The eigenvalue assignment for the fractional order linear time-invariant control systems is addressed in this paper and the existence of the solution to this problem is also analyzed based on the controllability theor...The eigenvalue assignment for the fractional order linear time-invariant control systems is addressed in this paper and the existence of the solution to this problem is also analyzed based on the controllability theory of the fractional order systems.According to the relationship between the solution to this problem and the solution to the nonlinear matrix equation,we propose a numerical algorithm via the matrix sign function method based on the rational iteration for solving this nonlinear matrix equation,which can circumvent the limitation of the assumption of linearly independent eigenvectors.Moreover,the proposed algorithm only needs to solve the linear system with multiple right-hand sides and it converges quadratically.Finally,the efficiency of the proposed approach is shown through numerical examples.展开更多
The major difficulty in achieving good performance of industrial polymerization reactors lies in the lack of understanding of their nonlinear dynamics and the lack of well-developed techniques for the control of nonli...The major difficulty in achieving good performance of industrial polymerization reactors lies in the lack of understanding of their nonlinear dynamics and the lack of well-developed techniques for the control of nonlinear processes, which are usually accompanied with bifurcation phenomenon. This work aims at investigating the nonlinear behavior of the parameterized nonlinear system of vinyl acetate polymerization and further modifying the bifurcation characteristics of this process via a washout filter-aid controller, with all the original steady state equilibria preserved. Advantages and possible extensions of the proposed methodology are discussed to provide scientific guide for further controller design and operation improvement.展开更多
基金National Natural Science Foundation of China(Grant Nos.11401305,11571171)Shenzhen Science and Technology Program(Grant No.JCYJ20230807142002006).
文摘The eigenvalue assignment for the fractional order linear time-invariant control systems is addressed in this paper and the existence of the solution to this problem is also analyzed based on the controllability theory of the fractional order systems.According to the relationship between the solution to this problem and the solution to the nonlinear matrix equation,we propose a numerical algorithm via the matrix sign function method based on the rational iteration for solving this nonlinear matrix equation,which can circumvent the limitation of the assumption of linearly independent eigenvectors.Moreover,the proposed algorithm only needs to solve the linear system with multiple right-hand sides and it converges quadratically.Finally,the efficiency of the proposed approach is shown through numerical examples.
基金Supported by the National Basic Research Programme(2012CB720500)the National Natural Science Foundation of China(21306100)
文摘The major difficulty in achieving good performance of industrial polymerization reactors lies in the lack of understanding of their nonlinear dynamics and the lack of well-developed techniques for the control of nonlinear processes, which are usually accompanied with bifurcation phenomenon. This work aims at investigating the nonlinear behavior of the parameterized nonlinear system of vinyl acetate polymerization and further modifying the bifurcation characteristics of this process via a washout filter-aid controller, with all the original steady state equilibria preserved. Advantages and possible extensions of the proposed methodology are discussed to provide scientific guide for further controller design and operation improvement.
