The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding L...The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding Legendre series. Matching the first three terms of the Legendre series of the loop gain with the desired one gives the PID controller parameters. The closed loop system stability conditions in terms of the Legendre basis function pole(λ) for a wide range of systems including the first order, second order, double integrator, first order plus dead time, and first order unstable plants are obtained. For first order and double integrator plants, the closed loop system stability is preserved for all values of λ and for the other plants, an appropriate range in terms of λ is obtained. The optimum value of λ to attain a minimum integral square error performance index in the presence of the control signal constraints is achieved. The numerical simulations demonstrate the benefits of the Legendre based PID controller.展开更多
Change in Arctic sea ice extent is one of the indicators of global climate changes. Spatio-temporal change and change patterns can be identified using various methods to facilitate human understanding global climate c...Change in Arctic sea ice extent is one of the indicators of global climate changes. Spatio-temporal change and change patterns can be identified using various methods to facilitate human understanding global climate changes. Three empirical orthogonal function(EOF) techniques are discussed and applied to decades of sea-ice concentration(SIC) dataset in Arctic area for identifying independent patterns. It was found that: 1) discrepancies exist in magnitude and scope for each EOF pattern, however, the first two leading EOFs of variability possess high similarities in structure and shape; 2) Even though there are somewhat differences in amplitude of each PC mode, the first two leading PC modes maintain consistent in overall trend and periodicity; 3) There are significant discrepancies and inconsistencies in the third and fourth leading EOF and PC modes. The accuracies of three techniques are further validated in representing the physical phenomena of SIC anomaly patterns.展开更多
文摘The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding Legendre series. Matching the first three terms of the Legendre series of the loop gain with the desired one gives the PID controller parameters. The closed loop system stability conditions in terms of the Legendre basis function pole(λ) for a wide range of systems including the first order, second order, double integrator, first order plus dead time, and first order unstable plants are obtained. For first order and double integrator plants, the closed loop system stability is preserved for all values of λ and for the other plants, an appropriate range in terms of λ is obtained. The optimum value of λ to attain a minimum integral square error performance index in the presence of the control signal constraints is achieved. The numerical simulations demonstrate the benefits of the Legendre based PID controller.
基金Project(41301420)supported by the National Natural Science Foundation of ChinaProject(12JJB005)supported by the Hunan Provincial Natural Science Foundation of China+1 种基金Project(2014VGE03)supported by the Key Lab of Virtual Geographic Environment from Ministry of Education,ChinaProject(LEND2013B04)supported by the NASA Key Laboratory of Land Environment and Disaster Monitoring,USA
文摘Change in Arctic sea ice extent is one of the indicators of global climate changes. Spatio-temporal change and change patterns can be identified using various methods to facilitate human understanding global climate changes. Three empirical orthogonal function(EOF) techniques are discussed and applied to decades of sea-ice concentration(SIC) dataset in Arctic area for identifying independent patterns. It was found that: 1) discrepancies exist in magnitude and scope for each EOF pattern, however, the first two leading EOFs of variability possess high similarities in structure and shape; 2) Even though there are somewhat differences in amplitude of each PC mode, the first two leading PC modes maintain consistent in overall trend and periodicity; 3) There are significant discrepancies and inconsistencies in the third and fourth leading EOF and PC modes. The accuracies of three techniques are further validated in representing the physical phenomena of SIC anomaly patterns.
