Active suspension control strategy design in vehicle suspension systems has been a popular issue in road vehicle applications. In this paper, we consider a quarter-car suspension problem. A nonlinear objective function together with a system of state-dependent ODEs is involved in the model. A differential equation approximation method, together with the control parametrization enhancing transform (CPET), is used to find the optimal proportional-integral-derivative (PID) feedback gains of the above model. Hence, an approximated optimal control problem is obtained. Proofs of convergences of the state and the optimal control of the approximated problem to those of the original optimal control problem are provided. A numerical example is solved to illustrate the efficiency of our method.

中文翻译：

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具有状态依赖的ODE的四分之一汽车悬架模型的PID增益的微分方程逼近和增强控制方法

车辆悬架系统中的主动悬架控制策略设计一直是公路车辆应用中的一个普遍问题。在本文中，我们考虑了四分之一汽车悬架问题。该模型涉及非线性目标函数以及状态依赖的ODE系统。微分方程近似方法与控制参数化增强变换（CPET）一起用于找到上述模型的最佳比例积分微分（PID）反馈增益。因此，获得了近似的最优控制问题。提供了状态收敛和近似问题的最优控制与原始最优控制问题的收敛证明。数值例子表明了该方法的有效性。