* Corresponding author 142 An International Journal of Optimization and Control: Theories & Applications ISSN: 2146-0957eISSN: 2146-5703 Vol.7, No.2, pp.142-148 (2017) https://doi.org/10.11121/ijocta.01.2017.00458 RESEARCH ARTICLE The road disturbance attenuation for quarter car active suspension system via a new static two-degree-of-freedom design Yusuf Altun * Department of Computer Engineering, Faculty of Engineerig, Duzce University, Turkey yusufaltun@duzce.edu.tr ARTICLE INFO ABSTRACT Article history: Received: 15 February 2017 Accepted: 13 April 2017 Available Online: 13 June 2017 The main aim of this paper is to attenuate the effects of the road disturbance on the quarter-car active suspension system (ASS) for the passenger comfort by using design. Therefore, a new static disturbance compensator is proposed by using linear matrix inequality method such that the disturbance compensator and feedback controller are simultaneously designed for the disturbances in the linear time-invariant systems, which are measurable or predictable. They have static structure, and the disturbance compensator is designed on the feedforward path. The design is applied against the road disturbance affecting the quarter car ASS. The effectiveness of the design is demonstrated with the simulations. Keywords: Active suspension Quarter car The road disturbance rejection feedforward compensation AMS Classification 2010: 37N35, 49N05, 70Q05 1. Introduction Feedforward compensator designs are used for the disturbance rejection or the reference-tracking problem where the external disturbances are measurable or predictable since the designed feedforward element produces an additional control signal according to the measured disturbance values. The disturbance compensator or controller designs to attenuate disturbances are applied to the many chemical and process systems [1-5]. For instance, in [5], a general structure is presented for single-input-single output (SISO) process system. The disturbance compensator/controller designs are used together with a feedback controller [2,3,6-8]. This is why, the feedback controller provides the stability of the system and the disturbance compensator/controller does not affect the stability. In these designs, there are two approaches. The first one: both of these are simultaneously designed as in [1]. The second one: previously the feedback controller is obtained, and then the disturbance compensator/controller is obtained as in [9,10]. In the literature, feedforward designs are proposed by using different approaches for the linear time invariant systems. In view of literature, there are a few studies based on H∞ approach. The forefront ones among the studies are as in [3,9-12]. In [3], H∞ dynamic feedforward design is tackled with obtaining the system inverse. In [9], a dynamic controller is obtained for linear parameter varying (LPV) systems. In [10], a static feedforward controller is proposed for LPV systems while there is a feedback controller. In [11], a reduced order H∞ controller is designed against the disturbances for active vibration system. In [12], the feedforward designs are obtained with mixed- sensitivity based on inverse of system. A vehicle suspension system comprises of the springs, damper and linkages that link its wheels to a vehicle. Its essential role is to reduce the vertical acceleration conveyed to the vehicle body. Because, this affects the passenger comfort. The vehicle suspension is generally designed to satisfy three requirements, which are road handling, passenger comfort and load carrying. The suspension system must provide the road handling, load carrying and the passenger comfort, which is provided by an efficient isolation of passengers from the road disturbances. The parameters of a passive suspension consisting of springs and dampers are mostly constant, which are chosen to achieve a specific performance level by considering the road handling, ride comfort and load carrying. Therefore, especially the performances are unchangeable during driving. As for an ASS, it can affect the performances of the road handling and ride comfort by introducing energy by adding an actuator to the system. In view of many road