Control Systems of Active Suspension of BikeTerm Project of Control System

NS Abdullah Bin Masood (2009-204)PC Mubashar Sharif (2009-462)

08/01/2014

Abstract

The shock absorber of a bike is a very significant element when we are considering the driver comfort.

Active suspension system is a type of shock absorber in which there is an actuator which gives a

controlled force to our system in order to absorb the shock and to settle the system in a desired/pre-

defined settling time.

In our project we have mathematically modeled the active suspension system of bike taking in account

the jerks and bumps that a bike passes over which are basically the “step Input” to the system and then

a controls system has been designed in order to absorb that shock in a particular time span (settling

time) and have proposed a PD Compensator to serve the purpose.

We have designed the control system for shock absorber of front wheel only, assuming that same will be

the system for rear wheel as well.

When we simulated our system (uncompensated), there was no stead-state error, i.e. zero steady-state

error, in the system response. Therefore, our only job was to control the settling-time of system. So, we

have designed the PD (proportional-differential) Compensator only instead of PID (proportional-integral-

differential) Compensator which is used when you have to minimize the steady-state error along with

the response time.

Actuator:

The actuator considered is hydraulic actuator. The PD compensator designed will control the force input

from actuator and apply it to the system in order to settle the system response in respective settling

time. Transfer function of hydraulic actuator is:

T= 60s+60

We are assuming the shock to be a steep/slope or a bump, the input will be step input. Say, the bump is

of 12 centimeters.

Design Conditions:

Settling time of uncompensated system = 8 seconds

Desired settling time = 2 seconds

% O.S. = 5 %

→ Damping ratio = ᶓ = 0.69

MATLAB Code of Uncompensated System

k1=3500;

c1=350;

k2=4000;

m1=100;

m2=20;

c2=70;

s = tf('s');

W1 = ((m1+m2)*s^2+c2*s+k2)/((m1*s^2+c1*s+k1)*(m2*s^2+(c1+c2)*s+(k1+k2))-

(c1*s+k1)*(c1*s+k1));

W2 = (-m1*c2*s^3-m1*k2*s^2)/((m1*s^2+c1*s+k1)*(m2*s^2+(c1+c2)*s+(k1+k2))-

(c1*s+k1)*(c1*s+k1));

W3=((-m1*c2*s^3-m1*k2*s^2)/((m1+m2)*s^2+c2*s+k2));

W4= 0.12 * W3;

W5= 60/(s+60);

W6=W4+W5;

total= W6* W1;

T1=-0.42 *(s+61.83) *(s+55.31) *(s+0.2897) *(s-0.2883);

T2=(s+60)*(s^2 + 1.026*s + 18.43)*(s^2 + 23.47*s + 379.7);

T=T1/T2;

Time Response of UNCOMPNESATED System:

Root Locus of UNCOMPNESATED System:

Root Locus of UNCOMPNESATED System with damping lines and gain point:

MATLAB Code of Compensated System

k1=3500;

c1=350;

k2=4000;

m1=100;

m2=20;

c2=70;

s = tf('s');

W1 = ((m1+m2)*s^2+c2*s+k2)/((m1*s^2+c1*s+k1)*(m2*s^2+(c1+c2)*s+(k1+k2))-

(c1*s+k1)*(c1*s+k1));

W2 = (-m1*c2*s^3-m1*k2*s^2)/((m1*s^2+c1*s+k1)*(m2*s^2+(c1+c2)*s+(k1+k2))-

(c1*s+k1)*(c1*s+k1));

W3=((-m1*c2*s^3-m1*k2*s^2)/((m1+m2)*s^2+c2*s+k2));

W4= 0.12 * W3;

W5= 60/(s+60);

W6=W4+W5;

total= W6* W1;

T1=-0.42*15.2*(s+61.83) *(s+55.31) *(s+0.2897) *(s-0.2883)*(s+2.44);

T2=(s+60)*(s^2 + 1.026*s + 18.43)*(s^2 + 23.47*s + 379.7);

T=T1/T2;

Time Response of COMPNESATED System :

Root Locus of COMPNESATED System :

Time Response of COMPNESATED System :

Conclusion:

Our expected settling time was 2 seconds from 8 seconds. Whereas, due to some error the settling time has not reduced to exact 2 seconds but to approx. 5 seconds.