高速公路主线的鲁棒限速控制

Robust speed limit control of freeway

将高速公路限速系统视为一个不确定性系统,该系统应当具备一定的鲁棒性与鲁棒稳定性,即对其中每一个对象都可以保证其反馈系统的内稳定。为了增强高速公路限速系统的鲁棒性与鲁棒稳定性,运用基于宏观交通流模型建立非线性状态方程的方法,使模型在一定扰动的情况下保持稳定。采取以下几个步骤进行分析和运算:(1)从整个不确定性仿射非线性系统出发,寻找它的公称状态空间模型;(2)应用状态反馈线性化方法,把公称的仿射非线性系统严密线性化;(3)通过考虑仿射非线性系统的不确定性,使得反馈线性化系统可以用加法不确定性线性系统或乘法不确定性系统来描述;(4)针对反馈线性化系统,用D-K迭代法或μ-K迭代法进行线性鲁棒控制器设计;(5)把线性鲁棒控制器回代到仿射非线性系统中,从而得到非线性鲁棒控制器。进而将这种方法运用在实际算例中,检验了该方法的实用性与可靠性。

As a kind of uncertain system, the speed limit system should be robust and robust steady, which means the internal stability of each system can be guaranteed. Aiming at this problem, by using the methods of macroscopic traffic flow model is established based on nonlinear state equation,the model is stable in the case of a certain disturbance. The following steps of analysis and calculation are taken：①Based on the uncertain affine nonlinear system, the nominal state space model is searched;②Application of state feedback linearization method, the nonlinear system of strict linear nominal; ③by considering affine nonlinear systems with uncertainties, the feedback linearization system can use the addition of linear uncertain systems or multiplicative uncertainty to describe system ; ④According to the feedback linearization system, design of linear robust controller using D-K iterative method or μ-K iterative method; ⑤the linear robust controller back to affine nonlinear system, so as to obtain the nonlinear robust controller.