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Executive summary

The report will help in simulating a quarter focused suspension principle. Passive as well as active suspensions were launched and tested. Instances suspension can be further simulated with the use of theory and computer methodologies. The suspension can be constructed as per the people data given and offered on diverse road documentation (Cvok et al., 2019). The outcomes of two methodology showcasing a closer contract. Potential changes have been discussed in detail along with a design advice given.

Sprung mass along with un-sprung mass

In an automobile that comes with suspension, similar to vehicle, tank, sprung focused mass is the part of the automobile’s complete mass that is helped focused on suspension. Such sprung focused weight normally consists the frame, the internal elements, people along with cargo however never consist of the mass of elements when suspended as part of suspended elements (Fauzi et al., 2018).

Quarter car focused model

This kind of quarter car model is simple as part of body of car along with suspension structure within the boundaries of every kind of wheel.

The system of suspension of automobile developed with characteristics normally shown as a passive form of suspension structure because there is no control form of eth structure.



The report discussed the active form of suspension principle is developed with yet PID control unit. The principle was designed while utilising MATLAB Simulink focused software as well as with the assignment of tutorials (Hamrouni et al., 2019).

Table. 1 Typical suspension parameters

Parameter  Value 
Ms [kg] 300 
Mu [kg] 50 
ks [N/m] 18000 
kt [N/m] 180000 
bs [Ns/m] 1200 
bt [Ns/m]

Analytical principle

Sprung focused mass

During the start of free body figure of sprung along with unsprung focused mass was decided with all reaction focused forces since it comes with spring forces (Ghasemalizadeh et al., 2017).




Free vibration

In order to achieve passive form of suspension with force implemented thus the EOM here managed to achieve simple mode. In the form of free vibration is under discussion, there are many undamped structures that are evaluated to find natural kind of frequencies (Hemanth et al., 2017).


The elements of number of matrices are measured here and discussed as part of equation thirteen is known as feature focused equation.



The calculation discussed above provide the solutions that are taken and discussed in following form of formulas.



Forced form of vibration

The transformation as part of road document x can be discussed in the form of harmonic exciting as per the equation 29 as well as answer focused on xs and xu in the form harmony activity as exhibited above (Ma et al., 2019). The standards of the quarter car model utilised same to achieve free vibration.



Tab. 2 Mass displacement with and without actuator force

Fa = 0 N Fa = 1500 N
ωt = π ωt = 2π ωt = π ωt = 2π
Xs 0.2369 m -0.1350 m 0.1520 m -0.0502 m
Xu 0.0695 m 0.0307 m 0.0693 m 0.0308 m

MATLAB simulation

This concept was developed model to achieve passive form of suspension that was changed for designing of active form of suspension (Qin et al., 2018). To achieve ideal form of lucidity in the form of subsystem was developed where form of EOM can be performed as discussed.


MATLAB code:

Free vibration 

ms = 300;

ks = 18000;

bs = 1200;

mu = 50;

ku = 180000;

bu = 0;

b = -ks/ms -ks/mu – ku/mu;

c = (ks*ku)/(ms*mu);

D = b^2 -4*c;

sqrtD = D^(1/2);

s1 = (-b+sqrtD)/(2);

s2 = (-b-sqrtD)/(2);

w1 = (s2)^(1/2);

w2 = (s1)^(1/2);

r1 = (ks-ms*(w1)^2)/ks;

r2 = (ks-ms*(w2)^2)/ks;

t = 0:0.001:2;

Xs = 1;

xs = Xs*cos(w1*t);

xu = r1*Xs*cos(w1*t);



title(‘w1 = 7.38 rad/s’)




xs2 = Xs*cos(w2*t);

xu2 = r2*Xs*cos(w2*t);



title(‘w2 = 62.97 rad/s’)





Forced vibration

ms = 300;

ks = 18000;

bs = 1200;

mu = 50;

kt = 180000;

bt = 0;

g = 9.81;

x = pi;     % phase angle (wt)

w = 1;

Xr = 0.05;

syms Xs Xu

Fa = 1500;

eqn1 = -ms*w^2*Xs*cos(x) + bs*w*Xu*sin(x) – bs*w*Xs*sin(x) – ks*Xu*cos(x) + ks*Xs*cos(x) == Fa -ms*g 

eqn2 = -mu*w^2*Xu*cos(x) – bs*w*Xu*sin(x) + bs*w*Xs*sin(x) + ks*Xu*cos(x) – ks*Xs*cos(x) – kt*Xr*cos(x) + kt*Xu*cos(x) == -Fa -mu*g

[A,B] = equationsToMatrix([eqn1, eqn2], [Xs, Xu])

X = linsolve(A,B);

Xs = X(1)

Xu = X(2)




Initially a model that is supported by passive form of suspension can be evaluated on road that comes with similar assumptions discussed above.


The similar condition was implemented for forced vibration that comes with implemented PID focused control and massive actuator kind of force.


The comparison of measured valuation that comes from analytical principle as well as Simulink principle for free form and forced vibration can be made the taken outcome is equal to specific ωt (Qin et al., 2017). The graphs discussed above can be seen with ideal performance can be reached which is not supported by PID control system for sinusoidal road kind.



The damped of the sprung masses along with unsprung that comes with hitting the pothole is clearer from diagrams. Because the spring focused stiffness is less relatively in order to tire focused stiffness and here M is more than M, the sprung here comes mass oscillate for longer period of time (Rathai et al., 2018).



This road documents that comes with systems have same kind of attitude. The one that is supported by PID control system exhibit little less kind of displacement for sprung focused mass (Singh and Aggarwal, 2017).




Utilising the internal data, the outcome exhibits, a less frequency develops high amount of displacement for sprung mass as well as for high level of frequencies with displacement reductions. Thus, a transformation on standards shows in order to improve the performance of suspended structure and decrease the noise.


The report is an active suspension structure was tested by analyses principle as well as MATLAB Simulink model. Free form of vibration evaluation was part of performance where natural form of frequencies along with mode of the structure were taken (Singh and Aggarwal, 2017). The force vibration focused loads that come from road transformation, active suspension structure along with gravitated forces were part of discussion as well as the displacement valuation of masses when part of comparison for both answers.



Cvok, I., Deur, J., Tseng, H.E. and Hrovat, D., 2019, August. Comparative Performance Analysis of Active and Semi-active Suspensions with Road Preview Control. In The IAVSD International Symposium on Dynamics of Vehicles on Roads and Tracks (pp. 1808-1818). Springer, Cham.

Fauzi, M.A.Z.I.M., Yakub, F., Salim, S.A.Z.S., Yahaya, H., Muhamad, P., Rasid, Z.A., Toh, H.T. and Talip, M.S.A., 2018. Enhancing Ride Comfort of Quarter Car Semi-active Suspension System Through State-Feedback Controller. In Proceedings of the Second International Conference on the Future of ASEAN (ICoFA) 2017–Volume 2 (pp. 827-837). Springer, Singapore.

Ghasemalizadeh, O., Taheri, S., Singh, A. and Singh, K.B., 2017, October. Analysis and Enhancement of Hybrid Skyhook-Groundhook Semi-Active Suspension Controller for Optimal Performance. In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers Digital Collection.

Hamrouni, E., Moreau, X., Benine-Neto, A. and Hernette, V., 2019. Skyhook and CRONE active suspensions: A comparative study. IFAC-PapersOnLine52(5), pp.243-248.

Hemanth, K., Kumar, H. and Gangadharan, K.V., 2017. Vertical dynamic analysis of a quarter car suspension system with MR damper. Journal of the Brazilian Society of Mechanical Sciences and Engineering39(1), pp.41-51.

Ma, X., Wong, P.K. and Zhao, J., 2019. Practical multi-objective control for automotive semi-active suspension system with nonlinear hydraulic adjustable damper. Mechanical Systems and Signal Processing117, pp.667-688.

Qin, Y., Xiang, C., Wang, Z. and Dong, M., 2018. Road excitation classification for semi-active suspension system based on system response. Journal of vibration and control24(13), pp.2732-2748.

Qin, Y., Zhao, F., Wang, Z., Gu, L. and Dong, M., 2017. Comprehensive analysis for influence of controllable damper time delay on semi-active suspension control strategies. Journal of Vibration and Acoustics139(3).

Rathai, K.M.M., Sename, O. and Alamir, M., 2018, November. A comparative study of different NMPC schemes for control of semi-active suspension system.

Singh, D. and Aggarwal, M.L., 2017. Passenger seat vibration control of a semi-active quarter car system with hybrid Fuzzy–PID approach. International Journal of Dynamics and Control5(2), pp.287-296.