Two-tank System Research Articles

Experimental sensorless control for a coupled two-tank system using high gain adaptive observer and nonlinear generalized predictive strategy

In this paper an adaptive control for a coupled two-tank system is proposed. This control strategy uses a generalized predictive controller, whose main method is to minimize a multistage cost function defined over a prediction horizon. Furthermore, to implement this controller in the framework of the sensorless control from the only measurement of the liquid level in the bottom tank, an adaptive interconnected high gain observer is developed for estimating the liquid level in the upper tank and the two constant parameters of the system. Two design features are worth to be emphasized. Firstly, the control calibration is achieved through the tuning of only two scalar design parameters. Secondly, the exponential convergence to zero of the state observation and parameter estimation errors is established under a well defined condition. Finally, the theoretical results are corroborated through simulation and experimental results which highlight the efficiency and applicability of the proposed observer–controller scheme.

A new Hammerstein model control strategy: feedback stabilization and stability analysis

This paper treats the identification, the control and the stability analysis of the discrete Hammerstein structure which is composed by a static nonlinearity gain associated with a linear dynamic subsystem. Its parameters are obtained from the subspace identification using the multivariable output error state space algorithm. The stabilization of this class of systems is generally leaded by a nonlinear control law, including an exact inverse of the static nonlinearity. Then, it is possible to use a linear state feedback controller to stabilize the Hammerstein system in closed-loop and to track the reference input. Thus, the performances of this method become limited when the considered static nonlinearity is approximately invertible. In this context, an approximate inverse of this component is investigated. Furthermore, based on the Lyapunov method, the stability conditions are obtained by solving a set of linear matrix inequalities constraints. The case of a coupled two-tank system is considered in order to illustrate the validity of the proposed approach.

Evaluation of energy density as performance indicator for thermal energy storage at material and system levels

The increase of the capacity factor of thermal processes which use renewable energies is closely linked to the implementation of thermal energy storage (TES) systems. Currently, TES systems can be classified depending on the technology for storing thermal: sensible heat, latent heat, and sorption and chemical reactions (usually known as thermochemical energy storage). However, there is no standardized procedure for the evaluation of such technologies, and therefore the development of performance indicators which suit the requisites of the final users becomes an important goal. In the present paper, the authors identified the energy density as an important performance indicator for TES, and evaluated it at both material and system levels. This approach is afterwards applied to prototypes covering the three TES technologies: a two-tank molten salts sensible storage system, a shell-and-tube latent heat storage system, and a magnesium oxide and water chemical storage system. The evaluation of the energy density highlighted the difference of its value at the material value, which presents a theoretical maximum, and the results at system level, which considers all the parts required for operating the TES, and thus presents a significantly lower value. Moreover, the proposed approach captured the effect of the complexity and overall size of the system, showing the relevance of this performance indicator for evaluating technologies for applications in which volume is a limiting parameter.

Robust Fuzzy Model Predictive Control of Discrete-Time Takagi–Sugeno Systems With Nonlinear Local Models

Robust fuzzy model predictive control of discrete nonlinear systems is investigated in this paper. A recently developed Takagi–Sugeno (T–S) fuzzy approach which uses nonlinear local models is adopted to approximate the nonlinear systems. A critical issue that restricts the practical application of classical model predictive control is the online computational cost. For model predictive control of T–S fuzzy systems, the online computational burden is even worse. Especially for complex systems with severe nonlinearities, parametric uncertainties, and disturbances, existing model predictive control of T–S fuzzy systems usually leads to a very conservative solution or even no solution in some occasions. However, more relaxed results can be achieved by the proposed fuzzy model predictive control approach which adopts T–S systems with nonlinear local models. Another advantage is that online computational cost of the optimization problem through solving matrix inequalities can be significantly reduced at the same time. Simulations on a numerical example and a two-tank system are presented to verify the effectiveness and advantages of the proposed method. Comparisons among several T–S fuzzy approaches are illustrated and show that the best settling time is achieved via the proposed method.

Earliest deadline first scheduling technique for different networks in network control system

The idea of this research is to determine the best network providing the reduced network time delay in network controlled system (NCS). NCS tackles robust and nonlinear processes that are time-varying or the requirements for the control change with the operating conditions using earliest deadline first (EDF) scheduling technique. It is very useful for minimizing the effects of parameter variations with respect to the process dynamics. The main advantage of applying EDF is that the parameters of the controller can be changed according to deadline along with the process changes. The main limiting factor is that auxiliary measurement should respond quickly to the process change. By applying the EDF algorithm in NCS schemes, the control of the two-tank water-level system is simulated using PID controllers and the control via Internet is simulated with the constant time delays and time-varying delay conditions. The drawbacks of NCS are network-induced delay, packet losses, bit errors, time-varying random transmission delay, lack of synchronization between devices, bandwidth limitations and integration of the modules. As the EDF scheduling approach is based on the mean time-delay parameters, they shift from one set to another when the mean time delay changes from one set to another. Therefore, time-delay issues are reduced by this algorithm. In this research work, the main challenge network-induced delay is reduced by scheduling technique and suitable network for PID control for EDF scheduling is determined among CAN, Ethernet, Switched Ethernet, TDMA and FDMA. CAN and Ethernet have the minimum of 1 ms network-induced time delay when compared with Switched Ethernet, TDMA and FDMA under overload condition. The integral of absolute error is employed to measure the quality of control of each control loop value for EDF scheduling 0.00354 and processor utilization is estimated as U = 0.12.

Study of ethanol fermentation reaction using Saccharomyces diastaticus in a two-tank fermentation system with cell recycling

Abstract Experimental data of ethanol fermentation in a two-tank system with cell recycling using sucrose as a substrate were investigated to establish a kinetic model that described the reaction. Flocculent yeast Saccharomyces diastaticus LORRE-316 was used as the fermenting yeast, and the fermentation medium comprised 80 g/L sucrose, 10 g/L yeast extract, 10 g/L peptone, 2 g/L potassium phosphate monobasic (KH2PO4), and 0.5 g/L magnesium sulfate heptahydrate (MgSO4·7H2O). Three models, the Monod model, the modified Monod model, and the extended-modified Monod model, were used to describe fermentation, and the extended-modified Monod model described the reaction more accurately than the other two models. The model took substrate limitations plus substrate and ethanol inhibitive effects into consideration, and was modified to include assumptions that included terms for substrates (sucrose, glucose and fructose) and product (ethanol). In addition, the ethanol concentration had a significant effect on cell growth. The results of Lineweaver–Burk plots showed that the maximum specific growth rate (μMAX) and the Monod constant (KS) were 0.72/h and 26.77 g/L, respectively. The models were suitable for describing the experimental data.

Cyclic performance of cascaded and multi-layered solid-PCM shell-and-tube thermal energy storage systems: A case study of the 19.9 MWe Gemasolar CSP plant

A shell-and-tube heat exchanger which incorporates a sensible or phase change material (PCM) as the storage medium offers a potentially commercially viable alternative to the two-tank molten salt system. In particular, cascaded PCMs and multi-layered solid-PCMs (MLSPCMs) were investigated as proposed systems which can reduce the amount of storage material used and ensure optimal storage utilization. In this work, the performance of various thermal energy storage (TES) alternatives integrated into the 19.9 MWe Gemasolar concentrated solar power (CSP) plant (located in Seville, Spain) were compared with the conventional two-tank system. These alternative storage configurations were characterized by a single tank filled with a single, cascaded, or multi-layered storage media. Importantly, as a system-level study, this paper compared the performance of the design alternatives integrated with other CSP components in order to capture the effect of dynamic interactions between the storage system and other CSP components. Through a validated numerical investigation of the annual performance of the integrated systems, all the design alternatives were compared in the context of annual electricity generation, which represents the ultimate criterion to judge the true potential of each alternative. To conduct an apples-to-apples comparison, the storage capacity and geometric parameters were fixed. The design alternatives were categorized based on the storage materials involved and their percentages of occupancy in the TES tank (i.e. 12 storage groups and a total number of 45 design alternatives). It was found that the well-designed TES designs with cascaded PCMs performed similarly in charging and discharging (i.e. with a similar amount of total stored or delivered energy per cycle). This contrasts with a single PCM system, where there exists a significant difference between charging and discharging performance. The results of annual cyclic performance, under real-time operational conditions, indicated that a MLSPCM design configuration that was filled with a high melting point PCM in the top 25% of the tank, sensible concrete in the middle 50%, and a low melting point PCM in the bottom 25% of the tank had the best performance among all design alternatives studied. Moreover, it was found that changing the filler portions any one cascaded PCM group cannot significantly change the annual performance of the system. Contrary to much of the available literature – literature which does not consider system integration – it was shown that the shell-and-tube alternatives can only approach the annual performance of two-tank systems under ‘extended’ operational conditions (i.e. allowing temperature set points to float relatively far away from their fixed design points).

Energy and Exergy Analyses of Recompression Brayton Cycles Integrated with a Solar Power Tower through a Two-Tank Thermal Storage System

AbstractEnergy and exergy analyses of a recompression supercritical carbon dioxide Brayton cycle integrated with a solar tower through a two-tank thermal storage system were conducted. A complete m...

General performance evaluation charts and effectiveness correlations for the design of thermocline heat storage system

One-tank molten salt thermocline heat storage system can reduce capital cost due to the use of cheap heat storage materials as compared with two-tank molten salt heat storage system. In order to develop a convenient method for the evaluation and design of the one-tank thermocline heat storage system, the idea of effectiveness-number of transfer unit method (ε-NTU) for heat exchanger design was employed in which three dimensionless design parameters are defined including the ratio between overall thermal conductance and the total thermal capacity of heat transfer fluid flowing through the system during discharging process (i.e., NTU), the ratio between thermal capacity of solid particles and total thermal capacity of heat transfer fluid through the system during the discharging process (i.e., Cs∗), the ratio between overall thermal conductance in the charging process and that in the discharging process (i.e., (hA)∗). A transient one-dimensional dispersion-concentric model is then applied to study the effects of three dimensionless parameters on the effectiveness of one-tank system. It is shown that the effectiveness of the one-tank thermocline heat storage system is closely related to NTU, Cs∗ and (hA)∗. Based on the simulated results, general performance evaluation charts and the related effectiveness correlations are also proposed for evaluation and design of the one-tank system. Moreover, the proposed effectiveness correlations are finally applied in the design of a one-tank molten salt thermocline heat storage system in a 50 MWe CSP plant.

Application of interacting multiple model-based fault detection method on a hydraulic two-tank system

This paper addresses the problem of designing a fault identification and detection algorithm for non-linear systems. Timely identification and detection of a fault in a system is crucial in condition monitoring systems. However, finding the source of the failure is not trivial in systems with large numbers of components and complex component relationships. In this paper, an efficient scheme to detect adverse changes in system reliability and find the failed component is proposed, based on the interacting multiple model (IMM) algorithm, with fault detection and diagnosis formulated as a hybrid multiple model estimation scheme. The proposed approach provides an integrated framework for fault detection, diagnosis and state estimation. Its performance is illustrated for fault detection of a non-linear two-tank system. The proposed method can be used with different kinds of filters, using the confusion matrix and classification accuracy as comparison metrics. A particle filter is used with the IMM algorithm and its performance is compared to the linear Kalman filter as a comparative case concerning the improvement that can be achieved when going beyond the consideration that the system is linear.

Parametric study of the thermocline filler concept based on exergy

In this work, an extensive parametric study of the molten salt thermocline storage concept with filler is presented. The parametric study is coupled with an optimization routine, allowing a better comparison, since it finds only those storage configurations, which can directly substitute the two-tank system in a given power plant. Results show that, compared to the two-tank molten salt system, the thermocline technology achieves high exergetic efficiency at only slightly increased storage volume size and a huge decrease in salt inventory.

Thermal Energy Storage Configurations for Small Modular Reactor Load Shedding

The increased penetration of intermittent renewable energy technologies such as wind and solar power can strain electric grids, forcing carbon-based and nuclear sources of energy to operate in a load-follow mode. For nuclear reactors, load-follow operation can be undesirable due to the associated thermal and mechanical stresses placed on the fuel and other reactor components. Various methods of thermal energy storage (TES) can be coupled to nuclear (or renewable) power sources to help absorb grid variability caused by daily load demand changes and renewable intermittency. Two TES techniques are investigated as candidate thermal reservoirs to be used in conjunction with a small modular reactor (SMR): a two-tank sensible heat storage system and a stratified chilled-water storage system. The goal when coupling the two systems to the SMR is to match turbine output and demand and bypass steam to the TES systems to maintain reactor power at approximately 100%. Simulations of integral pressurized water reactor dynamics are run in a high-fidelity FORTRAN model developed at North Carolina State University. Both TES systems are developed as callable FORTRAN subroutines to model the time-varying behavior associated with different configurations of these systems when connected to the SMR simulator. Simulation results reveal the sensible heat storage system is capable of meeting turbine demand and maintaining reactor power constant while providing enough steam to power four absorption chillers for chilled-water production and storage. The stored chilled water is used to supplement cooling loads of an adjacent facility.

Two-tank molten salts thermal energy storage system for solar power plants at pilot plant scale: Lessons learnt and recommendations for its design, start-up and operation

Abstract Renewable energies are main players to ensure the long-term energy supply. Solar power plants with thermal energy storage (TES) are one of the available renewable technologies which have more potential. Nowadays, there are still several aspects in the design and operation of these power plants which need to be improved, such as the correct operation of some specific instrumentation, the compatibility between TES materials and storage tanks materials, and operational process strategies. This paper presents the acquired experience during the design, start-up, and operation of a kWh scale pilot experimental facility built at the University of Lleida (Spain) together with Abengoa Research (Spain) in 2008. The versatility of this facility has allowed simulating real working conditions and therefore testing different TES systems, TES materials, solar power plant components, and operational strategies focused on TES for temperatures up to 400 °C. In the present paper, the authors show the lessons learnt at pilot and present the main problems and limitations encountered, and give advices of this experimental set-up to extrapolate the data to real plant, to provide solutions to technical problems and reduce the cost of commercial plants.

Data-driven model reference control of MIMO vertical tank systems with model-free VRFT and Q-Learning

This paper proposes a combined Virtual Reference Feedback Tuning–Q-learning model-free control approach, which tunes nonlinear static state feedback controllers to achieve output model reference tracking in an optimal control framework. The novel iterative Batch Fitted Q-learning strategy uses two neural networks to represent the value function (critic) and the controller (actor), and it is referred to as a mixed Virtual Reference Feedback Tuning–Batch Fitted Q-learning approach. Learning convergence of the Q-learning schemes generally depends, among other settings, on the efficient exploration of the state-action space. Handcrafting test signals for efficient exploration is difficult even for input-output stable unknown processes. Virtual Reference Feedback Tuning can ensure an initial stabilizing controller to be learned from few input-output data and it can be next used to collect substantially more input-state data in a controlled mode, in a constrained environment, by compensating the process dynamics. This data is used to learn significantly superior nonlinear state feedback neural networks controllers for model reference tracking, using the proposed Batch Fitted Q-learning iterative tuning strategy, motivating the original combination of the two techniques. The mixed Virtual Reference Feedback Tuning–Batch Fitted Q-learning approach is experimentally validated for water level control of a multi input-multi output nonlinear constrained coupled two-tank system. Discussions on the observed control behavior are offered.

Fault Diagnosis of Uncertain Hybrid Systems

This paper presents an online monitoring and fault diagnosis architecture for hybrid systems with nonlinear uncertain discrete-time dynamics. The architecture features a modular observer based on a modified hybrid automaton framework, that models each subsystem individually and the whole system as a composition of these models. The fault detection scheme can detect both discrete and parametric faults using a mode dependent time-varying threshold that guarantees no false-positives alarms due to modeling uncertainty. The fault isolation scheme can anticipate which fault events may have occurred and dynamically employs only the necessary number of isolation estimators that try to isolate the fault by calculating residual thresholds and approximating the unknown parameter values. Simulation results of a two-tank hybrid system example illustrate the effectiveness of the proposed approach.

Centralized Fault Detection of Complex Uncertain Hybrid Systems

This paper presents a centralized fault detection scheme for hybrid systems with nonlinear uncertain continuous dynamics and measurement noise. The scheme features a modular observer based on a modified hybrid automaton framework, that models each subsystem individually and the whole system as a composition of these models. The fault detection scheme employs a filtering approach, that attenuates the effect of measurement noise and allows tighter detection thresholds, and also an algorithm that handles autonomous mode transitions. As a result, the proposed approach can detect both discrete and parametric faults and guarantees no false alarms under all circumstances. Simulation results from a two-tank hybrid system example illustrate the effectiveness of the proposed scheme.

Economic Assessment of Condition-based Maintenance with Statistical Process Monitoring

Fault detection and identification methods have received extensive study in the literature, but very rarely demonstrate the economic impact of these interventions. In this paper, a simulation of a two-tank system with economic performance functions is presented as a test-bed for process monitoring methods. The simulation includes sensor noise and process variation, control loops, and safety interlocks, as well as sensor failures. Simple process monitoring, by principal component analysis and contribution methods, is applied to single- and successive-sensor failure simulations, and the economic benefit of the proposed condition-based maintenance approach demonstrated, even for cases in which the faulty sensor was not correctly identified. Challenges with fault identification, root cause analysis and fault prognosis are discussed. Proposals are made for further development of the simulation, which has been made available for future research.

Control of nonlinear two-tank hybrid system using sliding mode controller with fractional-order PI-D sliding surface

In this work, a sliding mode controller (SMC) with a fractional-order proportional plus integral plus derivative (FOPID) sliding surface for level control in a two-tank hybrid system is developed. A modified SMC with a fractional-order PI-D (FOPI-D) sliding surface is also proposed, in which the output of the system is directly applied to the derivative term of the sliding surface equation. The performance of the proposed controller is found to improve with an increase in the fractional value of the derivative term in the FOPI-D sliding surface. The performances of the two controller designs are compared with that of an SMC with a fractional-order PD (FOPD) sliding surface, taken from the literature. A simulation study, carried out with set points above and below a threshold value, revealed that the proposed SMC with the FOPI-D sliding surface delivers better closed-loop performance than conventional SMC, SMC with FOPD and SMC with FOPID sliding surfaces.

Demonstrating Cost Effective Thermal Energy Storage in Molten Salts: DLR’s TESIS Test Facility

The present paper gives an overview of a new test facility for molten salt thermocline storage systems and components, which is currently being constructed at DLR in Cologne. The paper also presents DLR thermocline-filler modelling and the potential of the novel storage technology compared to the two-tank state of the art molten salt storage. In this work, an extensive parametric study is combined with an optimization routine. The approach allows a better comparison, since it finds only those storage configurations, which can directly substitute the two-tank system in a given power plant. Results show that, compared to the two-tank molten salt system, the thermocline technology achieves high exergetic efficiency at only slightly increased storage volume size and a huge decrease in salt inventory.

Online average-based system modelling method for batch process

Online system identification provides a powerful tool to process control engineers for controller synthesis, process dynamics monitoring, real-time optimization and other purposes at a low computational cost. Instead of processing data in time, this paper intends to propose processing data in a different “direction” – in iteration/batch to improve the estimates tracking performance. However, directly changing the data processing direction gives rise to severe fluctuations on parameter estimates within a batch. To overcome this problem, two online identification methods with simple implementations are devised based on average. One method is applying average in the dual space, while the other in the primal space. The convergence of both approaches has been analyzed. An adaptive average strategy based on moving-window is also developed to track inter-batch dynamics drift. Finally, the simulation results on injection molding, two-tank system and continuous stirred tank reactor (CSTR) testify the improved performance of the methods proposed in this paper.