Pub Date : 2013-12-01DOI: 10.1109/AUCC.2013.6697277
Sei Zhen Khong, M. Cantoni, J. Manton
A differential geometric approach based on the gap metric is taken to examine the uniqueness of solutions of the equations describing a feedback interconnection. It is shown that under sufficiently small perturbations on the Fréchet derivative of a nonlinear plant as measured by the gap metric, the uniqueness property is preserved if solutions exist given exogenous signals. The results developed relate the uniqueness of solutions for a nominal feedback interconnection and that involving the derivative of the plant. Causality of closed-loop operators is also investigated. It is established that if a certain open-loop mapping has an inverse over signals with arbitrary start time (i.e. zero before some initial time), then the closed-loop operator is causal provided the latter is weakly additive.
{"title":"A gap metric perspective of well-posedness for nonlinear feedback interconnections","authors":"Sei Zhen Khong, M. Cantoni, J. Manton","doi":"10.1109/AUCC.2013.6697277","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697277","url":null,"abstract":"A differential geometric approach based on the gap metric is taken to examine the uniqueness of solutions of the equations describing a feedback interconnection. It is shown that under sufficiently small perturbations on the Fréchet derivative of a nonlinear plant as measured by the gap metric, the uniqueness property is preserved if solutions exist given exogenous signals. The results developed relate the uniqueness of solutions for a nominal feedback interconnection and that involving the derivative of the plant. Causality of closed-loop operators is also investigated. It is established that if a certain open-loop mapping has an inverse over signals with arbitrary start time (i.e. zero before some initial time), then the closed-loop operator is causal provided the latter is weakly additive.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121965924","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 : 2013-11-04DOI: 10.1109/AUCC.2013.6697276
J. Biggs, Craig Maclean, Albert Caubet
An analytical attitude motion planning method is presented that exploits the heteroclinic connections of an optimal kinematic control problem. This class of motion, of hyperbolic type, supply a special case of analytically defined rotations that can be further optimised to select a suitable reference motion that minimises accumulated torque and the final orientation error amongst these motions. This analytical approach could be used to improve the overall performance of a spacecraft's attitude dynamics and control system when used alongside current flight tested tracking controllers. The resulting algorithm only involves optimising a small number of parameters of standard functions and is simple to implement.
{"title":"Heteroclinic optimal control solutions for attitude motion planning","authors":"J. Biggs, Craig Maclean, Albert Caubet","doi":"10.1109/AUCC.2013.6697276","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697276","url":null,"abstract":"An analytical attitude motion planning method is presented that exploits the heteroclinic connections of an optimal kinematic control problem. This class of motion, of hyperbolic type, supply a special case of analytically defined rotations that can be further optimised to select a suitable reference motion that minimises accumulated torque and the final orientation error amongst these motions. This analytical approach could be used to improve the overall performance of a spacecraft's attitude dynamics and control system when used alongside current flight tested tracking controllers. The resulting algorithm only involves optimising a small number of parameters of standard functions and is simple to implement.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122111277","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 : 2013-11-04DOI: 10.1109/AUCC.2013.6697300
Wei Wang, R. Postoyan, D. Nešić
We investigate the stability of a class of dynamical systems that switch among a given finite family of hybrid systems. We propose sufficient conditions tailored to this particular type of hybrid systems which guarantee the uniform global pre-asymptotic stability (UGpAS) of a given closed set. We first assume this set to be UGpAS for each system of the family. A slow switching condition is then presented to maintain this property for the overall system. We introduce for this purpose the concept of hybrid dwell time which characterizes the length of the hybrid time intervals between two successive switching instants.
{"title":"On the uniform global pre-asymptotic stability of closed sets for switched hybrid systems","authors":"Wei Wang, R. Postoyan, D. Nešić","doi":"10.1109/AUCC.2013.6697300","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697300","url":null,"abstract":"We investigate the stability of a class of dynamical systems that switch among a given finite family of hybrid systems. We propose sufficient conditions tailored to this particular type of hybrid systems which guarantee the uniform global pre-asymptotic stability (UGpAS) of a given closed set. We first assume this set to be UGpAS for each system of the family. A slow switching condition is then presented to maintain this property for the overall system. We introduce for this purpose the concept of hybrid dwell time which characterizes the length of the hybrid time intervals between two successive switching instants.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123700422","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 : 2013-11-01DOI: 10.1109/AUCC.2013.6697308
C. J. Backi, J. Gravdahl
In this paper an approach for optimal boundary control of a parabolic partial differential equation (PDE) is presented. The parabolic PDE is the heat equation for thermal conduction. A technical application for this is the freezing of fish in a vertical plate freezer. As it is a dominant phenomenon in the process of freezing, the latent heat of fusion is included in the model. The aim of the optimization is to freeze the interior of a fish block below -18 °C in a predefined time horizon with an energy consumption that is as low as possible assuming that this corresponds to high freezing temperatures.
{"title":"Optimal boundary control for the heat equation with application to freezing with phase change","authors":"C. J. Backi, J. Gravdahl","doi":"10.1109/AUCC.2013.6697308","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697308","url":null,"abstract":"In this paper an approach for optimal boundary control of a parabolic partial differential equation (PDE) is presented. The parabolic PDE is the heat equation for thermal conduction. A technical application for this is the freezing of fish in a vertical plate freezer. As it is a dominant phenomenon in the process of freezing, the latent heat of fusion is included in the model. The aim of the optimization is to freeze the interior of a fish block below -18 °C in a predefined time horizon with an energy consumption that is as low as possible assuming that this corresponds to high freezing temperatures.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124989199","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 : 2013-11-01DOI: 10.1109/AUCC.2013.6697293
C. Zheng, M. J. Tippett, J. Bao, Jinfeng Liu
Process units may operate different time scales (for example, reactors with different volumes) thus requiring plantwide control systems with multiple sampling rates to avoid over or under sampling. Moreover, it may be preferable to sample critical variables at a higher rate than non-critical ones to decrease capital. Motivated by the above considerations, this paper addresses the issue of distributed multirate model predictive control design for chemical process networks. In order to ensure the closed-loop stability and achieve a minimum performance, dissipativity-based constraints are included in the design of the individual local controllers.
{"title":"Multirate dissipativity-based distributed MPC","authors":"C. Zheng, M. J. Tippett, J. Bao, Jinfeng Liu","doi":"10.1109/AUCC.2013.6697293","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697293","url":null,"abstract":"Process units may operate different time scales (for example, reactors with different volumes) thus requiring plantwide control systems with multiple sampling rates to avoid over or under sampling. Moreover, it may be preferable to sample critical variables at a higher rate than non-critical ones to decrease capital. Motivated by the above considerations, this paper addresses the issue of distributed multirate model predictive control design for chemical process networks. In order to ensure the closed-loop stability and achieve a minimum performance, dissipativity-based constraints are included in the design of the individual local controllers.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126961075","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 : 2013-11-01DOI: 10.1109/AUCC.2013.6697266
Yi Zhang, J. Yang, Honglei Xu, K. Teo
In this paper, we consider the practical set stability problem of a switched nonlinear system, in which every subsystem has one unique equilibrium point and these equilibrium points are different from each other. Based on the new concepts such as ε-practical set stability and a τ-persistent switching law, we explicitly construct a closed bounded set Γ and prove that under an appropriate τ-persistent switching law the switched system is ε-practically (asymptotically) set stable with respect to Γ. Finally, we present a numerical example to illustrate the results obtained.
{"title":"New results on practical set stability of switched nonlinear systems","authors":"Yi Zhang, J. Yang, Honglei Xu, K. Teo","doi":"10.1109/AUCC.2013.6697266","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697266","url":null,"abstract":"In this paper, we consider the practical set stability problem of a switched nonlinear system, in which every subsystem has one unique equilibrium point and these equilibrium points are different from each other. Based on the new concepts such as ε-practical set stability and a τ-persistent switching law, we explicitly construct a closed bounded set Γ and prove that under an appropriate τ-persistent switching law the switched system is ε-practically (asymptotically) set stable with respect to Γ. Finally, we present a numerical example to illustrate the results obtained.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128350864","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 : 2013-11-01DOI: 10.1109/AUCC.2013.6697319
S. Das, H. Pota, I. Petersen
This paper presents the design and implementation of a novel control architecture with a resonant controller, an integral controller, and a velocity feedback controller to improve the high speed imaging performance of a nanopositioning stage, piezoelectric tube scanner (PTS) used in most of the commercial atomic force microscopes (AFMs). The design of the controller is done by considering the lateral and longitudinal axes of the PTS as an independent single-input single-output (SISO) system. The controller proposed in this paper is able to achieve a bandwidth close to the first resonance frequency of the PTS and the controller is robust against the changes in resonance frequency of the scanner due to the load change on the scanner. The performance of the proposed controller is illustrated by comparing with an integral controller and it is shown that the bandwidth increased by the proposed controller is five times greater than the bandwidth that can be achieved by using the integral controller in a commercial scanner. Experimental images with the open-loop, closed-loop and built-in AFM proportional integral controller are presented at scanning rates of 15.62 Hz, 31.25 Hz, 62.5 Hz, and 125 Hz to demonstrate the advantage of the proposed controller.
{"title":"A new robust damping and tracking controller for high speed nanopositioning","authors":"S. Das, H. Pota, I. Petersen","doi":"10.1109/AUCC.2013.6697319","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697319","url":null,"abstract":"This paper presents the design and implementation of a novel control architecture with a resonant controller, an integral controller, and a velocity feedback controller to improve the high speed imaging performance of a nanopositioning stage, piezoelectric tube scanner (PTS) used in most of the commercial atomic force microscopes (AFMs). The design of the controller is done by considering the lateral and longitudinal axes of the PTS as an independent single-input single-output (SISO) system. The controller proposed in this paper is able to achieve a bandwidth close to the first resonance frequency of the PTS and the controller is robust against the changes in resonance frequency of the scanner due to the load change on the scanner. The performance of the proposed controller is illustrated by comparing with an integral controller and it is shown that the bandwidth increased by the proposed controller is five times greater than the bandwidth that can be achieved by using the integral controller in a commercial scanner. Experimental images with the open-loop, closed-loop and built-in AFM proportional integral controller are presented at scanning rates of 15.62 Hz, 31.25 Hz, 62.5 Hz, and 125 Hz to demonstrate the advantage of the proposed controller.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129092820","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 : 2013-11-01DOI: 10.1109/AUCC.2013.6697321
M. S. Rana, H. Pota, I. Petersen
The imaging performance of an atomic force microscope (AFM) at high scanning speeds is limited due to the nonlinear behavior of its scanning unit; i.e., the piezoelectric tube scanner (PTS). In order to increase the imaging speed of the AFM, a model predictive control (MPC) scheme is applied in both the X and Y piezo axes of the PTS to reduce its nonlinearity effects and a modified MPC-Notch scheme is used to improve in damping of the resonant mode. In order to verify the performance improvement achieved by the proposed schemes, scanned images from them, the existing AFM proportional-integral (PI) controller, and an open-loop AFM system are compared.
{"title":"On the performance of an MPC controller including a Notch filter for an AFM","authors":"M. S. Rana, H. Pota, I. Petersen","doi":"10.1109/AUCC.2013.6697321","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697321","url":null,"abstract":"The imaging performance of an atomic force microscope (AFM) at high scanning speeds is limited due to the nonlinear behavior of its scanning unit; i.e., the piezoelectric tube scanner (PTS). In order to increase the imaging speed of the AFM, a model predictive control (MPC) scheme is applied in both the X and Y piezo axes of the PTS to reduce its nonlinearity effects and a modified MPC-Notch scheme is used to improve in damping of the resonant mode. In order to verify the performance improvement achieved by the proposed schemes, scanned images from them, the existing AFM proportional-integral (PI) controller, and an open-loop AFM system are compared.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127552983","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 : 2013-11-01DOI: 10.1109/AUCC.2013.6697264
A. Argha, Li Li, S. Su, H. Nguyen
In this paper, the problem of applying Discrete Sliding Mode Control (DSMC) on spatially finite-dimensional systems arising from discretization of bi-variate Partial Differential Equations (PDEs) describing spatio-temporal systems is studied. To this end, heat transfer PDE is discretized to create 2D discrete dynamics and eventually this 2D spatiotemporal discrete form is represented in 1D vectorial form. In order to study the effect of discrepancy between original PDE dynamics and their discrete schemes, an uncertainty term is also considered for the obtained discrete dynamics. According to the notion of strong stability and, in addition, using scaling matrices (similarity transformation), a new method for considering the stability of discrete-time systems in the presence of general uncertainty term (matched and unmatched) is developed. It is also shown that the proposed method in this paper can be used for the case with spatial constraints on the actuation. Consequently, as special cases, the problem of spatially piece-wise constant, sparse and also boundary control input are studied.
{"title":"The application of Discrete sliding mode control in parabolic PDE dynamics","authors":"A. Argha, Li Li, S. Su, H. Nguyen","doi":"10.1109/AUCC.2013.6697264","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697264","url":null,"abstract":"In this paper, the problem of applying Discrete Sliding Mode Control (DSMC) on spatially finite-dimensional systems arising from discretization of bi-variate Partial Differential Equations (PDEs) describing spatio-temporal systems is studied. To this end, heat transfer PDE is discretized to create 2D discrete dynamics and eventually this 2D spatiotemporal discrete form is represented in 1D vectorial form. In order to study the effect of discrepancy between original PDE dynamics and their discrete schemes, an uncertainty term is also considered for the obtained discrete dynamics. According to the notion of strong stability and, in addition, using scaling matrices (similarity transformation), a new method for considering the stability of discrete-time systems in the presence of general uncertainty term (matched and unmatched) is developed. It is also shown that the proposed method in this paper can be used for the case with spatial constraints on the actuation. Consequently, as special cases, the problem of spatially piece-wise constant, sparse and also boundary control input are studied.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131122628","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 : 2013-11-01DOI: 10.1109/AUCC.2013.6697260
Md Norazlan Md Lazin, I. Darus, B. C. Ng, H. Kamar
This paper present the representation of the dynamic model of the temperature an automotive air conditioning system (AAC) as the speed of the air conditioning compressor is varied. The performance of system identification of an AAC system using Recursive Least Squares (RLS) and Particle Swarm Optimization (PSO) techniques measured and discussed. The input - output data are collected through an experimental study using an AAC system integrated with air duct system experimental rig complete with data acquisition and instrumentation system. The single input single output dynamic model was established by using Autoregressive with exogenous input (ARX) model. Recursive Least Squares and Genetic Algorithms were validated using one step-ahead prediction (OSA), mean squared error (MSE) and correlation tests. The comparison results between these parameter estimation optimization techniques were highlighted. It was found that the estimated models using these two methods proposed are comparable, acceptable and possible to be used as a platform of new controller development and evaluation the performance of AAC system in the future work. Amongst all, it was found that the Particle Swarm optimization method produce the best ARX model with the lowest prediction MSE value of 8.5472×10-5 as compared to the Recursive Least Squares performance.
{"title":"Identification for automotive air-conditioning system using Particle Swarm Optimization","authors":"Md Norazlan Md Lazin, I. Darus, B. C. Ng, H. Kamar","doi":"10.1109/AUCC.2013.6697260","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697260","url":null,"abstract":"This paper present the representation of the dynamic model of the temperature an automotive air conditioning system (AAC) as the speed of the air conditioning compressor is varied. The performance of system identification of an AAC system using Recursive Least Squares (RLS) and Particle Swarm Optimization (PSO) techniques measured and discussed. The input - output data are collected through an experimental study using an AAC system integrated with air duct system experimental rig complete with data acquisition and instrumentation system. The single input single output dynamic model was established by using Autoregressive with exogenous input (ARX) model. Recursive Least Squares and Genetic Algorithms were validated using one step-ahead prediction (OSA), mean squared error (MSE) and correlation tests. The comparison results between these parameter estimation optimization techniques were highlighted. It was found that the estimated models using these two methods proposed are comparable, acceptable and possible to be used as a platform of new controller development and evaluation the performance of AAC system in the future work. Amongst all, it was found that the Particle Swarm optimization method produce the best ARX model with the lowest prediction MSE value of 8.5472×10-5 as compared to the Recursive Least Squares performance.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133471712","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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