The Dynamic Analysis And Control Of A Class Of Governor System With Random Parameters

As a class of important natural science system,the governor system can describe the physical phenomena by means of mathematical model.By using the mathematical model,the governor systems can make a scientific explanation which is dynamic behavior and sliding mode control.As a result of random factors often existence in the real life,if the general deterministic method to analyze the dynamic behavior of the system,the conclusions and the actual situation will produce some differences.Therefore,in the governor system since considers the external disturbance,the influence of parameter excitation is necessary to study the dynamic characteristics of the system.There is no doubt that the impact of random parameters on the governor system can cause a series of problems such as performance changes,engineering errors,etc.Then how to analyze and study its dynamic characteristics and effective control is an important issues which has long been concerned about mathematician and physicists.The governor model is used to better reveal and reflect the governor's mechanism,rules and control strategies and measures.In this paper,the dynamic characteristics and sliding mode control of this model are analyzed according to the basic theory of nonlinear stochastic dynamics and the main method of random parameter structure for a class of governor systems with random parameters.Based on the theoretical analysis and method discussion of random parameter structure,the stochastic stability,random bifurcation and stochastic control of a class of governor systems with random parameters are further studied and explored.The main contents of this paper are as follows:1.The research status and development trend of uncertain parameter structure system,governor system,stochastic stability,random bifurcation,fractional order system and sliding mode control are briefly reviewed.At the same time,the basic concepts of Chebyshev polynomial orthogonal approximation,orthogonal decomposition,Lyapunov stability,bifurcation theory,central manifold theorem,singular boundary value theory and stochastic stability are expounded and summarized.2.We mainly study the dynamic behavior of a class of centrifugal governor systems with random parameters.The dynamic characteristics of such governor systems are analyzed by Chebyshev orthogonal polynomial approximation.Firstly,the Chebyshev orthogonal polynomial approximation method is used to transform the system,and the model becomes a deterministic model after the transformation.Then,the Routh-Hurwitz criterion is used to discuss and judge the stability of the system at the equilibrium point.At the same time,the conditions of Hopf bifurcation can be obtained according to the bifurcation theory.Finally,the model is simulated numerically.The results show that when the bifurcation parameter crosses the critical value of the bifurcation,the bifurcation occurs and the numericalsimulation is used to verify the correctness and feasibility of the method and the theoretical result.3.A class of hexagonal governor systems with parametric excitation is studied.The stochastic stability and random bifurcation of the system are analyzed directly by quasi-non-integrable Hamiltonian theory.Firstly,we use the central invariant manifold theorem to reduce the dimension of the system,and consider the direct calculation of drift and diffusion coefficient to calculate the multiple integral.Therefore,it is necessary to obtain It? stochastic differential equations and signatures,drift and diffusion coefficients by means of polar coordinate transformation and stochastic averaging.Then the local stability and global stability are analyzed by using the singular boundary theory and the maximum Lyapunov exponent.Then the stochastic bifurcation is analyzed by the invariant measure and and probability density.Finally,the model is simulated numerically.The results show that the stochastic stability of the model and the state of the random bifurcation change with the excitation and further verify the Hamilton method is effective.4.The sliding mode control of a fractional-order governor system with random parameters is studied.When considering the disturbance and randomness,the dynamic behavior of the governor systems will become more complex.The key lies in the control analysis of a class of fractional-order governor system.First,we designed the corresponding sliding mode controller according to the control law.Then through the design of the controller to achieve stable conditions when the fractional-order governor system with disturbance and randomness.Finally,numerical simulation was carried out.The results show that the design of the controller can make the model stable and the use this method to control is correct and effective.