含饱和、死区和时滞的主动悬架PID控制器设计

Design of PID controllers for the active suspension with saturation,dead zone and time delay

饱和、死区和时滞都是作动器常见的非线性现象,容易导致主动悬架系统性能下降甚至不稳定。建立1/4车体主动悬架系统动力学数学模型,运用描述函数法表述系统饱和、死区特性,通过欧拉公式描述系统时滞特性,得到含饱和、死区和时滞非线性的主动悬架系统传递函数模型。针对含PID控制器的主动悬架闭环控制系统,采用奇异频率解耦法获得矩阵形式的Hurwitz条件,再通过图解法获得PID控制器参数稳定范围。建立主动悬架仿真模型,实例研究闭环系统输出响应及非线性因素的影响。结果表明,所设计的PID控制器能保证非线性悬架正常稳定工作,可有效降低悬架系统的振动幅值,且对饱和、死区和时滞非线性因素具有一定的鲁棒性。该PID控制器设计方法可以方便地应用于工程实际,有利于提高非线性主动悬架的系统性能。

Saturation,dead zone and time delay,as some non-linear phenomena,are common for actuators,which may easily lead to performance degradation or even instability of the active suspension system. In this article,the dynamic mathematical model of the 1/4 vehicle-body active suspension system is worked out. The characteristics of saturation and dead zone are expressed by means of the description function method,and the characteristics of time delay are described by the Euler formula.Then,the transfer function model of the active suspension system with saturation,dead zone and time-delay non-linearity is set up. For the closed-loop control system of active suspension with the PID controller,the Hurwitz condition in the form of matrix is derived by means of the singular-frequency decoupling method,and the PID controlle’s parameter stability range is identified with the aid of the graphic method. The simulation model of active suspension is worked out,in order to explore both the output response of the closed-loop system and the influence of non-linear factors. The results show that the PID controller ensures the normal and stable operation of the non-linear suspension,effectively reduces the vibration amplitude of the suspension system,and has certain robustness to the saturation,dead zone and time-delay non-linear factors. This method of PID controller design easily applied to engineering practice is beneficial to improve the performance of the non-linear active suspension system.