具时滞单级倒立摆系统的稳定性分析

倒立摆本身是一个自然不稳定系统,时滞的存在更加恶化了系统性能。基于牛顿动力学方法建立了具时滞单级倒立摆系统的动力学模型,采用PID策略实施控制。将时滞环节采用一阶对称Padé逼近,得到系统的特征方程,利用Routh稳定判据和符号计算法计算出控制系统临界稳定的时滞量。仿真实验结果表明,时滞的存在降低了控制效果,甚至导致控制系统失效。

Stability Analysis of Single Inverted Pendulum System with Time Delay

Inverted pendulum itself was a naturally unstable system,the system performance was deteriorated by the existence of time delay.The dynamic model of single inverted pendulum system with time delay was set up based on newtonian dynamics method,and was controlled by PID algorithm.The characteristic equation was got through the time delay unit approximated by first-order symmetric Padé series.The critical stable value of time delay of the system was acquired according to routh stability criterion and symbols calculation method.The simulation results showed that the existence of time delay reduced control effect,and even caused control system failure.