## 7 Conclusions  
In this paper, the theory of RPC is expressed and analyzed step by step, and linear as well as nonlinear system conditions are considered. The convergence conditions of the iteration process on linear and nonlinear condition are discussed. Based on the convergence condition of iteration, the optimized control method for the iteration coefficient calculated by the vector norm is proposed. The method is modified and simplified to suit the real application.  
In order to verify the correctness of the iterative process analysis and the applicability of the two control strategies, a light motorcycle is used as the device under test. Using the electro-hydraulic servo road simulation vibration bench as the experimental equipment, the iteration experiment is carried out. In order to compare the advantages and disadvantages of the strategies, three manual strategies are set up according to the engineering experience for the experiment. The manual strategies are rise-up, constant and RMS-based. The experimental results show that the analysis of the iterative process is practical and the control strategy serves the purpose of optimizing the iterative and convergent control.  
The two control strategies proposed in this paper have different focuses. Method 1 focuses on convergence precision and iterative stability, while method 2 focuses on convergence speed. However, both control strategies are better than manual ones.  
Compared with traditional manual methods determined by experienced engineer, the RPC iteration process with the optimized methods will converge faster and be more stable with less human involvement.  
For a linear system and an ideal environment without interference, its TF does not change, and it naturally meets the iterative convergence condition of the linear system discussed in Section 2.2. Therefore, a good iterative process can be completed without the participation of the iteration coefficient. Since iterative parameters are not required, there is no need for iterative parameter calculation algorithm.  
However, interference is inevitable for the actual test environment. And in modern vehicles, chassis, suspension, and tires are almost always nonlinear systems. Even if the system is still linear or nearly linear, it may not meet the convergence condition, so the iteration coefficient is needed to control the size of driving correction, so that the iteration process will not diverge. For traditional RPC, iteration coefficient is totally dependent on engineering experience and manual adjustment, which not only consumes a lot of time and human cost, but also may lead to unsatisfactory final results. Therefore, this paper proposes to discuss the convergence condition with the theoretical iterative process of the nonlinear system and calculate the iteration coefficient according to the convergence condition so as to achieve better and more cost-effective iteration effects than that of a traditional RPC.  
We believe that the modification of traditional RPC based on the RPC iteration process of nonlinear system in this paper is original. And with the comparison experiment verification, it is confirmed that the improvement is valid, moreover has certain value to the practical application.  
In this paper, the non-convergence problem of RPC iterative process is partially solved. For nonlinear systems, an iterative coefficient optimization method based on TF estimation is proposed according to the iterative convergence condition, which can make the iterative process meet the convergence condition and ensure the realization of convergence. At the same time, compared with the traditional manual parameter method, it has certain advantages. The reason for the iterative non-convergence of RPC is not only the nonlinear characteristics of the system, but also the external interference. Only the former is discussed in this paper. The influence of external interference on iterative convergence is not discussed in this paper due to the limitation of the research progress and paper length.