this problem include a static HTS model, allowing considerations of system life cycle, time variability and spatial topology. Thereby, variation of heat demand and ground temperature within the DH area, insulation and pipe aging and/or terrain elevation profile are taken into account in the decision-making process. The HTS construction costs, pumping power, and heat losses are considered as objective functions. Inner pipe diameter, insulation thickness, temperatures and pumping stations locations are optimized during the decision-making process. Moreover, the variants of pipe-laying e.g. one pipeline with the larger diameter or two with the smaller might be considered during the optimization. The analyzed optimization problem is multicriteria, hybrid and nonlinear. Because of such problem properties, the genetic solver was applied.
The paper focuses on the presentation and comparison of basic nodal and expanded multi-nodal models of the Pressurized Water Reactor (PWR) core, which includes neutron kinetics, heat transfer between fuel and coolant, and internal and external reactivity feedback processes. In the expanded multi-nodal model, the authors introduce a novel approach to the implementation of thermal power distribution phenomena into the multi-node model of reactor core. This implementation has the form of thermal power distribution coefficients which approximate the thermal power generation profile in the reactor. It is assumed in the model that the thermal power distribution is proportional to the axial distribution of neutron flux in the un-rodded and rodded reactor core regions, as a result of control rod bank movements. In the paper, the authors propose a methodology to calculate those power distribution coefficients, which bases on numerical solutions of the transformed diffusion equations for the un-rodded and rodded reactor regions, respectively. Introducing power distribution coefficients into the expanded multi-nodal model allows to achieve advanced capabilities that can be efficiently used in design and synthesis of more advanced and complex control algorithms for PWR reactor core, for instance in the field of reactor temperature distribution control.
The nature of the processes taking place in a nuclear power plant (NPP) steam turbine is the reason why their modeling is very difficult, especially when the model is intended to be used for on-line optimal model based process control over a wide range of operating conditions, caused by changing electrical power demand e.g. when combined heat and power mode of work is utilized. The paper presents three nonlinear models of NPP steam turbine, which are: the static model, and two dynamic versions, detailed and simplified. As the input variables, the models use the valve opening degree and the steam flow properties: mass flow rate, pressure and temperature. The models enable to get access to many internal variables describing process within the turbine. They can be treated as the output or state variables. In order to verify and validate the models, data from the WWER-440/213 reactor and the 4 CK 465 turbine were utilized as the benchmark. The performed simulations have shown good accordance of the static and dynamic models with the benchmark data in steady state conditions. The dynamic models also demonstrated good behavior in transient conditions. The models were analyzed in terms of computational load and accuracy over a wide range of varying inputs and for different numerical calculation parameters, especially time step values. It was found that the detailed dynamic model, due to its complexity and the resultant long calculation time, is not applicable in advanced control methods, e.g. model predictive control. However, the introduced simplifications significantly decreased the computational load, which enables to use the simplified model for on-line control.
The real-time simulator of nuclear reactor basic processes
(neutron kinetics, heat generation and its exchange, poisoning and burn-
ing up fuel) build in a network environment is presented in this paper.
The client-server architecture was introduced, where the server is a pow-
erful computing unit and the web browser application is a client for user
interface purposes. The challenge was to develop an application running
under the regime of real-time, with a high temporal resolution, in an
environment which is not a native real-time. The problem of a real-time
operation taking into account the variable time of calculations and a
communication latency was solved using the developed mechanism of
step length adaptation. Results of multiple studies of a numerical com-
pliance with the reference simulator proved correctness of the developed
The importance of dissolved oxygen concentration controlinaerationtanksofabioreactoratﬂow-throughwastewater treatment plant (WWTP) can easily be justiﬁed by technological requirements as well as simple economics. Firstly, appropriate levels of dissolved oxygen concentration are essential for the vitality of microorganisms that comprise the bioreactor. Secondly, the costs of dissolved oxygen concentration control related to the blower station operation constitute up to 75% of the plantwide electric bill. This paper addresses a problem of Takagi– Sugeno fuzzy model identiﬁcation of dissolved oxygen dynamics (aeration process) for control design purposes. In the proposed approach the fuzzy partitions and the corresponding fuzzy sets are identiﬁed based on the knowledge of the process. Local (regional) model structure is obtained based on a larger wellestablished cognitive model from which a well-deﬁned parameter set follows. Thereafter, a parameter identiﬁcation is performed. A case study example of a bioreactor at Kartuzy WWTP illustrates the workﬂow of the proposed identiﬁcation algorithm.
Typically there are two main control loops with PI controllers operating at each turbo-generator set. In this paper a distributed model predictive controller DMPC, with local QDMC controllers for the turbine generator, is proposed instead of a typical PI controllers. The local QDMC controllers utilize step-response models for the controlled system components. These models parameters are determined based on the proposed black-box models of the turbine and synchronous generator, which parameters are identified on-line with the RLS algorithm. It has been found that the proposed DMPC controller realize the reference trajectories of the effective power and the angular velocity, and damp generator voltage oscillations with satisfactory quality in comparison to the typical control structure with the PID controllers.