Pub Date : 2018-07-01DOI: 10.1109/VSS.2018.8460243
G. Bartolini, A. Estrada, Elisabetta Punta
In this paper, the problem of control of nonlinear affine systems with uncertain time and state dependent high frequency gain matrix is addressed. The proposal is based on the use of the integral sliding mode control methodology in order to tackle the difficulties that arise for control of these class of systems. Via the introduction of integrators on the output of the dynamical system the validity of the results can be made global. A proposal for finite time transient altogether with a proposal for fixed time transient are presented.
{"title":"Multi-Input Nonlinear Systems with Time and State Dependent Uncertain Control Direction","authors":"G. Bartolini, A. Estrada, Elisabetta Punta","doi":"10.1109/VSS.2018.8460243","DOIUrl":"https://doi.org/10.1109/VSS.2018.8460243","url":null,"abstract":"In this paper, the problem of control of nonlinear affine systems with uncertain time and state dependent high frequency gain matrix is addressed. The proposal is based on the use of the integral sliding mode control methodology in order to tackle the difficulties that arise for control of these class of systems. Via the introduction of integrators on the output of the dynamical system the validity of the results can be made global. A proposal for finite time transient altogether with a proposal for fixed time transient are presented.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"22 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114019336","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 : 2018-07-01DOI: 10.1109/VSS.2018.8460227
M. Ruderman, L. Fridman
Low-accuracy sensing is very common for the large hydraulic machines and does not allow for directly measuring the relative velocity which can be, otherwise, required for the control and monitoring purposes. This paper provides a case study of designing the second-order sliding mode observer based on the super-twisting robust exact differentiator. The nominal part of the system dynamics is derived from the simple available system measurements and incorporated into the observer structure. Parasitic by-effects, arising from the sensor sampling, quantization, and non-modeled distortions due to mechanical sensor interface, are shown as the main causes of hampering the final (steady-state) convergence of the observer states. Two cases – a continuous chirp excitation and a sequence of the short square pulses –are demonstrated for the open-loop motion experiments performed on a hydraulic crane, for which an accurate estimation of the motion system states is obtained.
{"title":"Use of second-order sliding mode observer for low-accuracy sensing in hydraulic machines","authors":"M. Ruderman, L. Fridman","doi":"10.1109/VSS.2018.8460227","DOIUrl":"https://doi.org/10.1109/VSS.2018.8460227","url":null,"abstract":"Low-accuracy sensing is very common for the large hydraulic machines and does not allow for directly measuring the relative velocity which can be, otherwise, required for the control and monitoring purposes. This paper provides a case study of designing the second-order sliding mode observer based on the super-twisting robust exact differentiator. The nominal part of the system dynamics is derived from the simple available system measurements and incorporated into the observer structure. Parasitic by-effects, arising from the sensor sampling, quantization, and non-modeled distortions due to mechanical sensor interface, are shown as the main causes of hampering the final (steady-state) convergence of the observer states. Two cases – a continuous chirp excitation and a sequence of the short square pulses –are demonstrated for the open-loop motion experiments performed on a hydraulic crane, for which an accurate estimation of the motion system states is obtained.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122643092","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 : 2018-07-01DOI: 10.1109/VSS.2018.8460307
Kirtiman Singh, Harshal B. Oza
This paper gives a new control framework for connected rigid bodies using unit dual quaternion dynamics. The equations of motion are obtained by direct differentiation of dual quaternion that represents the pose and position of the end effector. The novelty lies in the synthesis of torque vector in dual quaternion space. This is based entirely on the second derivative of the dual quaternion tracking error. The key contribution is in achieving finite time stability while explicitly using equations of acceleration dynamics of the underlying dual quaternion error, a concept that has not been explored before. The presented results utilize the method of modeling of serial link robots using an abstraction of inverted pendulum proposing a suitable controller for each link. A second order sliding mode control is utilized to enforce finite time stability of the error dual quaternion and its first temporal derivative. The utility of this method is demonstrated using a planar two link robot where individual generalized force vectors in dual quaternion space are synthesized with a discussion on the physical meaning of a torque defined in dual quaternion space.
{"title":"Second order sliding mode control using unit dual-quaternion dynamics with application to robotics","authors":"Kirtiman Singh, Harshal B. Oza","doi":"10.1109/VSS.2018.8460307","DOIUrl":"https://doi.org/10.1109/VSS.2018.8460307","url":null,"abstract":"This paper gives a new control framework for connected rigid bodies using unit dual quaternion dynamics. The equations of motion are obtained by direct differentiation of dual quaternion that represents the pose and position of the end effector. The novelty lies in the synthesis of torque vector in dual quaternion space. This is based entirely on the second derivative of the dual quaternion tracking error. The key contribution is in achieving finite time stability while explicitly using equations of acceleration dynamics of the underlying dual quaternion error, a concept that has not been explored before. The presented results utilize the method of modeling of serial link robots using an abstraction of inverted pendulum proposing a suitable controller for each link. A second order sliding mode control is utilized to enforce finite time stability of the error dual quaternion and its first temporal derivative. The utility of this method is demonstrated using a planar two link robot where individual generalized force vectors in dual quaternion space are synthesized with a discussion on the physical meaning of a torque defined in dual quaternion space.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125228963","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 : 2018-07-01DOI: 10.1109/VSS.2018.8460426
Shamila Nateghi, Y. Shtessel, J. Barbot, G. Zheng, Lei Yu
In this work, the unknown cyber-attacks on cyber-physical systems are reconstructed using sliding mode differentiation techniques in concert with the sparse recovery algorithm, when only several unknown attacks out of a long list of possible attacks are considered non-zero. The approach is applied to a model of the electric power system, and finally, the efficacy of the proposed techniques is illustrated via simulations of a real electric power system.
{"title":"Cyber-Attack Reconstruction via Sliding Mode Differentiation and Sparse Recovery Algorithm: Electrical Power Networks Application","authors":"Shamila Nateghi, Y. Shtessel, J. Barbot, G. Zheng, Lei Yu","doi":"10.1109/VSS.2018.8460426","DOIUrl":"https://doi.org/10.1109/VSS.2018.8460426","url":null,"abstract":"In this work, the unknown cyber-attacks on cyber-physical systems are reconstructed using sliding mode differentiation techniques in concert with the sparse recovery algorithm, when only several unknown attacks out of a long list of possible attacks are considered non-zero. The approach is applied to a model of the electric power system, and finally, the efficacy of the proposed techniques is illustrated via simulations of a real electric power system.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126218980","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 : 2018-07-01DOI: 10.1109/VSS.2018.8460412
J. Samantaray, S. Chakrabarty, B. K. Roy
This paper presents a mathematical background of switching surface and its design steps in the light of a filter. Designing of a switching surface is the most important step while using sliding mode control (SMC) technique as it dictates the behaviour of the system during sliding. Its application is done here for the anti-synchronisation of the Lü chaotic system. The anti-synchronisation is done between two identical Lü systems using proportional-Integral (PI) and proportional-integral-derivative (PID) switching surface based SMC and a comparative study is done between the two approaches. Numerical simulations are presented to show the effectiveness of these designs.
{"title":"Switching Surface as a Filter and its Application to Anti-synchronisation of Lü Chaotic System","authors":"J. Samantaray, S. Chakrabarty, B. K. Roy","doi":"10.1109/VSS.2018.8460412","DOIUrl":"https://doi.org/10.1109/VSS.2018.8460412","url":null,"abstract":"This paper presents a mathematical background of switching surface and its design steps in the light of a filter. Designing of a switching surface is the most important step while using sliding mode control (SMC) technique as it dictates the behaviour of the system during sliding. Its application is done here for the anti-synchronisation of the Lü chaotic system. The anti-synchronisation is done between two identical Lü systems using proportional-Integral (PI) and proportional-integral-derivative (PID) switching surface based SMC and a comparative study is done between the two approaches. Numerical simulations are presented to show the effectiveness of these designs.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129268861","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 : 2018-07-01DOI: 10.1109/VSS.2018.8460414
I. Boiko
Loeb's criterion of orbital stability of periodic motions [1] is simple and convenient. It is based on the relationships between the Nyquist plot of the linear part of a nonlinear system and the describing function (DF) of the nonlinearity. However, as shown in the present paper, the original proof is not flawless, as it is based on one assumption, which does not hold. A proof based on the dynamic harmonic balance (DHB) principle and further investigations into this criterion are offered in the present paper.
{"title":"On Loeb's criterion of orbital stability of self-excited periodic motions","authors":"I. Boiko","doi":"10.1109/VSS.2018.8460414","DOIUrl":"https://doi.org/10.1109/VSS.2018.8460414","url":null,"abstract":"Loeb's criterion of orbital stability of periodic motions [1] is simple and convenient. It is based on the relationships between the Nyquist plot of the linear part of a nonlinear system and the describing function (DF) of the nonlinearity. However, as shown in the present paper, the original proof is not flawless, as it is based on one assumption, which does not hold. A proof based on the dynamic harmonic balance (DHB) principle and further investigations into this criterion are offered in the present paper.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127660921","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 : 2018-07-01DOI: 10.1109/VSS.2018.8460323
Tobias Posielek, K. Wulff, J. Reger
We propose a novel approach to design an integral sliding mode control (ISMC) for a nonlinear system in regular form. The control method is capable to compensate a class of matched and, in particular, unmatched uncertainties with respect to some given output. Conditions for stability and decoupling are presented. For the case of linear nominal dynamics these conditions take a very simple form. A direct comparison to conventional design methods for ISMC is given and the concepts are illustrated using a simulation example.
{"title":"Disturbance decoupling using a novel approach to integral sliding-mode","authors":"Tobias Posielek, K. Wulff, J. Reger","doi":"10.1109/VSS.2018.8460323","DOIUrl":"https://doi.org/10.1109/VSS.2018.8460323","url":null,"abstract":"We propose a novel approach to design an integral sliding mode control (ISMC) for a nonlinear system in regular form. The control method is capable to compensate a class of matched and, in particular, unmatched uncertainties with respect to some given output. Conditions for stability and decoupling are presented. For the case of linear nominal dynamics these conditions take a very simple form. A direct comparison to conventional design methods for ISMC is given and the concepts are illustrated using a simulation example.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127366444","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 : 2018-07-01DOI: 10.1109/VSS.2018.8460393
B. Tamhane, S. Kurode, B. Bandyopadhyay
Sensor or measurement noise is an immanent disturbance in all closed loop control systems. State observers are not robust to sensor noise. Higher Order Sliding Mode Observer (HOSMO) attenuates the estimation error to a small bound in presence of output noise. A strategy is proposed in this paper for HOSM observer design which provides a further attenuation of the estimation error. A recursively designed HOSM observer with integral surface is the proposed approach. The designed observer is also shown to comply continuity condition as required by super twisting controller. Simulation results are presented to validate the proposed method.
{"title":"Novel Higher Order Sliding Mode Observer for Output Noise Attenuation","authors":"B. Tamhane, S. Kurode, B. Bandyopadhyay","doi":"10.1109/VSS.2018.8460393","DOIUrl":"https://doi.org/10.1109/VSS.2018.8460393","url":null,"abstract":"Sensor or measurement noise is an immanent disturbance in all closed loop control systems. State observers are not robust to sensor noise. Higher Order Sliding Mode Observer (HOSMO) attenuates the estimation error to a small bound in presence of output noise. A strategy is proposed in this paper for HOSM observer design which provides a further attenuation of the estimation error. A recursively designed HOSM observer with integral surface is the proposed approach. The designed observer is also shown to comply continuity condition as required by super twisting controller. Simulation results are presented to validate the proposed method.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129097891","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 : 2018-07-01DOI: 10.1109/VSS.2018.8460325
A. Rosales, Luis Ibarra, L. Fridman, Y. Shtessel, P. Ponce, A. Molina
The unmodeled dynamics inside an SMC control loop such as actuators, sensors, time-delays, etc., dynamically perturb their close-loop response, inducing chattering. Dynamically perturbed SMC systems have been widely analyzed in the frequency domain via the Describing Function (DF), Tzypkin method, Locus of a Perturbed Relay System (LPRS), and others, that require a linear representation of the plant (usually given as a transfer function) to later estimate the resulting chattering parameters. However, if parametric variation/uncertainty is present, a unique value of the chattering parameters cannot be guaranteed. In this paper, a method to analyze dynamically perturbed SMC with parametric uncertainty is presented. Parametric uncertainty is addressed as a family of interval second-order transfer functions, formed by cascading a first-order actuator with a plant with relative-degree of one. The proposed method identifies (in closed-form) the member system among the interval, corresponding with the marginal chattering parameters. Hence, leading to the worst-case condition for the whole systems' family and enabling direct design criteria. Analytic and simulated examples to validate the proposed methods are presented.
{"title":"On Parametric Uncertainty in Dynamically Perturbed Sliding Mode Controlled Systems","authors":"A. Rosales, Luis Ibarra, L. Fridman, Y. Shtessel, P. Ponce, A. Molina","doi":"10.1109/VSS.2018.8460325","DOIUrl":"https://doi.org/10.1109/VSS.2018.8460325","url":null,"abstract":"The unmodeled dynamics inside an SMC control loop such as actuators, sensors, time-delays, etc., dynamically perturb their close-loop response, inducing chattering. Dynamically perturbed SMC systems have been widely analyzed in the frequency domain via the Describing Function (DF), Tzypkin method, Locus of a Perturbed Relay System (LPRS), and others, that require a linear representation of the plant (usually given as a transfer function) to later estimate the resulting chattering parameters. However, if parametric variation/uncertainty is present, a unique value of the chattering parameters cannot be guaranteed. In this paper, a method to analyze dynamically perturbed SMC with parametric uncertainty is presented. Parametric uncertainty is addressed as a family of interval second-order transfer functions, formed by cascading a first-order actuator with a plant with relative-degree of one. The proposed method identifies (in closed-form) the member system among the interval, corresponding with the marginal chattering parameters. Hence, leading to the worst-case condition for the whole systems' family and enabling direct design criteria. Analytic and simulated examples to validate the proposed methods are presented.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134549195","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 : 2018-07-01DOI: 10.1109/VSS.2018.8460305
Ángel Mercado‐Uribe, J. Moreno
In this paper we provide a homogeneous integral control by output feedback which is able to stabilize in Finite Time the origin of a SISO nonlinear system and reject matched Lipschitz perturbations. For the system in normal form, we construct a homogeneous Lyapunov function, that proves the stability of the closed loop system combining a state feedback discontinuous integral controller and a smooth state observer. We present the results for systems with relative degrees 2 and 3, although the developed Lyapunov based analysis and design method can be extended to the arbitrary relative degree case. Moreover, in contrast to previous works, the signal to be fed to the integral controller can be a fairly arbitrary function of the states.
{"title":"Output Feedback Discontinuous Integral Controller for SISO Nonlinear Systems","authors":"Ángel Mercado‐Uribe, J. Moreno","doi":"10.1109/VSS.2018.8460305","DOIUrl":"https://doi.org/10.1109/VSS.2018.8460305","url":null,"abstract":"In this paper we provide a homogeneous integral control by output feedback which is able to stabilize in Finite Time the origin of a SISO nonlinear system and reject matched Lipschitz perturbations. For the system in normal form, we construct a homogeneous Lyapunov function, that proves the stability of the closed loop system combining a state feedback discontinuous integral controller and a smooth state observer. We present the results for systems with relative degrees 2 and 3, although the developed Lyapunov based analysis and design method can be extended to the arbitrary relative degree case. Moreover, in contrast to previous works, the signal to be fed to the integral controller can be a fairly arbitrary function of the states.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129002112","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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