Fractional order PD controller design method based on N-W small world network model

Abstract

The invention discloses a fractional order PD controller design method based on an N-W small world network model. The method comprises steps that firstly, the stability characteristics and the balancepoint information of the N-W small world network model are analyzed; secondly, a fractional order PD controller is applied to the N-W small world network model, and a balance point is solved; thirdly, the controlled N-W small world network model is linearized at the balance point, and characteristic equations of the linearized controlled N-W small world network model are obtained; and lastly, delay parameters are selected as bifurcation parameters, and stability analysis and bifurcation analysis of the characteristic equations of the linearized N-W small world network model are carried out, proper fractional PD controller parameters are selected, and the controlled N-W small world network model is stabilized at the balance point. The method is advantaged in that relatively strong applicability is realized, generation of bifurcation can be effectively controlled by a fractional-order PD controller, so critical bifurcation is made ahead or lag.

Description

technical field [0001] The invention relates to a design method of a fractional-order PD (Proportion Differentiation) controller, in particular to a design method of a fractional-order PD controller based on an N-W (Newman-Watts) small-world network model, and belongs to the technical field of controllers. Background technique [0002] Watts et al. proposed a small-world network model network in 1998, which can describe a gradual change process from a regular network to a random network. In 1998, a well-known N-W model was proposed, but it did not take into account the communication delay of the system. In 2001, a time-delayed N-W model was proposed, and the influence of time-delay and nonlinear topology on the network was studied. However, the interaction of nonlinear invariants of this model failed to combine topology differences. To overcome this shortcoming, a more general nonlinear small-world network model was proposed in 2004. [0003] In complex networks, bifurcati...

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Problems solved by technology

In 1998, a well-known N-W model was proposed, but it did not take into account the communication delay of the system

In 2001, a N-W model with time delay was proposed, and the influence of time delay and nonlinear topology on the network was studied, but the interaction of nonlinear invariants of this model failed to combine topology differences

For example, the time-delay feedback controller is not sensitive enough to bifurcation control, the state feedback control is not suitable for the stability of some periodic orbits, and the design of fault-tolerant control technology is not only expensive but also complicated in control procedures

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