**1. Introduction**

112 Fuzzy Inference System – Theory and Applications

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Conventional car suspensions systems are usually passive, i.e have limitation in suspension control due to their fixed damping force. Semi-active suspension system which is a modification of active and passive suspension system has been found to be more reliable and robust but yet easier and cheaper than the active suspension system.

#### **1.1 Vehicle primary suspensions**

*Primary suspension* is the term used for suspension components connecting the wheel assemblies of a vehicle to the frame of the vehicle (Fig.1). This is in contrast to the suspension components connecting the frame and body of the vehicle, or those components located directly at the vehicle's seat, commonly called the secondary suspension. Usually a vehicle contains both primary and secondary suspension system but primary suspension is chosen for control. There are two basic types of elements in conventional suspension systems. These elements are springs and dampers. The role of the spring in a vehicle's suspension system is to support the static weight of the vehicle. The role of the damper is to dissipate vibrational energy and control the input from the road that is transmitted to the vehicle. Primary suspensions are divided into passive, active and semi active systems [Miller 1990], as will be discussed next, within the context of this study.

Fig. 1. Primary suspension system

Fuzzy Logic Controller for Mechatronics and Automation 115

In Fig 3, the model for one-quarter of a car is represented. The mass of this portion of the vehicle body (sprung mass) and one tire (unsprung mass) is defined respectively by *m*1 and *m*2 , with their corresponding displacements defined by *Y* and *X*. The suspension spring, <sup>1</sup> *k* , and damper, 1 *b* , are attached between the vehicle body and tire, and the stiffness of the tire is represented by 2 *k* . The relative velocity across the suspension damper of this model

Before modeling an automatic suspension system, a quarter car model (i.e. model for one of the four wheels) is used to simplify the problem to a one-dimensional (only vertical displacement of the car is considered) spring-damper system. The reason for choosing the quarter car model is to analyze and control the suspension for each wheel separately and

Body mass (*m1*)

Unsprung mass (*m2*)

accurately. The schematic diagram of a quarter car system is shown in Figure 4

*k1*

*rel v y x* (1)

Actuator with force MV

Parameters Amount

*b1*

is defined by

**1.5 Modeling of quarter car model** 

*y* 

*x* 

*w* 

Fig. 4. Modeling of quarter-car suspension system

Table 1. Parameters of the active suspension system

The parameters used for the system are shown in Table 1.

*m1* (Body Mass or sprung mass) 315 kg *m2* (Suspension Mass or unsprung mass) 45 kg *k2* (Tyre Stiffness) 190000N/m *k1* (Suspension spring constant) 40000N/m *b1* (Damping Constant of Suspension) 290N/m

*k2*

### **1.2 Passive damping**

A passive suspension system is one in which the characteristics of the components (springs and dampers) are fixed. A passive control system does not require an external power source. Passive control devices impart forces that are developed in response to the motion of the wheel hop.
