Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality
In this paper, the delay-dependent stability of haptic systems is studied by developing a new stability criterion. Firstly, the haptic system inevitably introduces time delays by using communication networks to transmit information between the controller and the haptic device. When discussing the st...
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| Format: | Article |
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MDPI AG
2021-07-01
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| Series: | Actuators |
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| Online Access: | https://www.mdpi.com/2076-0825/10/8/171 |
| _version_ | 1797525058245099520 |
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| author | Du Xiong Yunfan Liu Cui Zhu Li Jin Leimin Wang |
| author_facet | Du Xiong Yunfan Liu Cui Zhu Li Jin Leimin Wang |
| author_sort | Du Xiong |
| collection | DOAJ |
| description | In this paper, the delay-dependent stability of haptic systems is studied by developing a new stability criterion. Firstly, the haptic system inevitably introduces time delays by using communication networks to transmit information between the controller and the haptic device. When discussing the stability of the haptic system near its operating point, the original nonlinear system is modeled as a linear system with the time delay mentioned above. In addition, a suitable augmented Lyapunov–Krasovskii functional (LKF) with more integral forms is constructed and an auxiliary function-based integral inequality is applied to estimate the derivative of the proposed LKF. Then, a less conservative delay-dependent criterion in terms of the linear matrix inequality (LMI) is derived to calculate the delay margin for the haptic system. Finally, case studies are carried out based on a one degree of freedom haptic system. The results show that, compared with criteria in existing works, the proposed criterion can obtain more accurate results and require less calculation complexity, and, with the increase in virtual damping in a certain range, the stable upper bound of the haptic system increases at first and then decreases. |
| first_indexed | 2024-03-10T09:06:25Z |
| format | Article |
| id | doaj.art-8f73f55bb02c46ac8ec65969edd3eeda |
| institution | Directory Open Access Journal |
| issn | 2076-0825 |
| language | English |
| last_indexed | 2024-03-10T09:06:25Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Actuators |
| spelling | doaj.art-8f73f55bb02c46ac8ec65969edd3eeda2023-11-22T06:21:04ZengMDPI AGActuators2076-08252021-07-0110817110.3390/act10080171Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral InequalityDu Xiong0Yunfan Liu1Cui Zhu2Li Jin3Leimin Wang4School of Automation, China University of Geosciences, Wuhan 430074, ChinaSchool of Automation, China University of Geosciences, Wuhan 430074, ChinaSchool of Automation, China University of Geosciences, Wuhan 430074, ChinaSchool of Automation, China University of Geosciences, Wuhan 430074, ChinaSchool of Automation, China University of Geosciences, Wuhan 430074, ChinaIn this paper, the delay-dependent stability of haptic systems is studied by developing a new stability criterion. Firstly, the haptic system inevitably introduces time delays by using communication networks to transmit information between the controller and the haptic device. When discussing the stability of the haptic system near its operating point, the original nonlinear system is modeled as a linear system with the time delay mentioned above. In addition, a suitable augmented Lyapunov–Krasovskii functional (LKF) with more integral forms is constructed and an auxiliary function-based integral inequality is applied to estimate the derivative of the proposed LKF. Then, a less conservative delay-dependent criterion in terms of the linear matrix inequality (LMI) is derived to calculate the delay margin for the haptic system. Finally, case studies are carried out based on a one degree of freedom haptic system. The results show that, compared with criteria in existing works, the proposed criterion can obtain more accurate results and require less calculation complexity, and, with the increase in virtual damping in a certain range, the stable upper bound of the haptic system increases at first and then decreases.https://www.mdpi.com/2076-0825/10/8/171haptic systemstime delaystability analysisauxiliary function-based integral inequality |
| spellingShingle | Du Xiong Yunfan Liu Cui Zhu Li Jin Leimin Wang Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality Actuators haptic systems time delay stability analysis auxiliary function-based integral inequality |
| title | Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality |
| title_full | Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality |
| title_fullStr | Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality |
| title_full_unstemmed | Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality |
| title_short | Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality |
| title_sort | delay dependent stability analysis of haptic systems via an auxiliary function based integral inequality |
| topic | haptic systems time delay stability analysis auxiliary function-based integral inequality |
| url | https://www.mdpi.com/2076-0825/10/8/171 |
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