Rakhshan, Mohsen, Mardani, Mohammad Mehdi, ShaSadeghi, Mokhtar, Mardaneh, Mohammad (2012). Relaxed Stabilization Conditions via Sum of Squares Approach for the Nonlinear Polynomial Model. , 12(1), 24-30.
Mohsen Rakhshan; Mohammad Mehdi Mardani; Mokhtar ShaSadeghi; Mohammad Mardaneh. "Relaxed Stabilization Conditions via Sum of Squares Approach for the Nonlinear Polynomial Model". , 12, 1, 2012, 24-30.
Rakhshan, Mohsen, Mardani, Mohammad Mehdi, ShaSadeghi, Mokhtar, Mardaneh, Mohammad (2012). 'Relaxed Stabilization Conditions via Sum of Squares Approach for the Nonlinear Polynomial Model', , 12(1), pp. 24-30.
Rakhshan, Mohsen, Mardani, Mohammad Mehdi, ShaSadeghi, Mokhtar, Mardaneh, Mohammad Relaxed Stabilization Conditions via Sum of Squares Approach for the Nonlinear Polynomial Model. , 2012; 12(1): 24-30.

Relaxed Stabilization Conditions via Sum of Squares Approach for the Nonlinear Polynomial Model

The Modares Journal of Electrical Engineering
Article 4, Volume 12, Issue 1, 2012, Pages 24-30    PDF (707.42 K)
Authors
Mohsen Rakhshan1; Mohammad Mehdi Mardani2; Mokhtar ShaSadeghi* 3; Mohammad Mardaneh4
1M.Sc. Students, Control Dept., Electrical and Electronic Engineering Faculty, Shiraz University of Technology, Shiraz, Iran.
21M.Sc. Students, Control Dept., Electrical and Electronic Engineering Faculty, Shiraz University of Technology, Shiraz, Iran.
3Associate professor, Control Dept., Electrical and Electronic Engineering Faculty, Shiraz University of Technology, Shiraz, Iran.
4Assistant professor, Power Dept., Electrical and Electronic Engineering Faculty, Shiraz University of Technology, Shiraz, Iran
Abstract
In this paper, stabilization conditions and controller design for a class of nonlinear systems are proposed. The proposed method is based on the nonlinear feedback, quadratic Lyapunov function and heuristic slack matrices definition. These slack matrices in null products are derived using the properties of the system dynamics. Based on the Lyapunov stability theorem and Sum of Squares (SOS) decomposition techniques, the conditions are derived in terms of SOS. This approach has two main advantages. First, using the polynomial model, the proposed method uses the polynomial state space matrices in the model description. Therefore, it does not need any existing modeling methods such as the Takagi Sugeno (T-S) fuzzy model which can be a source of conservativeness in the control design conditions, because the membership function information cannot be used completely in the derivation of the controller design conditions. Second, using slack matrices, one can find the matrices that leads to applicable controller design which this means it provides extra degrees of freedom. To show the effectiveness of the proposed method, a PMSM is considered in the numerical simulation.
Keywords
Nonlinear feedback control; Permanent Magnet Synchronous Motor (PMSM); Polynomial model; Quadratic Lyapunov function; Sum of Squares (SOS)
Statistics
Article View: 74
PDF Download: 83
Statistics
Number of Journals45
Number of Issues2,171
Number of Articles24,674
Article View24,394,671
PDF Download17,535,017