Adaptive Cruise Control System Design

The assignment focuses on designing an adaptive cruise control (ACC) system employing a fuzzy logic controller. It outlines how the system utilizes radar sensors to detect vehicles ahead, calculate safe distances based on vehicle velocity and driver-set parameters, and maintain a desired separation distance. The assignment delves into the equations of motion for the system, explores free and forced vibration responses, and examines critical damping. Additionally, it analyzes potential disadvantages of the ACC system and suggests areas for improvement.

DEMONSTRATION PROBLEMS
i) For free vibration
After the first vibration, the system meets its own disturbance, that vibration is called as free
vibration. The free vibrations are represented by homogeneous Ordinary Differential Equations.
The Types of free vibration of single degree of freedom systems
1. harmonic motion,
2. Free vibration of undamped SDOF systems,
3. Free vibration of damped SDOF systems
ii) For forced vibration
If any external force is applied to the system, the reaction of the system is called as forced
vibration. The frequency of the system is matched with external force frequency, it leads to
heavy oscillation because of the occurred resonance. The forced vibrations are represented by
Non homogeneous Ordinary Differential Equations.
Types of forced vibration of single degree of freedom systems
1. Harmonic excitation
2. Base excitation

iii) This figure shows the response of car due to the road roughness and road defects. Due to
the road roughness, the car dynamics, drainage, ride quality and dynamic loads is affected.
The nonlinear motion of the object is getting time delayed and the harmonics are
dampering from the domain so the vibration control is under progress to develop the
stablilization in the system. The developing protocol in the dampering circuit creates
additional damping in the oscillations developed
IV) Include in your Simulink model suitable non-linearity’s, discuss and show how or if
these will affect the previous analysis. You may have to generate some extreme road defects
to show the operation of the non-linear properties.

This is the single degree of freedom simulation model. The Simulink is used to provide the
simulation model.it provides more response factor. The input of model is mass. It is used to
perform the summation operations. By using the Integrator, the expression is decoded and the
output is controlled.
Result:
This is the implemented single degree of freedom response. This done by Matlab. The input for
response is mass value and sine wave. The output shows the amplitude and bias range.

The development of the system enhances the domain in the single degree of freedom
response and this MATLAB is enhanced with the development of the idea in the tenangrad
of the sinusoidal output where the region of the stabilization takes place
v) Damping helps to isolating vibration and reduces transmitted vibration. Based on your
analysis write a paragraph on the effect of damping in affecting your car’s performance i.e.
Where would be better to use high damping; Where would it be better to use low damping;
and how does the damping levels you have chosen in your car affect passenger comfort and
the wheel road contact force.
Damping is major features of noise proofing an existing or fresh wall structure.
Damping is used to decreasing or avoiding kept energy shaped by sound. If a structure has
low damping, sound vibration can travel across it for great distances. The tires have the
automobile characteristics of handling and ride. It has the reaction point of vehicle at the
roadway. It has ability to manage the problem at the road. Because it is the final link from the
driver. The springs, linkages and dampers are used to manage the tires basic functions. The
damping is used to control the spring effect in the vehicle (vibration).Damping is used to
compare engineering material for the applications. High damping is used in vibration control,
reducing increased heat, and shock absorption and noise control. Low damping is used for
increasing sensitivity in sensors and definite accuracy instrumentation.
In the increasing sensitivity of the the module due to heat and other mass related transfer
functions the newton’d Raphson model is included and the research have been developed
to control the shock absorption and other damping oscillations of the accuracy
transmissions.

i)Two equation of motion is
m1 ´x1 +(c1 +c2 ) ´x1−c2 ´x2 +(k1 +k2 ) x1−k2 x2=F1
m2 ´x2 +(c1+ c2 ) ´x2−c2 ´x1+(k2 +k 3) x2 −k2 x1=F2
ii)Equation of motion in matrix form
[m] ´
x
→
(t)+[c] ´
x
→
(t)+[k ] x
→
(t)=F
→
(t )
Here,
[m]is the mass matrix
[c ]is the damping matrix
[k ]is the stiffness matrix
X ( t)is the displacement vector
F (t)is the force vector
[m]=[m1 0
0 m2
] [c ]=[c1 +c2 −c2
−c2 c1 +c2
] [k ]=[k1 +k2 −k2
−k2 k2 +k3
]
iii) To finding the Natural frequecies and mode shaping using the eigen values and eigrn vectors
in matlab is shown in below code.
Matlab code:

Results

iv) The natural frequencies and mode shape of 2DOF from the matlab output, the two degree
of freedom system has two normal modes of vibration corresponding to the two natural
frequencies.
v) The vibration solution for 2DOF in road surface
Matlab code

Result

vi) In 2DOF modelling the natural frequencies and mode shapes are analysed.The multiple
degree of freedom will be investigated by using this 2DOF modelling in future analysis.

Simulation of PID controller for m=100,c=1000,k=5000
Result

Simulation of PID controller for m=5,c=2,k=1
Result:

a) The Simulink model in PID controller is done by using the value of M=5, damper=2 and k=3.
The results gives the rise time faster and overshoot is less. By using the value of m=100kg
k=5000 and c=1000 means then it gives the maximum overshoot problem.
b) In PID controller the parameter values are assumed in matlab/Simulink. The proportional (P)
value is assumed as 1 and integral (I) value is assumed as 1 and derivative (D) value is assumed
as 0.
c) The value for PID is (p=0, I=0, D=0) is applied in the simulink.in these assumed value, PID is
failed to produce the desired movement.
d) Two forces are derived from the hydraulic dram. The hydraulic friction force (Ff) and
hydraulic actuating force (Fa) are the two forces. The hydraulic actuating force is a control input
nonlinear function. The desired damper force is determined from suspension system. The damper
force on the PID controller is used to tune the PSO technique. The spring is required to balance
the applied force for ending the system at equilibrium stage.
e) The stability performance in PID controller is unstable. Here the excess gain value is
used .Instability is caused by the excess gain.by using the value of m=5 then we get the more
stability performance in the output of the system
f) Simulation of PID controller by increasing mass 200kg
Simulation of PID controller for m=200,c=1000,k=5000

Result
b) Demonstrate the operation of the brake control
Introducing a brake controller is a genuinely simple undertaking. The initial step includes
essentially mounting the brake controller in a range that is anything but difficult to get to. The

vast majority put it under the dashboard and straightforwardly over the correct leg; this keeps the
brake controller in see, where we can screen any potential issues.
Brake controllers normally accompany a four-wire design, which can be captured to the
stopping mechanism's wiring. The four separate associations are:
Battery power – It deliveries power to the brake controller.
Ground – It attaches the brake controller to a negative and grounded source
Brake switch – It is the wire that transfers power after the brake pedal is pressed.
Trailer feed – This deliveries brake power to the trailer connector
c) Provide a measure of the stability of the cruise control system
Cruise control is a shrewd type of journey control that backs off and accelerates
consequently to keep pace with the auto before you. The driver sets the most extreme speed —
similarly as with journey control — then a radar sensor looks for activity ahead, locks on to the
auto in a path, and teaches the auto to stay 2, 3, or 4 seconds behind the individual auto in front
of it (the driver sets the take after separation, inside reason). It is currently quite often matched
with a pre-crash framework that cautions you and regularly starts braking.
The information factors of the fuzzy controller are the deviation of the theoretical safe
distance Sa and relative distance Sr and the relative velocity between the previous target vehicle
velocity Vp and the cruise vehicle velocity Vh, where the theoretical safety distance can be
acquired by the accompanying articulation considering the response time of the drivers tf, the
response time of brake system tx, the braking force increasing ts, the deceleration of the cruise
vehicle ah and the stopping separation do, Sa= Vh.( tf+ ts/2+ tx)+( Vh2/2 ah + do). Here, the
theoretical safe distance is generally secure on the grounds that the former vehicle is stationary
for presumptions. The relative distance can be measured by Lidar. The deviation of the
separation RD is computed from the distinction of the theoretical safety distance and the actual
measured distance, that is, RD= Sa- Sr
The following algorithm provides the stability of the cruise controller

d) Comment on the disadvantages of your controller and possible improvements or
investigations
1. Drivers will not apply constant pressure on the pedal when the cruise control is activated,
this leads to accidents.
2. Cruise control when conveyed will endeavor to keep the auto at a consistent speed set by
the driver. On the off chance that the vehicle speed has been set to a specific speed, the auto will
naturally enter a corner at that speed. On the off chance that this is an improper speed for the
corner the resulting braking to lessen speed will, while cornering, influence the adjust of the
vehicle which may thusly prompt precariousness in the vehicle.

3. This will influence the vehicle taking care of and if not effectively adjusted for by the
driver, can, in a most pessimistic scenario, result in lost control of the vehicle.
4. Wet streets altogether influence the hold of the tire and this thusly can make remedial
activities by the driver considerably harder to judge.
5. The absence of need to keep up steady pedal weight can expand the danger of vehicle
mischances caused by 'interstate spellbinding'.
6. The driver will most likely be unable to react as quickly and adequately to a crisis
circumstance.

Determine the equation of motion for the system*, calculate the free vibration Response, forced
vibration, critical damping* and Magnification Factor*. *Express in terms of J, m 1, m2, k1, K2,
c1, c2 and L. State and explain any assumptions you make.
Equation of motion for rotating system
Free body diagram at θ1
τ a+J 1 α1+ Br 1 (ω1 −ω2 )+ Kr θ1=0
J1 ´θ1+ Br 1 ´θ1 + Kr θ1−Br 1 ´θ2=−τ a
Free body diagram at θ2
J2 α2 + Br 1 ω2 −Br 1 (ω1−ω2 )=0
J2 ´θ1+(Br 2−Br 1) ´θ2−Br 1 ´θ1=0
The equation of motion for the system in terms of m, k, and c becomes
In dynamic system model the free vibration and forced vibration are the main reply of creating
the system.
For critical damping
Critical damping constant is denoted as

Critical damping ratio is defined as
Then,
The general equation of critical damping,