The analysis and design of the extended state observer （ESO） involves a continuous non-smooth structure, thus the study of the ESO dynamic requires mathematical tools of the nonlinear systems analysis. This paper es...The analysis and design of the extended state observer （ESO） involves a continuous non-smooth structure, thus the study of the ESO dynamic requires mathematical tools of the nonlinear systems analysis. This paper establishes the sufficient conditions for absolute stability of the ESO. Based on this study, a methodology to estimate several nonlinear functions in dy- namics systems is proposed.展开更多
In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical exam...In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical examples to illustrate the efficiency of frequency domain-based condition.展开更多
发电机组的一次调频控制回路中由于数字电液调节系统与机械液压调节系统的并存,使得本应发挥高灵敏度作用的 DEH 调节系统中设置了和机械液压机组相同的调频死区。考虑到调频死区这一非线性环节的存在使二次调频回路中控制器的受控对象...发电机组的一次调频控制回路中由于数字电液调节系统与机械液压调节系统的并存,使得本应发挥高灵敏度作用的 DEH 调节系统中设置了和机械液压机组相同的调频死区。考虑到调频死区这一非线性环节的存在使二次调频回路中控制器的受控对象发生了改变,因此需要用相应的非线性控制的方法来选择二次调频控制回路中的 PI 控制器的参数。该文研究了调频死区对二次调频回路中的 PI 控制器的受控对象特性的影响,用 Popov 稳定判据作为选择 PI 参数使系统稳定的数学工具,讨论了 PI 参数的变化对系统频率控制质量的影响。展开更多
Two model reference adaptive system （MRAS） estimators are developed for identifying the parameters of permanent magnet synchronous motors （PMSM） based on the Lyapunov stability theorem and the Popov stability crit...Two model reference adaptive system （MRAS） estimators are developed for identifying the parameters of permanent magnet synchronous motors （PMSM） based on the Lyapunov stability theorem and the Popov stability criterion, respectively. The proposed estimators only need online measurement of currents, voltages, and rotor speed to effectively estimate stator resistance, inductance, and rotor flux-linkage simultaneously. The performance of the estimators is compared and verified through simulations and experiments, which show that the two estimators are simple, have good robustness against parameter variation, and are accurate in parameter tracking. However, the estimator based on the Popov stability criterion, which can overcome parameter variation in a practical system, is superior in terms of response speed and convergence speed since there are both proportional and integral units in the estimator, in contrast to only one integral unit in the estimator based on the Lyapunov stability theorem. In addition, the estimator based on the Popov stability criterion does not need the expertise that is required in designing a Lyapunov function.展开更多
New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F...New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F（z）, in negative feedback with a matrix of periodic/aperiodic gains A（k）, k = 0,1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities φp（-）, without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features： i） They involve the positive definiteness of the real part （as evaluated on ｜z｜ = 1） of the product of Г （z） and a matrix multiplier function of z. ii） For periodic A（k）, one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A（k）, but for aperiodic A（k）, which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of （A（k ＋ 1）,A（k））, k = 1, 2 iii） They are distinct from and less restrictive than recent results in the literature.展开更多
We present here a stability condition and its verification method for the time\|invariant nonlinear system. This stability condition is based on the small gain theorem in regard to L\-2 gain, and its verification ...We present here a stability condition and its verification method for the time\|invariant nonlinear system. This stability condition is based on the small gain theorem in regard to L\-2 gain, and its verification method is described by the Nyquist criterion and the modified M\|circle set(alike to Popov’s criterion). In order to verify the above system stability, we assume the system nonlinear part as a non\|linear subsystem with a free parameter q≥0, and focus on the change of some peak value of the relative position between the vector locus of the open loop frequency response characteristic and the modified M\|circle set, which may be available for stability analysis and robust design of the control system.展开更多
基金supported by Programa de Jovenes Investigadores e Innovadores COLCIENCIAS (DFIA-0494)Universidad Nacional de Colombia Manizales (12475),Vicerrectoría de Investigación,DIMA.
文摘The analysis and design of the extended state observer （ESO） involves a continuous non-smooth structure, thus the study of the ESO dynamic requires mathematical tools of the nonlinear systems analysis. This paper establishes the sufficient conditions for absolute stability of the ESO. Based on this study, a methodology to estimate several nonlinear functions in dy- namics systems is proposed.
文摘In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical examples to illustrate the efficiency of frequency domain-based condition.
文摘发电机组的一次调频控制回路中由于数字电液调节系统与机械液压调节系统的并存,使得本应发挥高灵敏度作用的 DEH 调节系统中设置了和机械液压机组相同的调频死区。考虑到调频死区这一非线性环节的存在使二次调频回路中控制器的受控对象发生了改变,因此需要用相应的非线性控制的方法来选择二次调频控制回路中的 PI 控制器的参数。该文研究了调频死区对二次调频回路中的 PI 控制器的受控对象特性的影响,用 Popov 稳定判据作为选择 PI 参数使系统稳定的数学工具,讨论了 PI 参数的变化对系统频率控制质量的影响。
基金supported by China Scholarship Council, National Natural Science Foundation of China (No. 60634020)Scientific Research Foundation of Education Ministry for the Doctors(No. 20060532026)
文摘Two model reference adaptive system （MRAS） estimators are developed for identifying the parameters of permanent magnet synchronous motors （PMSM） based on the Lyapunov stability theorem and the Popov stability criterion, respectively. The proposed estimators only need online measurement of currents, voltages, and rotor speed to effectively estimate stator resistance, inductance, and rotor flux-linkage simultaneously. The performance of the estimators is compared and verified through simulations and experiments, which show that the two estimators are simple, have good robustness against parameter variation, and are accurate in parameter tracking. However, the estimator based on the Popov stability criterion, which can overcome parameter variation in a practical system, is superior in terms of response speed and convergence speed since there are both proportional and integral units in the estimator, in contrast to only one integral unit in the estimator based on the Lyapunov stability theorem. In addition, the estimator based on the Popov stability criterion does not need the expertise that is required in designing a Lyapunov function.
文摘New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F（z）, in negative feedback with a matrix of periodic/aperiodic gains A（k）, k = 0,1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities φp（-）, without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features： i） They involve the positive definiteness of the real part （as evaluated on ｜z｜ = 1） of the product of Г （z） and a matrix multiplier function of z. ii） For periodic A（k）, one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A（k）, but for aperiodic A（k）, which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of （A（k ＋ 1）,A（k））, k = 1, 2 iii） They are distinct from and less restrictive than recent results in the literature.
文摘We present here a stability condition and its verification method for the time\|invariant nonlinear system. This stability condition is based on the small gain theorem in regard to L\-2 gain, and its verification method is described by the Nyquist criterion and the modified M\|circle set(alike to Popov’s criterion). In order to verify the above system stability, we assume the system nonlinear part as a non\|linear subsystem with a free parameter q≥0, and focus on the change of some peak value of the relative position between the vector locus of the open loop frequency response characteristic and the modified M\|circle set, which may be available for stability analysis and robust design of the control system.
