International Journal of Automotive Engineering Vol. 7, Number 4, Dec 2017 Optimum sliding mode controller design based on skyhook model for nonlinear vehicle vibration model M. Salehpour, A. Jamali*, A. Bagheri, N. Nariman-zadeh Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran. P.O. Box: 3756, ali.jamali@guilan.ac.ir Abstract In this paper a new type of multi-objective differential evolution employing dynamically tunable mutation factor is used to optimally design non-linear vehicle model. In this way, non-dominated sorting algorithm with crowding distance criterion are combined to fuziified mutation differential evolution to construct multi-objective algorithm to solve the problem. In order to achieve fuzzified mutation factor, two inputs as generation number and population diversity and one output as the mutation factor are used in the fuzzy inference system. The objective functions optimized simultaneously are namely, vertical acceleration of sprung mass, relative displacement between sprung mass and unsprung mass and control force. Optimization processes have been done in two bi- and three objective areas. Comparison of the obtained results with those in the literature has shown the superiority of the proposed method of this work. Further, it has been shown that the results of 3-objective optimization include those of bi-objective one, and therefore it gives more optimum options to the designer. Keywords: non-linear vehicle model, Pareto, Multi-objective optimization, Differential evolution, Fuzzified mutation 1. Introduction Suspension system in a typical vehicle is a significant part which affects ride comfort and road holding capability considerably [1]. Generally speaking, there are three types of suspension systems which are namely, passive, semi-active and active [1- 3]. Passive suspension is composed of parallel installation of spring and damper between the vehicle body (sprung mass) and wheel-axle assembly (unsprung mass) [2-3]. Active suspension needs an external power source which supplies control force to improve the passive components [3-4]. Semi-active one is in-between the two aforementioned suspensions. This kind of suspension dissipates low level of energy [3] and with its varying damping properties can achieve a better performance than passive one [2]. Active suspensions offer appreciable behavior under different road excitations in comparison with passive and semi-active ones [2, 4]. Therefore several control approaches have been proposed by the researchers in the field of the design of the active suspension such as, optimal control [5], preview control [6], robust control [7-8], neural networks [9], back-stepping control [2], fuzzy control [10-11] and so forth. Model reference is used to have a real suspension plant go along it [12]. For this purpose, skyhook model has been employed by some authors [13-15] as a theoretical reference model. Sliding mode control is a useful method to design systems which are robust to external disturbances or parameters uncertainties. It can provide invariability if the bounds of variations are clear and the sliding condition is fulfilled [16]. By choosing a proper sliding surface the appropriate dynamic performance of the system can be achieved [12]. Kim and Ro [17] proposed a method based on the combination of sliding mode control and skyhook model to design active suspensions considering non-linearites. It should be noted that finding an exact model of a real suspension plant and acceptable estimation of road irregularities are complicated tasks. On the other hand, in the sliding mode control design, the system with uncertainties and disturbances can be stabilized if the bounds of them are plain. Since, road irregularities may change considerably, achieving such bounds seems a difficult task. In order to overcome this shortage, in [12] inertial delay control method has been used to estimate the non-linearities [ DOI: 10.22068/ijae.7.4.2537 ] [ Downloaded from www.iust.ac.ir on 2023-05-04 ] 1 / 14