二阶系统模糊自适应PID变阻尼控制仿真研究

Simulation of Variable Damping Ratio Control of the 2^(nd) Order System with Fuzzy Adaptive PID

为了改善二阶系统的动态性能,通常用速度反馈增大等效阻尼比的方法减小输出响应振荡和超调量,但阻尼比增大,系统响应迟钝,快速性变差。当无阻尼自然振荡角频率一定时,阻尼比是影响二阶系统性能的主要因素。在线调整速度反馈通道增益以改变阻尼比从而改善系统性能。由于很难准确建立系统跟踪偏差和偏差变化率与速度反馈通道增益之间的数学模型,所以,模糊自适应PID变阻尼控制结合PID控制和模糊控制的优点,运用模糊推理方法根据系统输出响应的不同阶段在线实时调整系统的阻尼比,从而提高系统快速性和稳定性。仿真结果表明该方法可行,系统动态性能得到明显改善,无超调现象,并具有良好的抗干扰性。

In order to improve dynamic property, the 2nd order systems generally decrease the oscillation and overshoot of output response by increasing equivalent damping ratio with velocity feedback. But output response will be larger and system＇ s speediness property will be worse because of damping ratio＇ s increment. When the undamped natural frequency is determinate, the damping ratio is the key parameter affecting the dynamic property of the 2na - order system. Adjusting the velocity feedback gain can change a damping ratio, then improve the system＇ s property. But generally, because it is difficult to construct a math model between the tracking error or error change rate and the velocity feedback gain, variable damping ratio control by fuzzy adaptive PID may adjust system＇ s damping ratio in real - time on line on the base of output response＇ s different phases, so improve system＇s dynamic property. Simulation results show that the method is feasible, the improvement of dynamic property is prominent, the system has no overshoot phenomenon, and disturbance rejection property is well.