Stability Analysis and Controller Design of First-Order Inverted Pendulum with Time-Varying Delay

This paper studies the stability problem of the stability control of the inverted pendulum system with interval time-varying delay, obtains the time-varying delay margin of the inverted pendulum system with time delay based on PI control, and obtains the parameters of the PI controller when the conditions are met. First, considering the transmission delay from the control center to the regulator and the sensor to the control center,A model of the inverted pendulum system based on PI control was established; secondly, under the condition that the upper bound of the interval time-varying delay is not zero, ac-cording to the improved Lyaounov-Krasovskii functional (LKF), the stability criterion of the inverted pendulum control system with time-varying delay is derived. The nonlinear term of time-varying delay square is introduced in the expansion of LKF. Using the negative definite integral inequality transformation lemma, the nonlinear matrix inequality in the stability criterion can be equivalently transformed into a linear matrix inequality without introducing extra conservatism. Finally, MATLAB LMItoolbox is used to obtain the maximum stability margin and controller parameters of the inverted pendulum system. The effectiveness of the stability criterion is verified through simulink virtual simulation and simulation experiments that compile the system to hardware based on Rtlab software.