A new approach to the calculation of the points at which the root locus crosses the imaginary axis is proposed and the corresponding parameters are given. Further, this method to analyze polynomial convexity is used. ...A new approach to the calculation of the points at which the root locus crosses the imaginary axis is proposed and the corresponding parameters are given. Further, this method to analyze polynomial convexity is used. Examples are given for illustration. It is shown that this approach is simple and useful to determine the Hurwitz stable polynomial.展开更多
It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing （RTDHT）. This paper focuses on the delay-dependent stability and adde...It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing （RTDHT）. This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT. The exponential delay term is transferred into a rational fraction by the Pad6 approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique. First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure. The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness. For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay. For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode. Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable. Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.展开更多
An explicit unconditionally stable algorithm for hybrid tests,which is developed from the traditional HHT-α algorithm,is proposed.The unconditional stability is first proven by the spectral radius method for a linear...An explicit unconditionally stable algorithm for hybrid tests,which is developed from the traditional HHT-α algorithm,is proposed.The unconditional stability is first proven by the spectral radius method for a linear system.If the value of α is selected within [-0.5,0],then the algorithm is shown to be unconditionally stable.Next,the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system.The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening.To improve the stability of the proposed method,the structure stiffness is then identified and updated.Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability.展开更多
This paper aims to investigate the critical stability of a multi-degree-of-freedom(multi-DOF)real-time hybrid simulation(RTHS).First,the critical time-delay analysis models are developed using the continuous-and discr...This paper aims to investigate the critical stability of a multi-degree-of-freedom(multi-DOF)real-time hybrid simulation(RTHS).First,the critical time-delay analysis models are developed using the continuous-and discrete-time root locus(RL)techniques,respectively.A bilinear transform is introduced into the first-order Padéapproximation while conducting the discrete RL analysis.Based on this technique,the time delay can be explicitly used as the gain factor and thus the instability mechanism of the multi-DOF RTHS system can be analyzed.Subsequently,the critical time delays calculated by the continuous-and discrete-time RL techniques,respectively,are compared for a 2-DOF RTHS system.It is shown that assuming the RTHS system to be a continuous-time system will result in overestimating the critical time delay.Finally,theoretically calculated critical delays are demonstrated and validated by numerical simulation and a set of RTHS experiments.Parametric analysis provides a glimpse of the effects of time step,frequency and damping ratio in a performing partitioning scheme.The constructed analysis model proves to be useful for evaluating the critical time delay to predict stability and performance,therefore facilitating successful RTHS.展开更多
This paper presents an adaptive equivalent-input-disturbance(AEID)approach that contains a new adjustable gain to improve disturbance-rejection performance.A linear matrix inequality is derived to design the parameter...This paper presents an adaptive equivalent-input-disturbance(AEID)approach that contains a new adjustable gain to improve disturbance-rejection performance.A linear matrix inequality is derived to design the parameters of a control system.An adaptive law for the adjustable gain is presented based on the combination of the root locus method and Lyapunov stability theory to guarantee the stability of the AEID-based system.The adjustable gain is limited in an allowable range and the information for adjusting is obtained from the state of the system.Simulation results show that the method is effective and robust.A comparison with the conventional EID approach demonstrates the validity and superiority of the method.展开更多
The Activated Sludge Process(ASP) exhibits highly nonlinear properties. The design of an automatic control system that is robust against disturbance of inlet wastewater flow rate and has short process settling times i...The Activated Sludge Process(ASP) exhibits highly nonlinear properties. The design of an automatic control system that is robust against disturbance of inlet wastewater flow rate and has short process settling times is a challenging matter. The proposed control method is an I-P modi fied controller automatic control system with state variable feedback and control canonical form simulation diagram for the process. A more stable response is achieved with this type of modern control. Settling times of 0.48 days are achieved for the concentration of microorganisms,(reference value step increase of 50 mg·L-1) and 0.01 days for the concentration of oxygen(reference value step increase of 0.1 mg·L-1). Fluctuations of concentrations of oxygen and microorganisms after an inlet disturbance of5 × 103m3·d-1are small. Changes in the reference values of oxygen and microorganisms(increases by 10%, 20% and 30%) show satisfactory response of the system in all cases. Changes in the value of inlet wastewater flow rate disturbance(increases by 10%, 25%, 50% and 100%) are stabilized by the control system in short time. Maximum percent overshoot is also taken in consideration in all cases and the largest value is 25% which is acceptable. The proposed method with I-P controller is better for disturbance rejection and process settling times compared to the same method using PI controller. This method can substitute optimal control systems in ASP.展开更多
This paper presents an enhanced Root Locus diagram that consists of the representation of the phase and the magnitude of the transfer function G（s） of a system. The magnitude is represented in decibels and the phase...This paper presents an enhanced Root Locus diagram that consists of the representation of the phase and the magnitude of the transfer function G（s） of a system. The magnitude is represented in decibels and the phase is represented by colors. It also presents how to use it to calculate different kinds of controllers. An important characteristic of this diagram is that permits to read the phase and the gain margins directly and the imaginary axis cut represents the Bode diagram. It is also possible to put the grid with damping ratio ξ and frequency ωn.展开更多
Maize（Zea mays L.） root morphology exhibits a high degree of phenotypic plasticity to nitrogen（N） de ficiency,but the underlying genetic architecture remains to be investigated Using an advanced BC_4F_3 population...Maize（Zea mays L.） root morphology exhibits a high degree of phenotypic plasticity to nitrogen（N） de ficiency,but the underlying genetic architecture remains to be investigated Using an advanced BC_4F_3 population,we investigated the root growth plasticity under two contrasted N levels and identi fied the quantitative trait loci（QTLs） with QTL-environment（Q×E）interaction effects. Principal components analysis（PCA） on changes of root traits to N de ficiency（D LN-HN） showed that root length and biomass contributed for 45.8% in the same magnitude and direction on the first PC,while root traits scattered highly on PC_2 and PC_3. Hierarchical cluster analysis on traits for D LN-HN further assigned the BC_4F_3 lines into six groups,in which the special phenotypic responses to N de ficiency was presented These results revealed the complicated root plasticity of maize in response to N de ficiency that can be caused by genotype environment（G×E） interactions. Furthermore,QTL mapping using a multi-environment analysis identi fied 35 QTLs for root traits. Nine of these QTLs exhibited signi ficant Q×E interaction effects. Taken together,our findings contribute to understanding the phenotypic and genotypic pattern of root plasticity to N de ficiency,which will be useful for developing maize tolerance cultivars to N de ficiency.展开更多
基金supported by the Innovation Program of Shanghai Municipal Education Commission (Grant No.08YZ73)the Shanghai Leading Academic Discipline Project (Grant No.T0401)the Scientific Computing Key Laboratory of Shanghai Universities
文摘A new approach to the calculation of the points at which the root locus crosses the imaginary axis is proposed and the corresponding parameters are given. Further, this method to analyze polynomial convexity is used. Examples are given for illustration. It is shown that this approach is simple and useful to determine the Hurwitz stable polynomial.
基金State Key Laboratory of Hydroscience and Engineering Under Grant No.2008-TC-2National Natural Science Foundation of China Under Grant No.90510018,50779021 and 90715041
文摘It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing （RTDHT）. This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT. The exponential delay term is transferred into a rational fraction by the Pad6 approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique. First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure. The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness. For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay. For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode. Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable. Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.
基金Scientific Research Fund of the Institute of Engineering Mechanics,CEA under Grant Nos.2017A02,2016B09 and 2016A06the National Science-technology Support Plan Projects under Grant No.2015BAK17B02the National Natural Science Foundation of China under Grant Nos.51378478,51408565,51678538 and 51161120360
文摘An explicit unconditionally stable algorithm for hybrid tests,which is developed from the traditional HHT-α algorithm,is proposed.The unconditional stability is first proven by the spectral radius method for a linear system.If the value of α is selected within [-0.5,0],then the algorithm is shown to be unconditionally stable.Next,the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system.The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening.To improve the stability of the proposed method,the structure stiffness is then identified and updated.Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability.
基金National Natural Science Foundation of China under Grant Nos.51725901 and 51639006。
文摘This paper aims to investigate the critical stability of a multi-degree-of-freedom(multi-DOF)real-time hybrid simulation(RTHS).First,the critical time-delay analysis models are developed using the continuous-and discrete-time root locus(RL)techniques,respectively.A bilinear transform is introduced into the first-order Padéapproximation while conducting the discrete RL analysis.Based on this technique,the time delay can be explicitly used as the gain factor and thus the instability mechanism of the multi-DOF RTHS system can be analyzed.Subsequently,the critical time delays calculated by the continuous-and discrete-time RL techniques,respectively,are compared for a 2-DOF RTHS system.It is shown that assuming the RTHS system to be a continuous-time system will result in overestimating the critical time delay.Finally,theoretically calculated critical delays are demonstrated and validated by numerical simulation and a set of RTHS experiments.Parametric analysis provides a glimpse of the effects of time step,frequency and damping ratio in a performing partitioning scheme.The constructed analysis model proves to be useful for evaluating the critical time delay to predict stability and performance,therefore facilitating successful RTHS.
基金This work was supported by National Natural Science Foundation of China(No.61873348)National Key R&D Program of China(No.2017YFB1300900)+1 种基金Hubei Provincial Natural Science Foundation of China(No.2015CFA010)the 111 Project,China(No.B17040).
文摘This paper presents an adaptive equivalent-input-disturbance(AEID)approach that contains a new adjustable gain to improve disturbance-rejection performance.A linear matrix inequality is derived to design the parameters of a control system.An adaptive law for the adjustable gain is presented based on the combination of the root locus method and Lyapunov stability theory to guarantee the stability of the AEID-based system.The adjustable gain is limited in an allowable range and the information for adjusting is obtained from the state of the system.Simulation results show that the method is effective and robust.A comparison with the conventional EID approach demonstrates the validity and superiority of the method.
文摘The Activated Sludge Process(ASP) exhibits highly nonlinear properties. The design of an automatic control system that is robust against disturbance of inlet wastewater flow rate and has short process settling times is a challenging matter. The proposed control method is an I-P modi fied controller automatic control system with state variable feedback and control canonical form simulation diagram for the process. A more stable response is achieved with this type of modern control. Settling times of 0.48 days are achieved for the concentration of microorganisms,(reference value step increase of 50 mg·L-1) and 0.01 days for the concentration of oxygen(reference value step increase of 0.1 mg·L-1). Fluctuations of concentrations of oxygen and microorganisms after an inlet disturbance of5 × 103m3·d-1are small. Changes in the reference values of oxygen and microorganisms(increases by 10%, 20% and 30%) show satisfactory response of the system in all cases. Changes in the value of inlet wastewater flow rate disturbance(increases by 10%, 25%, 50% and 100%) are stabilized by the control system in short time. Maximum percent overshoot is also taken in consideration in all cases and the largest value is 25% which is acceptable. The proposed method with I-P controller is better for disturbance rejection and process settling times compared to the same method using PI controller. This method can substitute optimal control systems in ASP.
文摘This paper presents an enhanced Root Locus diagram that consists of the representation of the phase and the magnitude of the transfer function G（s） of a system. The magnitude is represented in decibels and the phase is represented by colors. It also presents how to use it to calculate different kinds of controllers. An important characteristic of this diagram is that permits to read the phase and the gain margins directly and the imaginary axis cut represents the Bode diagram. It is also possible to put the grid with damping ratio ξ and frequency ωn.
基金supported by the Ministry of Science and Technology of China(2011CB100305,2012AA100304)National Natural Science Foundation of China(31172015,31421092,31572186)+2 种基金Danish Strategic Research Council(NUTRIEFFICIENT 10-093498)European Community the Seventh Framework Programme for Research(NUE-CROPSFP7-CP-IP 222645)Chinese Universities Scientific Fund(2015ZH001)
文摘Maize（Zea mays L.） root morphology exhibits a high degree of phenotypic plasticity to nitrogen（N） de ficiency,but the underlying genetic architecture remains to be investigated Using an advanced BC_4F_3 population,we investigated the root growth plasticity under two contrasted N levels and identi fied the quantitative trait loci（QTLs） with QTL-environment（Q×E）interaction effects. Principal components analysis（PCA） on changes of root traits to N de ficiency（D LN-HN） showed that root length and biomass contributed for 45.8% in the same magnitude and direction on the first PC,while root traits scattered highly on PC_2 and PC_3. Hierarchical cluster analysis on traits for D LN-HN further assigned the BC_4F_3 lines into six groups,in which the special phenotypic responses to N de ficiency was presented These results revealed the complicated root plasticity of maize in response to N de ficiency that can be caused by genotype environment（G×E） interactions. Furthermore,QTL mapping using a multi-environment analysis identi fied 35 QTLs for root traits. Nine of these QTLs exhibited signi ficant Q×E interaction effects. Taken together,our findings contribute to understanding the phenotypic and genotypic pattern of root plasticity to N de ficiency,which will be useful for developing maize tolerance cultivars to N de ficiency.
