In order to figure out the dynamical behaviour of a fractional-order chaotic system and its relation to an integer- order chaotic system, in this paper we investigate the synchronization between a class of fractional-...In order to figure out the dynamical behaviour of a fractional-order chaotic system and its relation to an integer- order chaotic system, in this paper we investigate the synchronization between a class of fractional-order chaotic systems and integer-order chaotic systems via sliding mode control method. Stability analysis is performed for the proposed method based on stability theorems in the fractional calculus. Moreover, three typical examples are carried out to show that the synchronization between fractional-order chaotic systems and integer-orders chaotic systems can be achieved. Our theoretical findings are supported by numerical simulation results. Finally, results from numerical computations and theoretical analysis are demonstrated to be a perfect bridge between fractional-order chaotic systems and integer-order chaotic systems.展开更多
A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fract...A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.展开更多
An analytical approach was developed to design a single uniformly sloping lateral in the micro-irrigation systems.Emission uniformity was used as the water application uniformity criterion.Energy relations based on th...An analytical approach was developed to design a single uniformly sloping lateral in the micro-irrigation systems.Emission uniformity was used as the water application uniformity criterion.Energy relations based on the energy-gradient-line approach were revamped to account for the spatial variance of emitter outflow and the emitter connections local energy losses.Four pressure head grade line profiles were distinguished:uphill,horizontal,gentle downhill and steep downhill.Analytical expressions of emission uniformity by hydraulic variation for each pressure profile were developed based on the design variables:length and diameter of lateral,emitter spacing,emitter flow equation parameters,equivalent length characterizing local losses and ground slope.The design conditions for selecting emitter type,the number of emitters per plant and designing the diameter of the uphill and steep downhill laterals were also developed.The nonlinear equations for determining lateral diameter and lateral length were solved iteratively by using the built-in root-finding function of(Tools>Goal Seek…)in the calculation spreadsheet of Microsoft Excel.The procedures also provide the options to fix the design lateral diameter with the commercial standard size or fix the design lateral length based on the field size.The operating inlet pressure and maximum amplitude of the pressure head throughout the lateral could also be determined easily by the procedure.Two numerical applications with various slope combinations indicate that the proposed analytical approach produces results close to the accurate stepwise numerical solutions.In comparison with Keller method,the proposed approach could produce more appropriate designs.展开更多
Permanent magnet synchronous motor (PMSM) is widely used in mining, and there exists chaotic behav- ior when it runs. In order to dispel its adverse effect on security in mining, the chaotic system of PMSM was analyze...Permanent magnet synchronous motor (PMSM) is widely used in mining, and there exists chaotic behav- ior when it runs. In order to dispel its adverse effect on security in mining, the chaotic system of PMSM was analyzed. With noise disturbances, the complex dynamic characteristics of chaos were also analyzed, and proved the objective existence of chaos. As we all know, it is very difficult for conventional PMSM control to meet the design requirements, therefore, in order to ensure the robustness of the system, the chaotic orbits were stabilized to arbitrary chosen fixed points and periodic orbits by means of sliding mode method. Finally MATLAB simulations were presented to confirm the validity of the controller. The results show that the PMSM with the sliding mode control has a good dynamic performance and steady state accuracy.展开更多
The ultimate proof of our understanding of nature and engineering systems is reflected in our ability to control them.Since fractional calculus is more universal, we bring attention to the controllability of fractiona...The ultimate proof of our understanding of nature and engineering systems is reflected in our ability to control them.Since fractional calculus is more universal, we bring attention to the controllability of fractional order systems. First,we extend the conventional controllability theorem to the fractional domain. Strictly mathematical analysis and proof are presented. Because Chua＇s circuit is a typical representative of nonlinear circuits, we study the controllability of the fractional order Chua＇s circuit in detail using the presented theorem. Numerical simulations and theoretical analysis are both presented, which are in agreement with each other.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.51109180)
文摘In order to figure out the dynamical behaviour of a fractional-order chaotic system and its relation to an integer- order chaotic system, in this paper we investigate the synchronization between a class of fractional-order chaotic systems and integer-order chaotic systems via sliding mode control method. Stability analysis is performed for the proposed method based on stability theorems in the fractional calculus. Moreover, three typical examples are carried out to show that the synchronization between fractional-order chaotic systems and integer-orders chaotic systems can be achieved. Our theoretical findings are supported by numerical simulation results. Finally, results from numerical computations and theoretical analysis are demonstrated to be a perfect bridge between fractional-order chaotic systems and integer-order chaotic systems.
基金supported by the National Natural Science Foundation of China (Grant No. 51109180)the Personal Special Fund of Northwest Agriculture and Forestry University,China (Grant No. RCZX-2009-01)
文摘A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.
基金supported by the Special Foundation of National Science & Technology Supporting Plan( 2011BAD29B02)the "111" Project (B12007)
文摘An analytical approach was developed to design a single uniformly sloping lateral in the micro-irrigation systems.Emission uniformity was used as the water application uniformity criterion.Energy relations based on the energy-gradient-line approach were revamped to account for the spatial variance of emitter outflow and the emitter connections local energy losses.Four pressure head grade line profiles were distinguished:uphill,horizontal,gentle downhill and steep downhill.Analytical expressions of emission uniformity by hydraulic variation for each pressure profile were developed based on the design variables:length and diameter of lateral,emitter spacing,emitter flow equation parameters,equivalent length characterizing local losses and ground slope.The design conditions for selecting emitter type,the number of emitters per plant and designing the diameter of the uphill and steep downhill laterals were also developed.The nonlinear equations for determining lateral diameter and lateral length were solved iteratively by using the built-in root-finding function of(Tools>Goal Seek…)in the calculation spreadsheet of Microsoft Excel.The procedures also provide the options to fix the design lateral diameter with the commercial standard size or fix the design lateral length based on the field size.The operating inlet pressure and maximum amplitude of the pressure head throughout the lateral could also be determined easily by the procedure.Two numerical applications with various slope combinations indicate that the proposed analytical approach produces results close to the accurate stepwise numerical solutions.In comparison with Keller method,the proposed approach could produce more appropriate designs.
基金supported in part by the National Natural Science Foundation of China (No. 50879072)the Fundamental Research Funds for the Central Universities of CUMT (No.2010QNB33)The National Undergraduate Innovation Programof CUMT (No. 101029013)
文摘Permanent magnet synchronous motor (PMSM) is widely used in mining, and there exists chaotic behav- ior when it runs. In order to dispel its adverse effect on security in mining, the chaotic system of PMSM was analyzed. With noise disturbances, the complex dynamic characteristics of chaos were also analyzed, and proved the objective existence of chaos. As we all know, it is very difficult for conventional PMSM control to meet the design requirements, therefore, in order to ensure the robustness of the system, the chaotic orbits were stabilized to arbitrary chosen fixed points and periodic orbits by means of sliding mode method. Finally MATLAB simulations were presented to confirm the validity of the controller. The results show that the PMSM with the sliding mode control has a good dynamic performance and steady state accuracy.
基金supported by the National Natural Science Foundation of China(Grant Nos.51109180 and 51479173)the Fundamental Research Funds for the Central Universities,China(Grant No.201304030577)+1 种基金the Northwest A&F University Foundation,China(Grant No.2013BSJJ095)the Scientific Research Foundation on Water Engineering of Shaanxi Province,China(Grant No.2013slkj-12)
文摘The ultimate proof of our understanding of nature and engineering systems is reflected in our ability to control them.Since fractional calculus is more universal, we bring attention to the controllability of fractional order systems. First,we extend the conventional controllability theorem to the fractional domain. Strictly mathematical analysis and proof are presented. Because Chua＇s circuit is a typical representative of nonlinear circuits, we study the controllability of the fractional order Chua＇s circuit in detail using the presented theorem. Numerical simulations and theoretical analysis are both presented, which are in agreement with each other.
