Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790273
J. Rawlings, W. Witkowski, John W. Eaton
This paper provides an overview of modelling, measurement, and control issues arising in systems modeUled by population balances. The population balance is a partial differential equation describing the dynamics of some general particle size distribution. The independent variables in the PDE are time and one or more internal particle coordinates, such as size, age, activity, etc., that fully characterize the state of the particle. Population balance models therefore can present a different set of issues than those arising in standard distributed parameter systems in which the independent variables are time and spatial location. The remaining process states, such as concentrations and temperature, are modelled -with integro-differential equations. The integrodifferential equations and the population balance's nonlocal boundary conditions are the sources of interesting and problematic dynamic behavior in continuous processes. This behavior includes open-loop instability and long period oscillations. The solution of optimal control profiles for batch processes is also difficult and computationally expensive. Accurate, on-line measurement of the particle size distribution for feedback control has been a long-standing hurdle, but has become possible in some situations due to improvements in measurement technologies such as laser light scattering and digital imaging. Crystallization from solution is used in this paper as an example of population balance models to illustrate each of these issues and demonstrate useful methods for model identification and process control.
{"title":"Control Issues Arising in Population Balance Models","authors":"J. Rawlings, W. Witkowski, John W. Eaton","doi":"10.23919/ACC.1989.4790273","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790273","url":null,"abstract":"This paper provides an overview of modelling, measurement, and control issues arising in systems modeUled by population balances. The population balance is a partial differential equation describing the dynamics of some general particle size distribution. The independent variables in the PDE are time and one or more internal particle coordinates, such as size, age, activity, etc., that fully characterize the state of the particle. Population balance models therefore can present a different set of issues than those arising in standard distributed parameter systems in which the independent variables are time and spatial location. The remaining process states, such as concentrations and temperature, are modelled -with integro-differential equations. The integrodifferential equations and the population balance's nonlocal boundary conditions are the sources of interesting and problematic dynamic behavior in continuous processes. This behavior includes open-loop instability and long period oscillations. The solution of optimal control profiles for batch processes is also difficult and computationally expensive. Accurate, on-line measurement of the particle size distribution for feedback control has been a long-standing hurdle, but has become possible in some situations due to improvements in measurement technologies such as laser light scattering and digital imaging. Crystallization from solution is used in this paper as an example of population balance models to illustrate each of these issues and demonstrate useful methods for model identification and process control.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114466207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790220
R. Lingarkar, Li Liu, M. Elbestawi, N. Sinha
A knowledge-based system approach for designing an adaptive controller is introduced in this paper. The proposed scheme has been used successfully in designing a self-tuning controller for force regulation in a computer numerically controlled (CNC) milling machine. In this scheme, frames [3] are used for knowledge representation and rules of logic for reasoning. Frames are knowledge structures that provide inheritance and data encapsulation, thereby allowing structured implementation and also enhancing maintainability of programs. This synergistic combination of frames and rules provides an ideal environment for intelligent control. As a consequence of representing knowledge in frames, the large amount of "safety net" of logics that goes along with most conventionally designed adaptive controllers to ensure safe operation, is considerably reduced. Procedural attachments to the slots in the frame which behave as daemons replace the "safety net" in the knowledge based controller. The self-tuning controller for the CNC milling machine is implemented on a 32 bit microprocessor based computer running at 20MHz. The knowledge representation and the reasoning process is implemented in PROLOG, whereas the numerical algorithms are written in C.
{"title":"Knowledge-Based Approach to Adaptive Computer Control in Manufacturing Systems","authors":"R. Lingarkar, Li Liu, M. Elbestawi, N. Sinha","doi":"10.23919/ACC.1989.4790220","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790220","url":null,"abstract":"A knowledge-based system approach for designing an adaptive controller is introduced in this paper. The proposed scheme has been used successfully in designing a self-tuning controller for force regulation in a computer numerically controlled (CNC) milling machine. In this scheme, frames [3] are used for knowledge representation and rules of logic for reasoning. Frames are knowledge structures that provide inheritance and data encapsulation, thereby allowing structured implementation and also enhancing maintainability of programs. This synergistic combination of frames and rules provides an ideal environment for intelligent control. As a consequence of representing knowledge in frames, the large amount of \"safety net\" of logics that goes along with most conventionally designed adaptive controllers to ensure safe operation, is considerably reduced. Procedural attachments to the slots in the frame which behave as daemons replace the \"safety net\" in the knowledge based controller. The self-tuning controller for the CNC milling machine is implemented on a 32 bit microprocessor based computer running at 20MHz. The knowledge representation and the reasoning process is implemented in PROLOG, whereas the numerical algorithms are written in C.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114493944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790574
Yu Tang, R. Ortega, L. Praly
Here we depart from the standard stabilization objective of adaptive control and assume that for the plant to be controlled a parametrization of the regulator insuring closed-loop stability is known. The structure, dynamic order and number of adjustable parameters of the compensator are at the designer's disposal and no assumptions, except linearity are imposed on the plant. We propose an on-line tuning procedure for the controller parameters intended to improve performance and such that global stability is preserved. Performance of the adaptive system is evaluated in two ways: deriving uniform bounds on the sup value of the tracking error; giving conditions under which RMS performance index decreases when adaptation is turned on.
{"title":"On Performance Improvement of Adaptive Tuners","authors":"Yu Tang, R. Ortega, L. Praly","doi":"10.23919/ACC.1989.4790574","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790574","url":null,"abstract":"Here we depart from the standard stabilization objective of adaptive control and assume that for the plant to be controlled a parametrization of the regulator insuring closed-loop stability is known. The structure, dynamic order and number of adjustable parameters of the compensator are at the designer's disposal and no assumptions, except linearity are imposed on the plant. We propose an on-line tuning procedure for the controller parameters intended to improve performance and such that global stability is preserved. Performance of the adaptive system is evaluated in two ways: deriving uniform bounds on the sup value of the tracking error; giving conditions under which RMS performance index decreases when adaptation is turned on.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"268 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116245591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790562
M. Aynsley, D. Peel, A. Morris
The ability to control a highly non-linear and time variant fermentation process is of considerable importance to the biotechnological industries which are continually striving to obtain higher yields and improved uniformity of production. Many industrial fermentations are operated in a fed-batch mode using a pre-defined (open loop) substrate feeding regime based on years of empirical development. Experienced operators continually monitor the process and hold microbial growth to an "ideal" trajectory using heuristics and process knowledge to make adjustments to the feeding strategy in order to compensate for variations between batches. These modifications can be quite significant since even a small increase in product yield can considerably affect process profitability by making more efficient use of carbon substrate. This paper describes the application of a real-time knowledge based system (RTKBS) to provide supervisory control of fed-batch fermentation processes. The system also performs sensor validation, fault detection/ fault diagnosis and incorporates relevant expertise and experience drawn from both the process engineering domain and the control engineering domain. The system has been developed using the G2 Real-Time Expert System (Gensym Corp.) and runs on a SUN 3/60 workstation which is linked to pilot scale fermenters via an Ethernet connection to a IBM PS/2. The PS/2 carries out local monitoring and control of the fermentation process through an RS232 serial connection to a number of industrial signal processors which are in turn directly linked to the process.
{"title":"A Real-Time Knowledge-Based System for Fermentation Control","authors":"M. Aynsley, D. Peel, A. Morris","doi":"10.23919/ACC.1989.4790562","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790562","url":null,"abstract":"The ability to control a highly non-linear and time variant fermentation process is of considerable importance to the biotechnological industries which are continually striving to obtain higher yields and improved uniformity of production. Many industrial fermentations are operated in a fed-batch mode using a pre-defined (open loop) substrate feeding regime based on years of empirical development. Experienced operators continually monitor the process and hold microbial growth to an \"ideal\" trajectory using heuristics and process knowledge to make adjustments to the feeding strategy in order to compensate for variations between batches. These modifications can be quite significant since even a small increase in product yield can considerably affect process profitability by making more efficient use of carbon substrate. This paper describes the application of a real-time knowledge based system (RTKBS) to provide supervisory control of fed-batch fermentation processes. The system also performs sensor validation, fault detection/ fault diagnosis and incorporates relevant expertise and experience drawn from both the process engineering domain and the control engineering domain. The system has been developed using the G2 Real-Time Expert System (Gensym Corp.) and runs on a SUN 3/60 workstation which is linked to pilot scale fermenters via an Ethernet connection to a IBM PS/2. The PS/2 carries out local monitoring and control of the fermentation process through an RS232 serial connection to a number of industrial signal processors which are in turn directly linked to the process.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116391893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790555
A. G. Hill, Norachat Ruksakij
Methods are described to estimate process and disturbance parameters based on curve fitting the transient response of a closed loop control system. The objectives are : 1) to mathc the process transfer function to a first order plus dead time model and 2) to match the disturbance to a first order model unit step response that enters the loop at the end of the process. The curve fitting methods identify : process parameters kp(gain), ¿p, (time constant), and ¿d (dead time); and disturbance parameters kl(gain), and ¿l(time constant). The methods are based on fitting time domain equations for closed loop response. These are derived using both continuous system analysis and sampled data system analysis.
{"title":"Process and Disturbance Identification by Curve Fitting The Closed Loop Response","authors":"A. G. Hill, Norachat Ruksakij","doi":"10.23919/ACC.1989.4790555","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790555","url":null,"abstract":"Methods are described to estimate process and disturbance parameters based on curve fitting the transient response of a closed loop control system. The objectives are : 1) to mathc the process transfer function to a first order plus dead time model and 2) to match the disturbance to a first order model unit step response that enters the loop at the end of the process. The curve fitting methods identify : process parameters kp(gain), ¿p, (time constant), and ¿d (dead time); and disturbance parameters kl(gain), and ¿l(time constant). The methods are based on fitting time domain equations for closed loop response. These are derived using both continuous system analysis and sampled data system analysis.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121972241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790461
B. Wittenmark
In most control schemes it is advantageous to introduce integrators to eliminate off-set due to load disturbances. It is, however, also important to introduce nonlinearities, for instance due to limitations in actuators. The interaction between the integrator and the nonlinearities will cause problems with reset windup. Ways to handle anti-reset windup for different controller configurations are discussed in the paper. Simple PID-controllers, cascade loops, state feedback controllers and pole-placement controllers are given a unified treatment. The discussion is supplemented with simulations.
{"title":"Integrators, Nonlinearities, and Anti-reset Windup for Different Control Structures","authors":"B. Wittenmark","doi":"10.23919/ACC.1989.4790461","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790461","url":null,"abstract":"In most control schemes it is advantageous to introduce integrators to eliminate off-set due to load disturbances. It is, however, also important to introduce nonlinearities, for instance due to limitations in actuators. The interaction between the integrator and the nonlinearities will cause problems with reset windup. Ways to handle anti-reset windup for different controller configurations are discussed in the paper. Simple PID-controllers, cascade loops, state feedback controllers and pole-placement controllers are given a unified treatment. The discussion is supplemented with simulations.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122113511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790268
Athanasios Sideris
A efficient algorithm to check the robust stability of a polytope of polynomials is proposed. This problem is equivalent with a zero exclusion condition at each frequency. It is shown that such a condition has to be checked at only a finite number of frequencies. We formulate this problem as a parametric linear program which can be solved by the Simplex procedure with additional computations between steps, consisting of polynomial evaluations and calculation of positive polynomial roots. Our algorithm requires a finite number of steps (corresponding to frequency checks) and in the important case of the polytope of parameters being a hypercube, this number is at most of order O(m3n), where n is the degee of the polynomials in the family and m is the number of parameters.
{"title":"A Polynomial time Algorithm for Checking the Robust Stability of a Polytope of Polynomials","authors":"Athanasios Sideris","doi":"10.23919/ACC.1989.4790268","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790268","url":null,"abstract":"A efficient algorithm to check the robust stability of a polytope of polynomials is proposed. This problem is equivalent with a zero exclusion condition at each frequency. It is shown that such a condition has to be checked at only a finite number of frequencies. We formulate this problem as a parametric linear program which can be solved by the Simplex procedure with additional computations between steps, consisting of polynomial evaluations and calculation of positive polynomial roots. Our algorithm requires a finite number of steps (corresponding to frequency checks) and in the important case of the polytope of parameters being a hypercube, this number is at most of order O(m3n), where n is the degee of the polynomials in the family and m is the number of parameters.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124002916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790312
M. M. Hadiji, M. Sawan
This paper presents a solution to the singular linear minimum-vaviance estimation problem in the discrete time case. An expression for the transfer function of the Kalman-Bucy filter with nonsingular correlated noises is derived using the spectral factorization in the zdomain. The case of singular correlated noises is then handled as a special case.
{"title":"Kalman-Bucy Filters with Singular Correlated Noises","authors":"M. M. Hadiji, M. Sawan","doi":"10.23919/ACC.1989.4790312","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790312","url":null,"abstract":"This paper presents a solution to the singular linear minimum-vaviance estimation problem in the discrete time case. An expression for the transfer function of the Kalman-Bucy filter with nonsingular correlated noises is derived using the spectral factorization in the zdomain. The case of singular correlated noises is then handled as a special case.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124061974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-06-21DOI: 10.1109/ACC.1989.4173606
K. Kaiser, G. Nessler
Flat rolled steel strip is reduced to its final thickness in a tandem cold mill. This mill consists of a series of close coupled rolling stands. In order to maximize strip quality it is necessary to have precise and quick response mill drives. During a modernization study of an existing mill it was discovered that the mill had a low torsional resonance that would be excited by improved, fast drives. This paper summarizes the steps taken to analyze and understand this problem. These steps included measuring the torsional resonance frequencies on the mill, modeling the mechanical and electrical systems and tuning the models. The measured resonance frequencies were found to vary with operating variables. A finite element model of the mechanical system was developed and tuned. Studies with this model showed that changes in the mechanical system to increase the frequencies by increasing stiffness were not practical. A model of the control and drive system was developed and tuned. The model was used to determine the effectiveness of applying analog filters in the control system to reduce the excitation of the resonant frequency.
{"title":"Mechanical and Control System Analysis of a Tandem Cold Mill to Solve a Torsional Drive System Problem","authors":"K. Kaiser, G. Nessler","doi":"10.1109/ACC.1989.4173606","DOIUrl":"https://doi.org/10.1109/ACC.1989.4173606","url":null,"abstract":"Flat rolled steel strip is reduced to its final thickness in a tandem cold mill. This mill consists of a series of close coupled rolling stands. In order to maximize strip quality it is necessary to have precise and quick response mill drives. During a modernization study of an existing mill it was discovered that the mill had a low torsional resonance that would be excited by improved, fast drives. This paper summarizes the steps taken to analyze and understand this problem. These steps included measuring the torsional resonance frequencies on the mill, modeling the mechanical and electrical systems and tuning the models. The measured resonance frequencies were found to vary with operating variables. A finite element model of the mechanical system was developed and tuned. Studies with this model showed that changes in the mechanical system to increase the frequencies by increasing stiffness were not practical. A model of the control and drive system was developed and tuned. The model was used to determine the effectiveness of applying analog filters in the control system to reduce the excitation of the resonant frequency.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125781319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790511
H. Kuraoka, N. Ohka, M. Ohba, S. Hosoe, F. Zhang
This study seeks to apply H∞ robust control theory to the design of an automotive diesel pump control system, and also to compare the results with those when optimal regulator theory is applied. A diesel pump control system must respond quickly and undeviatingly whenever a driver pedals the accelerator. Fuel viscosity changes due to temperature variations exert a great influence on the control system, both statically and dynamically. First, we constructed a feedback system by applying optimal regulator theory to the diesel pump control. However, the control has to be achieved by switching several feedback gains in relation to the fuel temperature variations. Thus, the aim of the present study was directed to design a robust control system that can withstand parameters perturbation. To do this, we used a type one robust feedback system constructed by application of H∞ robust control theory.
{"title":"Application of H∞ optimal design to automotive fuel control","authors":"H. Kuraoka, N. Ohka, M. Ohba, S. Hosoe, F. Zhang","doi":"10.23919/ACC.1989.4790511","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790511","url":null,"abstract":"This study seeks to apply H∞ robust control theory to the design of an automotive diesel pump control system, and also to compare the results with those when optimal regulator theory is applied. A diesel pump control system must respond quickly and undeviatingly whenever a driver pedals the accelerator. Fuel viscosity changes due to temperature variations exert a great influence on the control system, both statically and dynamically. First, we constructed a feedback system by applying optimal regulator theory to the diesel pump control. However, the control has to be achieved by switching several feedback gains in relation to the fuel temperature variations. Thus, the aim of the present study was directed to design a robust control system that can withstand parameters perturbation. To do this, we used a type one robust feedback system constructed by application of H∞ robust control theory.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125903973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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