FULL CAR ACTIVE DAMPING SYSTEM FOR VIBRATION CONTROL

Http://www.ijetmr.com©International Journal of Engineering Technologies and Management Research [1] FULL CAR ACTIVE DAMPING SYSTEM FOR VIBRATION CONTROL G. Yakubu , G. Sani , S. B. Abdulkadir , A. A. Jimoh , M. Francis 3 1 PG Student, Department of Mechatronics and Systems Engineering, Abubakar Tafawa Balewa University, Bauchi, Bauchi State, Nigeria. 2 Department of Electrical Engineering Technology, Abubakar Tatari Ali Polytechnic Bauchi, Bauchi State, Nigeria. 3 PG Student (PhD) Department of Mechanical Engineering, University of Maiduguri, Borno State, Nigeria Abstract: Full car passive and active damping system mathematical model was developed. Computer simulation using MATLAB was performed and analyzed. Two different road profile were used to check the performance of the passive and active damping using Linear Quadratic Regulator controller (LQR)Road profile 1 has three bumps with amplitude of 0.05m, 0.025 m and 0.05 m. Road profile 2 has a bump with amplitude of 0.05 m and a hole of -0.025 m. For all the road profiles, there were 100% amplitude reduction in Wheel displacement, Wheel deflection, Suspension travel and body displacement, and 97.5% amplitude reduction in body acceleration for active damping with LQR controller as compared to the road profile and 54.0% amplitude reduction in body acceleration as compared to the passive damping system. For the two road profiles, the settling time for all the observed parameters was less than two (2) seconds. The present work gave faster settling time for mass displacement, body acceleration and wheel displacement.


Introduction
Effective control vibration usually requires several techniques, each of which contributes to a quieter environment [1]. For most applications, vibration can be controlled using four methods, namely Absorption, Use of barriers and enclosures, Structural damping and Vibration isolation/suspension [1].Although there is a certain degree of overlap in these classes, each method may yield a significant reduction in vibration and noise by proper analysis of the problem and application of the technique. The principles behind the use of absorption materials and heavy mass barrier layers are generally understood, so this thesis will focus on active damping/suspension, which deal with reducing vehicle vibration.
The implementation of control systems can improve a vehicle performance by reducing the vibration levels to acceptable values, defined for each case [2]. This can be achieved by several control devices that can be used to apply forces to the vehicle, calculated by a specific control algorithm.
[3] Defines vibration as a repetitive motion of an object in alternatively opposite direction from the equilibrium position when that equilibrium has been disturbed, which occurs in machines, structures, and dynamic systems leading to unwanted consequences.
[3] describes vibration as a problem due to unwanted motion, noise and stresses that may lead to failure and /or fatigue of a machines or structures, losses in energy, reliability decreased and low performance below expectation.
According to [4] there are three types of damping system namely, passive damping, semi-active damping and active damping system. 'Active damping control' is realized by regarding the piezos as either sensors or actuators, to be used within a control loop, Contrary to passive vibration control. For active vibration control, two situations are often distinguished: collocation and non-collocation.

Vehicle Model Review
A Quarter-car model ( Figure 1) is usually used for the analysis of suspension, because of it simplicity and can take the significant features of the full car model [5] & [6].According to [7] the equation for the model motions are found by adding upwafd and downward (vertical) forces on the car body (sprung mass) and the wheel and axle (unsprung mass).According to [7] the car body or sprung mass is represented by M1 while the tyre and axle or unsprung mass is represented byM2, what make up the damping system are the spring, damper, and a force-generating element that is variable and is positioned between the car body and the tyre and axle. Generally, the roll and pitch angle can be obtained from the connection between the car body and the wheel and axle masses. From [7], the quarter car and full car model are the same, just that there is other additional consideration that most b added when dealing with full car. These are; Rolling, Pitching and Bouncing which are represented in the X, Y and Z axis respectively.  [8] and [9] shows the quarter, half and full car model respectively.

Bouncing; Sprung Mass
For each side of Wheel Motion (Vertical Direction)  [6] The state variables of the system are shown in Table 1 and the definition of each state variables are given in Table 2.
Followed by, covert equation into the matrix yield Where,

Mathematical Modeling; Active Damping
Mathematical modeling of active damping is derived from Figure 4. [7] The equations of motion for full car model can be derived as follows.  [8] equation (9) ~ equation (15) shows the equation of rolling, pitching and bouncing motion of the sprung mass and wheel motion.

Rolling Motion; Sprung Mass
Pitching motion; Sprung Mass Bouncing; Sprung Mass For each side of Wheel Motion (Vertical Direction) Equations (9) ~equations (15) can be written instate space form as below  ]

Linear Quadratic Regulator (LQR) Controller Design
The LQR control approaches in controlling a linear active damping system was presented by [16].
[7] concluded that the LQR control approach will give a better performance in terms of ride comfort.
This study considered the following state variable feedback regulator.
Where is the state feedback gain matrix.
Optimization of control system consists of determining the control input , which minimizes the performance index (J), which represents the performance characteristics requirement as well as controller input limitations [16]. The performance index Where = actuator force (N) and are positive definite weighting matrices [17].
Linear optimal control theory provides the solution of equation (18)  Then the feedback regulator is given by

Result Analysis
The computer simulation work based on equation (1) ~ (16) has been performed. Comparison between passive and active suspension for full car model was observed. For the LQR controller, the weighing matrix Q and weighing matrix R are set to obtain suitable feedback gain k.

Discussion of Result
The control force generated by the actuator for road profiles 1 and 2 are shown in Figure 5, and Figure 14. The body displacement which represents the ride quality for both Passive and Active damping with LQR have very low amplitude with very fast settling time for road profiles 1 and 2 as can be seen in Figure 6 and Figure 12. The Suspension Travel for the two road profiles ( Figure  10 and Figure 16), the active damping system shows very lower amplitude and very fast settling time. Wheel Displacement with road profiles 1 and 2 ( Figure 9 and Figure 14), also shows a balance in the amplitude, that is, no amplitude rises. The wheel displacement represents the car handling performance. For the Body Acceleration, for active damping, there is amplitude that makes few oscillations (Figure 7 and Figure 13) but, it settles faster with a settling time of less than 2 seconds. While that of the passive damping generates a continuous harmonic. Therefore, more modification is required on the passive damping system in regard to Body Acceleration. The Body Displacement which represents the ride quality shows a balance using active damping with LQR controller for the three road profiles. The Active damping with LQR controller gives lower amplitude and fast settling time for all the parameters compared to passive damping system. The output performance is the same because each pairs of wheel set have the same output performance due to the mathematical modeling; this shows that there is relationship between these wheels that is, front wheel right and left and rear wheel right and left receives same types of disturbance.
The table below shows the amplitude reduction in all parameters by passive and active damping as compared to the road profile with amplitude of 0.05m. The amplitude reduction for the active is given by: peak value of passive − peak value of active peak value of passive X 100 for all parameters.

Conclusion
Mathematical model for Passive and Active damping system for a full car were derived and validated. Simulation of the Passive and Active damping system with LQR controller was performed and comparison were made between the Passive and Active damping system. The Active damping with LQR gives lower amplitude and faster settling time of less than 2 seconds as compared to the Passive damping and other controllers (e.g. PID) that have been used in Active damping system.