A Sliding Mode Control Algorithm with Elementary Compensation for Input Matrix Uncertainty in Affine Systems
This paper aims to develop a sliding mode control (SMC) approach with elementary compensation for input matrix uncertainty in affine systems. As a multiplicative uncertainty regarding the control inputs, input matrix uncertainty adversely modifies the control effort and even further causes the insta...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/6/1337 |
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| author | Ruizhi Sha Zuren Feng |
| author_facet | Ruizhi Sha Zuren Feng |
| author_sort | Ruizhi Sha |
| collection | DOAJ |
| description | This paper aims to develop a sliding mode control (SMC) approach with elementary compensation for input matrix uncertainty in affine systems. As a multiplicative uncertainty regarding the control inputs, input matrix uncertainty adversely modifies the control effort and even further causes the instability of systems. To solve this issue, a sliding mode control algorithm is developed based on a two-step design strategy. The first step is to design a general sliding mode controller for the system without input matrix uncertainty. In the second step, a control term is specially designed to compensate for input matrix uncertainty. In order to realize the elementary compensation for input matrix uncertainty, this term is obtained by solving a nonlinear vector equation which is derived from the Lyapunov function inequality. Theorems and lemmas based on the convex cone theory are proposed to guarantee the existence and uniqueness of the solution to the vector equation. Additionally, an algorithmic process is proposed to solve the vector equation efficiently. In the simulation part, the proposed controller is applied to two systems with different structures and compared with two state-of-the-art SMC algorithms. The comprehensive simulation results demonstrate that the proposed method is able to provide the closed-loop system with a competitive performance in terms of convergence level, overshoot reduction and chattering suppression. |
| first_indexed | 2024-03-11T06:13:33Z |
| format | Article |
| id | doaj.art-9d7f11aee51247079e7eed254aade8a3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T06:13:33Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9d7f11aee51247079e7eed254aade8a32023-11-17T12:27:10ZengMDPI AGMathematics2227-73902023-03-01116133710.3390/math11061337A Sliding Mode Control Algorithm with Elementary Compensation for Input Matrix Uncertainty in Affine SystemsRuizhi Sha0Zuren Feng1State Key Laboratory for Manufacturing System Engineering, Systems Engineering Institute, Xi’an Jiaotong University, Xi’an 710049, ChinaState Key Laboratory for Manufacturing System Engineering, Systems Engineering Institute, Xi’an Jiaotong University, Xi’an 710049, ChinaThis paper aims to develop a sliding mode control (SMC) approach with elementary compensation for input matrix uncertainty in affine systems. As a multiplicative uncertainty regarding the control inputs, input matrix uncertainty adversely modifies the control effort and even further causes the instability of systems. To solve this issue, a sliding mode control algorithm is developed based on a two-step design strategy. The first step is to design a general sliding mode controller for the system without input matrix uncertainty. In the second step, a control term is specially designed to compensate for input matrix uncertainty. In order to realize the elementary compensation for input matrix uncertainty, this term is obtained by solving a nonlinear vector equation which is derived from the Lyapunov function inequality. Theorems and lemmas based on the convex cone theory are proposed to guarantee the existence and uniqueness of the solution to the vector equation. Additionally, an algorithmic process is proposed to solve the vector equation efficiently. In the simulation part, the proposed controller is applied to two systems with different structures and compared with two state-of-the-art SMC algorithms. The comprehensive simulation results demonstrate that the proposed method is able to provide the closed-loop system with a competitive performance in terms of convergence level, overshoot reduction and chattering suppression.https://www.mdpi.com/2227-7390/11/6/1337sliding mode controlinput matrix uncertaintyaffine systemselementary compensation |
| spellingShingle | Ruizhi Sha Zuren Feng A Sliding Mode Control Algorithm with Elementary Compensation for Input Matrix Uncertainty in Affine Systems Mathematics sliding mode control input matrix uncertainty affine systems elementary compensation |
| title | A Sliding Mode Control Algorithm with Elementary Compensation for Input Matrix Uncertainty in Affine Systems |
| title_full | A Sliding Mode Control Algorithm with Elementary Compensation for Input Matrix Uncertainty in Affine Systems |
| title_fullStr | A Sliding Mode Control Algorithm with Elementary Compensation for Input Matrix Uncertainty in Affine Systems |
| title_full_unstemmed | A Sliding Mode Control Algorithm with Elementary Compensation for Input Matrix Uncertainty in Affine Systems |
| title_short | A Sliding Mode Control Algorithm with Elementary Compensation for Input Matrix Uncertainty in Affine Systems |
| title_sort | sliding mode control algorithm with elementary compensation for input matrix uncertainty in affine systems |
| topic | sliding mode control input matrix uncertainty affine systems elementary compensation |
| url | https://www.mdpi.com/2227-7390/11/6/1337 |
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