**2. MR fluid damper analysis**

## **2.1. MR fluid damper**

386 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

moderate complexity and is widely applied in building controls. Once the characteristic parameters of the Bouc-Wen model are determined, the model can obtain the linearity and the smoothness of the transition from the pre-yield to the post-yield region. One of the major problems in the Bouc-Wen model is the accurate determination of its characteristic parameters which is obtained by using optimization or trial error techniques. Consequently, these techniques demand high computational cost to generate the model parameters. Moreover, the fact that each set of constant parameters is valid only for single vibration conditions makes the Bouc-Wen model inappropriate for varying excitation environments. Therefore, many researches on how to develop a MR fluid damper model for higher accuracy and higher adaptability in estimating the behavior of the damper have been done. Spencer *et al* [21] successfully developed a phenomenological model to improve the model accuracy with an additional internal dynamical variable. Choi and Lee [22] designed a hysteresis damper model based on a polynomial and a curve fitting to predict better the damping force when compared with conventional models. Dominguez *et al* [23] proposed a methodology to find out the characteristic parameter of Bouc-Wen model and then designed a new non-linear model to simulate the behavior of the MR fluid dampers. Kwok *et al* designed a hysteretic model based on a particle swarm optimization [24] or using GA technique [25] to modify the Bonc-Wen model and identify the characteristic parameters of the models. The effectiveness of these models with their identification process was proved through the experimental test data. However, the parametric modeling methods require assumptions regarding the structure of the mechanical model that simulates the system's behavior. These approaches could be divergent if the initial assumptions for the model structures are flawed or if the proper constraints are not applied to the parameters [24,25].

Unrealistic parameters such as negative mass or stiffness may be obtained [29].

high precision, the model architectures and the training methods were complex.

Once an accurate model for the MR fluid damper is built, it is very useful to investigate the damper characteristics before applying to suspensions. In addition, the well-done model can effectively function as a virtual sensor to estimate the damping force which is used for closed-loop damping control systems with a self-sensing behavior. Self-sensing describes the technique of using a transducer to both actuate and sense concurrently [30,31]. Compared to typical self-sensing damping control systems using separated or integrated actuators and sensors [32], this technique can offer several advantages. A reduction in the

On the contrary, non-parametric methods could avoid these drawbacks of the parametric approaches for modeling both the linear, nonlinear, and hysteretic systems with high adaptability. For modeling MR fluid dampers, some researches have been done. Chang and Roschke [26] proposed a non-parametric model using multilayer perceptron neural network with optimization method for a satisfactory representation of a damper behavior. Schurter and Roschke [27] investigated the modeling of MR fluid dampers with an adaptive neurofuzzy inference system. The fuzzy structure was simple for modeling; nevertheless, the training model process relied on input and output information on MR fluid dampers and took much computation time. Wang and Liao [28,29] explored the modeling of MR fluid dampers by using a trained direct identification based on recurrent neural network. Although, the designed models could predict the dynamic responses of the dampers with

> For later discussions on modeling and control of MR fluid dampers, a MR fluid damper of the small size damper series, RD-1005-3, manufactured by LORD Corporation was used. The damper RD-1005-3 can be adapted to a wide variety of applications because of its simple design, quiet operation, and compact shock absorption with low voltage and current demands that allow for damping control. Specifications of this damper are displayed in Table 1.

The purpose of this research is to investigate the characteristics of the damper RD-1005-3 which are then used to derive the accurate damper models as well as to design the forcesensorless controller for damping systems using this damper. Therefore, a test rig employing the damper RD-1005-3, named as TR01, is needed for following tasks:


The optimized BBM model as well as the proposed force-sensorless control system based on BBM and IBBM models might be applied not only on this system but also on other damping systems using the same dampers. Consequently, the ability of using these models for modeling and damping control needs to be verified. Therefore, a second damping system, which is named TR02, is indispensable for following purposes:




**Table 1.** Technical data for the MR fluid damper RD-1005-3

Based on the dimensions and characteristics of the damper RD-1005-3 as well as the design purposes, the two testing systems were designed and set up as described below.
