In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a ...In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation.展开更多
In this paper, the stabilization of neutral time-delay systems is investigated. An efficient numerical approach is presented in an algorithm to establish results so that stability of such systems is achieved and stabi...In this paper, the stabilization of neutral time-delay systems is investigated. An efficient numerical approach is presented in an algorithm to establish results so that stability of such systems is achieved and stabilizing PID parameters are determined directly. It is based on determining the rightmost characteristic roots and Nyquist plot. The Newton-Raphson’s iterative method based on Lambert W function is used for the calculation of these stabilizing roots directly from the closed-loop characteristic equation of the neutral time-delay system and then stability is checked by Nyquist plot and step response of closed-loop system. Two numerical examples are included to illustrate the effectiveness of the proposed approach.展开更多
We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random env...We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.展开更多
基金supported by the National Natural Science Foundation of China (Grant 11372354)the Fund of the State Key Lab of Mechanics and Control of Mechanical Structures (Grant MCMS-0116K01)
文摘In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation.
文摘In this paper, the stabilization of neutral time-delay systems is investigated. An efficient numerical approach is presented in an algorithm to establish results so that stability of such systems is achieved and stabilizing PID parameters are determined directly. It is based on determining the rightmost characteristic roots and Nyquist plot. The Newton-Raphson’s iterative method based on Lambert W function is used for the calculation of these stabilizing roots directly from the closed-loop characteristic equation of the neutral time-delay system and then stability is checked by Nyquist plot and step response of closed-loop system. Two numerical examples are included to illustrate the effectiveness of the proposed approach.
基金the National Natural Science Foundation of China (Grant Nos. 10271020,10471012)SRF for ROCS, SEM (Grant No. [2005]564)
文摘We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.
