Optimal integrated passive/active design of the suspension system using iteration on the Lyapunov equations

In this paper, an iterative technique is proposed to solve linear integrated active/passive design problems. The optimality of active and passive parts leads to the nonlinear algebraic Riccati equation due to the active parameters and some associated additional Lyapunov equations due to the passive parameters. Rather than the solution of the nonlinear algebraic Riccati equation, it is proposed to consider an iterative solution method based on the Lyapunov equations in the Newton optimization scheme for both active and passive parameters. The main contribution of the paper is considered as the concept that it doesn't require to optimize controller when the plant is not optimal. The proposed method is verified by designing a one-quarter active suspension system. The results indicate that the algorithm is more efficient as compared to solving the problem through the direct Riccati solution based method while its derivation and application is simple. Significant improvements can be seen in comparison to the previous method.