In this work, we propose using extremum seeking control (ESC) as a tool for maximum power point tracking in micro hydro power plants. The phasor ESC, which is based on estimating the phasor of the plant output at the perturbation frequency, was modified by stimating the phasors of multiple harmonics of this frequency. This modification will improve the performance of ESC by reducing the luctuations in control variables that may appear in noisy environments as a result of high-amplitude perturbation signals. A test rig was used to experimentally verify the proposed approach and to demonstrate the usability of ESC in hydro power plants.
The Combinator is an important part in Kaplan turbine control. It ensures that the turbine will operate in an optimum way, in terms of maximum efficiency of the plant. This work suggests a new sinusoidal perturbation based extremum seeking algorithm based on the phasor of the output. We propose to use this algorithm for generating the required data to build and correct the combinator. Simulations are presented showing the applicability of the proposed methods.
In this letter, we address a multi-objective on-line optimization problem for unknown dynamical systems by providing a generalization of the Pareto seeking controller (PSC). The idea of the PSC is to drive the system to the Pareto front in the absence of knowledge of the values of the objectives or the input values to achieve Pareto optimality. Two special cases are presented, for two objectives and three objectives. A stability analysis is presented for the case of two objectives and two inputs, which shows that the controller practically drives the system into the neighborhood of the Pareto front, for any initial condition. Two simulation examples for the special cases are also presented
In this work, we present a modification for theclassic and phasor extremum seeking control algorithms in orderto improve the accuracy by removing or reducing the convergenceerror. The modulation signals were replaced by a sum of sinusoidsin order to remove the equilibrium shift in the controlled variableof the averaged system. The convergence error is calculated as afunction of the number of sinusoids used in the modulation signal.A simulation example is presented to illustrate the improvement.
This work presents a dynamic model for prediction of flow and output size distribution of cone crushers. The main purpose of the model is for simulation of closed-loop control using the Closed Side Setting (CSS) and the eccentric speed (ω) as manipulated variables. The idea of modeling crushers as cascaded zones is adopted throughout this work. The capacity, the length, the stroke, and the compression ratio of each zone are taken into consideration. Simulation results are presented in the form of the Crusher Performance Map (CPM) and the dynamic response for production of different size classes to steps input in ω and CSS. The simulations also include operation with recycling of oversize output, as well as the input of mixed materials. As an example, closed-loop control of the ratio of the large-size output to the total size output was simulated.
We present an extremum seeking control algorithm based on the estimation of the phasor of the perturbation frequency in the output of the plant. The phasor estimator is based on a continuous time Kalman filter, which is reduced into a variable gain observer by explicitly solving the special case of the Riccati equation. Local stability of the proposed al- gorithm for general non-linear dynamic systems using averaging and singular perturbations is presented for the single input case. The advantage of the presented algorithm is that it can be used on plants with large and even variable phase lag.
In this work we present a semi-global practical asymptotic stability analysis for phasor extremum seeking control with a general non-linear dynamic system. With the same technique applied to the classic band pass filter algorithm, we present a more relaxed (less constrained) semi-global practical asymptotic stability condition compared to earlier work. The results are based on a non approximated averaging for both control techniques.
This article demonstrates the ability of on-lineoptimization of cone crushers, specifically maximization of thetotal throughput of the crusher by adjusting the eccentric speed(ω). The on-line optimization was based on the Extremum-Seeking Control (ESC) approach, which is advantageous whenoptimizing systems with unknown time varying characteristics.Two types of gradient based approaches are tested in simulation,the traditional Band-pass filters method and a methodutilizing the Extended Kalman Filter (EKF). Both methodsperform satisfactory, demonstrating the good potential of ESCfor online-optimization of cone crushers. To deal with unwantedbehavior of the EKF based approach for situations when thegradient is not correctly estimated, a modification is suggestedbased on detecting this condition and accommodating for it.
This work presents an extension and validation for a control oriented model of cone crushers. Compared to earlier work, the aspect of energy consumption was added to the model. Validation was carried out using measurement data from two different crusher models and was based both on laboratory data and field experiment data. Using the results from the field trials, a plant simulator for a secondary crushing circuit has been implemented.
In this paper, we propose a perturbation amplitude adaption scheme for phasor extremum seeking control based on the plant's estimated gradient. By using phasor extremum seeking instead of classical extremum seeking, the problem of algebraic loops in the controller formulation is avoided. Furthermore, a stability analysis for the proposed method is provided, which is the first stability analysis for extremum seeking controllers using adaptive amplitudes. The proposed method is illustrated using numerical examples and it is found that changes in optimum can be tracked accurately while the steady-state perturbations can be reduced significantly.
A model-based fault detection algorithm for linear systems with uncertain parameters is treated. An error system, bilinear in the uncertainties, generates the residual. The residual is compared to a threshold, which is generated by a linear system with the unknown uncertainty upper bounds as parameters. These unknown uncertainty upper bounds can be substituted by design parameters and this article suggests an algorithm to choose design parameter values such that the threshold is larger than the residual when no fault is present. This parameter design algorithm is applied to a sensor fault detection algorithm for a jet engine.
An observer based approach for detecting clogging in valves in flotation processes is investigated. Integral action and linear feedback applied to a nonlinear process model constitutes the observer for which local stability is shown. The integral terms give estimates of the clogging in the valves of the process and this estimate is compared to a constant threshold. Experiments on real data from Boliden's flotation series at the Boliden Area Concentrator, Sweden, show no false alarm during any of the two working conditions, PI control and LQ control. It is also shown that cloggings, simulated by manipulating measurement data, are promptly detected. The observer based fault detection algorithm is compared to an algorithm based on parameter estimation and advantages of the two approaches are highlighted.
This article treats the problem of finding a linear system whose impulse response is an upper bound for the modulus of the impulse response of another given system. These upper bounds are required for a newly developed fault detection algorithm1). Three different methods to calculate a realizable upper bound for an impulse response, which contains multiple real poles and distinct complex poles, are presented. The triangular inequality and linear optimization are used in the first and second method, respectively. In the third method, the original impulse response is used combined with time-delays. The upper bounds are calculated for a fictitious impulse response and compared with its modulus.
Robust thresholds for observer-based residuals are developed for the purpose of detecting clogging in the valves of a flotation process. The observer in the residual generator is a linear model of the flotation process extended with integrators and corrected with a linear feedback term. The integral states in the observer constitute the residual. Contribution to the residual comes not only from the faults but also from uncertainties in measurements, estimates and working point To avoid false alarms generated by these uncertainties, robust time-varying thresholds depending on the uncertainties are derived. Experiments on a froth flotation process with four cascade coupled tanks are carried out successfully. The data was provided by Boliden Area Concentrator in Boliden, Sweden.
A dynamic threshold generator is employed for detecting faults in λ-tuned control loops. To this end, an optimizationalgorithm for dynamic threshold generators is proposed. The a priori-information from λ-tuning is used in designing astate estimator with integral action. A dynamic threshold generator for the residual of this state estimator is derived and the optimization algorithm is applied. Simulations with measurement data from an experimental water tank setup show that the method is capable of detecting a small fault without generating false alarms.
A model-based fault detection algorithm assuming uncertain process parameters is used for detecting poorly operating lambda-tuned control loops. The a priori information obtained from lambda-tuning is used to create an observer as residual generator. The observer has integral action which makes it possible to obtain a tight fault detection threshold. A linear optimization approach is used for finding the parameters in the threshold.
Styrsystemen i bruken består av tusentals reglerloopar och det är svårt att få en helhetssyn, och förstå de komplicerade sambanden mellan de olika processtegen. Med de nya verktygen blir det möjligt att analysera strukturen och generera helhetsstrategier för optimal styrning från ved till färdig pappersprodukt.
This paper presents a new application software for control conguration selection of interconnected industrial processes,called ProMoVis. Moreover, ProMoVis is able to visualize process models and process layout at the physical leveltogether with the control system dynamics. The software consists of a builder part where the visual representationof the interconnected process is created and an analyzer part where the process is analyzed using dierent controlconguration selection tools.The conceptual idea of the software is presented and the subsequent design and implementation of ProMoVis isdiscussed. The implemented analysis methods are briey described including their usage and implementation aspects.The use of ProMoVis is demonstrated by an application study on the stock preparation process at SCA Obbola AB,Sweden. The results of this study are compared with the currently used control strategy.The study indicates that ProMoVis introduces a systematic and comprehensive way to perform control congurationselection. ProMoVis has been released under the Apache Open Source license.
This paper discusses a new approach to interactive modeling, visualization and analysis of complex industrial processes. A theoretical framework based on signal flow graphs for modeling and visualization is presented. Using this framework a software tool is designed, called ProMoVis, which can be used to model a process, to visualize the models together with process construction and control system, and to perform analysis regarding e.g. feasible control strategies for the process. Moreover, a case study is conducted, where ProMoVis is used to model, visualize and analyze a stock preparation plant. The results indicate that the proposed methods and tools improve work flows, increase process understanding and simplify decision making on control strategies for complex process.
This paper summarizes the implementation and industrial experiences of a model-based control and gas-leakage detection system in a coal injection plant. It describes how advanced control and monitoring can be implemented in an industrial environment while taking human–machine interface aspects into consideration. The operation of the advanced and the conventional concept are compared regarding evaluation data, experiences and observations of operators and maintenance personnel. It is shown that the advanced control and monitoring system improves plant performance without disturbing routines in plant operation and, moreover, is positively accepted by the plant operators.
This paper deals with design and implementation of a combined model-based control and gas leakage detection system applied to the pulverized coal injection plant at SSAB Tunnplåt AB in Luleå, Sweden. The structure and functions of the in-house control and process monitoring system SafePCI are described. SafePCI is experimentally tested and has successfully completed two weeks test operation. The evaluation of the test operation indicate that combined model-based control and gas leakage detection is a major improvement for control systems in the process industry.
Modeling, control, and gas leakage detection in the coal injection process are discussed. It is shown that by use of model-based methods, the flow and pressure of the coal injection vessel are reliably controlled. With the new control law, the coal mass flow can be used as a control parameter for the blast furnace. High injection rates can be used and more coke substituted, This is expected to yield a cost reduction in the iron production. An experimental comparison of the conventional control unit with the one suggested in this article shows that an improvement of the process efficiency can be reached by other means than increasing the capacity of the plant
Experiences from field tests of a model-based molten metal analysis estimation system for the LD converter process are reported. Experiments have been carried out during a six-months long period on two converters at SSAB Tunnplat AB in Lulea, Sweden. The results achieved prove the viability of the approach taken and indicate its high potential regarding estimation accuracy and robustness. It is also concluded that some further system development is necessary to enable modeling of additives and lance level before the system can be recommended for permanent installation
Experiences from field tests of a model-based molten metal analysis estimation system for the Linz and Donawitz converter process are reported. Experiments have been carried out during a six-month-long period on two converters at SSAB Tunnplat AB, Lulea, Sweden. The achieved results prove viability of the approach taken and indicate its high potential regarding estimation accuracy and robustness. It is also concluded that some further system development is necessary to enable modeling of additives and lance level before the system can be recommended for permanent installation
We consider a novel method to design H-infinity observers for a class of uncertain nonlinear systems subject to unknown inputs. First, the main system dynamics are rewritten as an augmented system with state vector including both the state vector of the main system and the unknown inputs. Then, we design a H-infinity reduced-order observer to estimate both state variables and unknown inputs simultaneously. Based on a Lyapunov functional, we derive a sufficient condition for existence of the designed observer which requires solving a nonlinear matrix inequality. To facilitate the observer design, the achieved condition is formulated in terms of a set of linear matrix inequalities (LMI). By extending the proposed method to a multiobjective optimization problem, the maximum bound of the uncertainty and the minimum value of the disturbance attenuation level are found. Finally, the proposed observer is illustrated with an example.
A physical model of a continuous paper pulp digester is simplified and two subprocesses selected from the digester are modelled by coupled linear partial differential equations. This study focuses on the parameter identification of the simplified linear models. Finite-dimensional approximation of the model is made and a software package developed for identification of distributed parameter processes is applied. This identification system is developed for flexibility to allow identification for different choices of subprocesses and process variables. Unknown parameters of the subprocess models are estimated and the results are illustrated by process simulation and model validation.
A physical model of a nonlinear subprocess in a continuous paper pulp digester is discussed and simplified. Model approximation is carried out in order to produce a simple linear model to be used for unknown parameter estimation of the physical model. The Taylor series expansion and the orthogonal collocation method are applied for the model linearization and model lumping, respectively. The reduced model is expressed as a standard state space form. The model parameters are estimated in the least squares sense, and the parameters retain their own physical meanings. The results of the parameter estimation are discussed and the model is verified using validation data.
This paper studies the application of reduced models of a distributed parameter system for robust process control and state estimation. We take the approach of integrating model reduction, parameter identification, and model uncertainty analysis, in purpose to find an appropriate trade-off between complexity and robust performance. The application example is the temperature system in a continuous paper pulp digester. Physical modeling of this process results in coupled linearized partial differential equations which are then reduced into low-order nominal process models using an orthogonal collocation approximation method.Two different approaches to obtaining a model uncertainty description are adapted for use on a distributed parameter system with low-order nominal model and shown to produce similar results when tested with measurement data. It is also demonstrated how this uncertainty description, in combination with the reduced model, may be used for robust control design and verification of the control performance on the distributed parameter system.Finally, the possibility of estimating the distributed process state using a state observer for the reduced process is demonstrated. Measurements of the process state in a certain position is available and is shown to agree with the estimated state at the same position.
Proceedings for Swedish Control Meeting (Reglermöte 2008) 4-5 June 2008. The proceedings contains all the manuscripts that were presented at the conference in Luleå. Manuscripts are in Swedish and/or English.
En processindustrianläggning karaktäriseras av många delprocesser som är kopplade genom t.ex. materialflöden, gemensamma resurser, regulatorer osv. Detta förhållande ger upphov till tre typer av problem. 1. Det stora antalet processvariabler gör det orimligt att lägga ner stora arbetsinsatser på varje enskild variabel för t.ex. regulatordesign och övervakning. 2. De dynamiska kopplingarna mellan processvariablerna gör anläggningen till ett enormt stort dynamiskt system som inte är realistiskt att hantera som en helhet vid design av regulatorer och övervakningsalgoritmer. 3. Den komplexa strukturen kan ge upphov till komplicerad och svårförutsägbar dynamik i anläggningen som helhet, vilket kan ge upphov till t.ex. oscillationer. Arbetet i projektet fördelas på tre arbetspaket som angriper delproblem under de tre punkterna ovan. Alla tre arbetspaket förväntas resultera i verktyg som i förlängningen kan ingå som värdefulla komponenter på den plattform som en operatörssimulator utgör.
The model validation problem for linear systems with time-varying parameter uncertainty and additive disturbances is addressed. The disturbance are modelled using the window norm, which is a generalization of the l-infinity-norm and is shown to be attractive for optimal control. An approximation of the nonlinear operator from parameters to output is found based on the Fréchet derivative. Using this approximation, a sufficient condition for invalidation of a process model is formulated as a linear feasibility problem. In this condition, an upper bound for the approximation error is included. An overhead crane is used as an illustrative example to show that the model validation test is realistic to perform even with large data sets.
We explore the signal flow graph as a setup for visualizing and analyzing interconnected systems. Two operations for facilitating interpretation of signal flow graphs are defined. These are hiding of unimportant nodes and elimination of self-references and it is shown that the operations commute under some conditions and that the hiding operation preserves the physical structure of the system in a certain sense. Also, the Loop Gain Index (LGI) is introduced as a measure of the relative importance of the edges in terms of dynamic behavior of the interconnected system. The LGI isillustrated with a numerical example.
We report some results from the application of a flipped classroom setup for a basic course in automatic control. The course setup has been developed with the specific intention of avoiding extrinsic motivators for the students.For a group of 34 students, gender, exam score, and attendance in classroom activities was recorded and a linear regression model for how exam score relates to attendance in classroom activities and gender was developed using Matlab. It is shown that student attendance in classroom activities that require a great deal of time-on-task and student-student interactions is closely related to exam score. In contrast, other classroom activities, and also gender, is shown to have no significant impact on exam score.
Fault detection and isolation is a potentially powerful tool for achieving security and effective maintenance in various types of processes. The motivation for performing leakage detection in the coal injection plant is mainly the inflammability of pulverized coal. A leakage of air into an injection vessel could have catastrophic consequences. Nonlinear physical gray-box models of the plant are developed. Values of the unknown parameters are estimated by identification. Observers are constructed for these models and the residual is shown to be an estimate of the leakage flow.The Generalized Likelihood Ratio is employed to compare the residual to predefined typical leakage functions. When evaluating the residual, it is desirable to represent the essential dynamics concisely while removing irrelevant behaviour and noise. In order to ease the computational burden while preserving the essential dynamic behaviour of a leakage, a truncated Laguerre series representation of the signals is used. The developed algorithms are implemented in the commercially available product SafePCI and installed at SSAB Tunnplåt, Luleå.
A generic structure for dynamic models of cone crushers is presented, in the form of a partial differential equation depending on both time and a spatial variable as well as the size distribution of the particles. Assumptions on the sizeclassification of the flow through the crusher and the velocity of the particles enable modelling the effect of the main manipulated variables, i.e. closed side setting and rotational velocity. It is also shown how the model may be discretized and approximated by an ordinary differential equation. Simulations show that the model exhibits the expected behavior of a cone crusher. Notable is the effect of changing the rotational speed, which suggests that this variable is potentially valuable for improving the control of the crusher.
Access to measurements is a necessity in most technical applications, in order to detect faults, monitor performance, or exercise control. In some cases, however, installing measurement equipment is very expensive or even impossible. In such a case, estimates can be produced instead. In an observer, this is done by combining process knowledge, in the form of an analytical process model, with information, in the form of indirect measurements. If the process model is in the form of a system of linear differential equations, then the problem of constructing an observer is essentially solved by the Kalman filter and the Luenberger observer. For a system of nonlinear differential equations, however, there is no generic solution, which is the reason for extensive research in this area for the past decades. This thesis treats the development and analysis of nonlinear observers for three applications in the steel industry. The first application is the detection of gas leakages in a pulverized coal injection plant. An observer whose residual is sensitive to the gas leakage flow, has been designed for a nonlinear process model. A Generalized Likelihood Ratio test was applied to the residual to distinguish between different types of leakages. The method has been implemented in the plant and tested successfully with actual leakages. Furthermore, a Laguerre spectrum representation of the residual was utilized, to reduce disturbances and computational effort. The second application is the detection of clogging in pulverized coal injection lines. An observer, with a state variable that represents clogging, has been designed for a time-varying process model. An adaptive threshold for the estimated clogging variable was calculated. In experiments with data from the plant, the method was shown to detect clogging successfully, without producing false alarms. The third application is the estimation of metal analysis in the steel converter process. A nonlinear, physical process model was utilized and an observer was proposed, whose feedback is weighted by the sensitivity of the output with respect to the state. Experiments with data from a converter plant show that this strategy provides accurate estimates of the carbon content in the converter. Furthermore, a generalization of the proposed observer structure has been analyzed in terms of asymptotic stability and region of attraction.
We explore the signal flow graph as a setup for visualizing and analyzing interconnected systems. Two operations for facilitating interpretation of signal flow graphs are defined. These are hiding of unimportant nodes and elimination of self-references and it is shown that the hiding operation preserves the physical structure of the system in a certain sense. Also, two analysis tools are introduced for determining the relative importance of the edges in terms of dynamic behavior and controllability of the complex system. The analysis tools are illustrated with numerical examples.
Two desirable properties of a signal norm to be used for the purpose of optimal control or fault detection are highlighted. These properties are shift-invariance and the permitting of persistent signals. A class of norms, called the window norms, is analyzed. Among norms considered for control purposes, they appear to be the only ones, save the L∞-norm, that satisfy both properties. The signal spaces defined by the window norms, however, include some interesting signals that are not in the L∞-space. The window norms have been found suitable for application in fault detection and are here also considered for optimal control. It is shown that they can be taken as a support for the concept of L1-control but may also suggest a new class of optimal controllers.
The model validation problem assuming time-varying parameter uncertainty is addressed. A particular form of this uncertainty description, here named the biaffine input/output system is shown to be quite general and yet lead to simple solutions of the model validation problem, in the form of linear feasibility problems. An overhead crane is used as an illustrative example.
The problem of developing robust thresholds for fault detection is addressed. An inequality for the solution of a linear system with uncertain parameters is provided and is shown to be a valuable tool for developing dynamic threshold generators for fault detection. Such threshold generators are desirable for achieving robustness against model uncertainty in combination with sensitivity to small faults.The usefulness of the inequality is illustrated by developing an algorithm for detection of clogging in the valves of a flotation process. Simulations with measurement data show that the algorithm detects faults without generating false alarms.
The problem of developing robust thresholds for fault detection is addressed. An inequality for the solution of a linear system with uncertain parameters is provided and is shown to be a valuable tool for developing dynamic threshold generators for fault detection. Such threshold generators are desirable for achieving robustness against model uncertainty in combination with sensitivity to small faults. The usefulness of the inequality is illustrated by developing an algorithm for detection of sensor faults in a turbofan engine. The proposed algorithm consists of a state observer with integral action. A dynamic threshold generator is derived under the assumption of parametric uncertainty in the process model. Successful simulations with measurement data show that the algorithm is capable of detecting faults without generating false alarms.
This paper deals with gas-leakage detection and isolation in a fine coal injection vessel for a blast furnace process. Functions describing the expected time-domain behaviour of different leakages are developed, thus reducing the leakage isolation problem to pattern recognition. In order to lower the computational burden while preserving the essential dynamic behaviour of a leakage, a truncated Laguerre series representation is used. The Generalized Likelihood Ratio methos is employed to compare the Laguerre of the residual with the Laguerre spectra of the predefined typical leakage functions. Tests of the developed algorithm have been successfully performed at SSAB Tunnplåt, Luleå.
A nonlinear observer, with the feedback gain weighted by the sensitivity of the output with respect to the state, is developed for systems with nonlinear output map. The observer can be obtained from the extended Kalman filter by a special choice of time-varying weighting matrices. It is shown that the estimation error dynamics are asymptotically stable and a region of attraction is derived. The observer is applied to the top blown converter process for estimating the content of impurities in the liquid metal. Using plant data from the converter at SSAB Oxelösund AB, the observer is shown to provide accurate estimates of the carbon content.
This paper deals with the detection of clogging in the coal injection lines of a blast furnace. A physical model is developed and augmented with a signal that represents clogging. A nonlinear observer is proposed and shown to have any predefined convergence rate. An adaptive detection threshold scheme which is robust against time-varying uncertainties is employed. Simulations and experiments with real data are carried out to illustrate the usefulness of the methods.
This paper deals with the detection of clogging in the coal injection lines of a blast furnace. A physical model is developed and augmented with a signal that represents clogging. An observer is proposed and shown to have any predefined convergence rate. An adaptive detection threshold scheme which is robust against time-varying uncertainties is employed. Simulations and experiments with real data are carried out to illustrate the usefulness of the methods.