Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interac...Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interaction between the agents is described with an undirected communication graph with a fixed topology. It is shown that the leader-following consensus problem for the considered agents could be converted to the asymptotic stability analysis of a discrete-time fractional order system. Based on this idea, sufficient conditions to reach the leader-following consensus in terms of the controller parameters are extracted. This leads to an appropriate region in the controller parameters space. Numerical simulations are provided to show the performance of the proposed leader-following consensus approach.展开更多
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
文摘Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interaction between the agents is described with an undirected communication graph with a fixed topology. It is shown that the leader-following consensus problem for the considered agents could be converted to the asymptotic stability analysis of a discrete-time fractional order system. Based on this idea, sufficient conditions to reach the leader-following consensus in terms of the controller parameters are extracted. This leads to an appropriate region in the controller parameters space. Numerical simulations are provided to show the performance of the proposed leader-following consensus approach.
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.
