Abstract：The stability and stochastic bifurcation problems of generalized DVP system with time-delayed fractional order PID controller under correlated white noise excitation are studied in this paper. According to the principle of minimal mean square error， the approximate expression of the time-delayed fractional order PID controller is obtained， so as to transform the system into an equivalent integer system. The stability and the stochastic D-bifurcation behavior of the system are analyzed by the singular boundary theory and the invariant measure of the dynamic system. The stationary probability density function of the amplitude of the system is obtained by stochastic averaging method， and the effects of fractional integral， fractional derivative， time-delay and noise correlation coefficient of time-delayed fractional PID controller on the stochastic P-bifurcation of the system are analyzed. It is found that the changes of fractional integral， fractional derivative and time-delay will lead to stochastic P-bifurcation of the system， while the noise correlation coefficient not cause stochastic P-bifurcation of the system by using Matlab.
王慧男,张建刚,王 芳. 相关噪声激励下含时滞分数阶PID控制器系统的稳定性和随机分岔[J]. 华中师范大学学报(自然科学版), 2025, 59(1): 125-134.
WANG Huinan,ZHANG Jiangang,WANG Fang. Stability and stochastic bifurcation of system with time-delayed fractional order PID controller excited by correlated noise. journal1, 2025, 59(1): 125-134.
2025, Vol. 59 
