CRUISE CONTROL
CRUISE CONTROL SIMULATION USING MATLAB
DR. AKEEL.A.LAMI
HAIDAR ALKRAR SLMAN
CRUISE CONTROL
• Cruise control (speed control, auto-cruise
or tempomat) is a system that automatically
controls the speed of a motor vehicle. The system
takes over the throttle of the car to maintain a
steady speed as set by the driver.
SYSTEM MODELLING
•
O feedback control system
O purpose is to maintain a constant vehicle
speed despite external disturbances, such
as changes in wind or road grade.
•
O accomplished by
i. measuring the vehicle speed
ii. comparing it to the desired or reference speed
iii. automatically adjusting the throttle according
to a control law
PHYSICAL SETUP: FBD
u = force generated at the road/tire interface
we will assume that:
i. u can be controlled directly
ii. the dynamics of the powertrain, tires, etc are 0
iii. bv, due to rolling resistance and wind drag varies linearly
with the vehicle velocity, v, and act in the direction opposite the
vehicle's motion
• Mass m
• Control force u
• Resistive forces bv
• Vehicle velocity v
FIRST ORDER EQUATION
• We are considering a first order mass-damper
system.
Summing forces in the x-direction and applying
Newton's 2nd law, we arrive at the following
system equation:
m(dv/dt)+bv=u
Since v is the required output:
y=v
TRANSFER FUNCTION
• Taking the Laplace transform and assuming
zero initial conditions, we find the transfer
function of the cruise control system to be:
P(s) = V(s)/U(s)
= 1/(ms+b)
PID CONTROL
PARAMETERS
O m vehicle mass 1000 kg
O b damping coefficient 50 N.s/m
O r reference speed 10 m/s
O Rise time < 5 s
O Overshoot < 10%
O Steady-state error < 2%
BLOCK DIAGRAM
Unity gain feedback controller
C(s) = Kp + Ki/s + Kd.s
PROPORTIONAL CONTROL
O The root-locus plot shows the locations of
all possible closed-loop poles when a single
gain is varied from zero to infinity.
O Only a proportional controller Kp will be
considered to solve this problem. The
closed-loop transfer function becomes:
Y(s)/R(s)=Kp/(ms+ (b + Kp))
PROPORTIONAL CONTROL
O MATLAB command sgrid
O Used to display an acceptable region of the
root-locus plot
O Damping ratio (zeta) and the natural
frequency (Wn) need to be determined
PROPORTIONAL CONTROL
PROPORTIONAL CONTROL
O We can then find a gain to place the closedloop poles in the desired region by
employing the rlocfind command
O specific loop gain
[Kp,poles]=rlocfind(P_cruise)
O In between the dotted lines (zeta > 0.6) and
outside the semi-ellipse (wn > 0.36)
LAG CONTROLLER
O With the gain Kp being the only functional
gain and Ki and Kd being zero, the rise time
and the overshoot criteria have been met
O A steady-state error of more than 10%
remains
O To reduce the steady-state error, a lag
controller is added to the system
LAG CONTROLLER
O To reduce the steady-state error, a lag
controller will be added to the system.
O A pole and a zero, not too distant spacingwise are introduced i.e:
LAG CONTROLLER
O With the gain Kp being the only functional
gain and Ki and Kd being zero, the rise time
and the overshoot criteria have been met
O A steady-state error of more than 10%
remains
O To reduce the steady-state error, a lag
controller is added to the system
O the steady-state error will be reduced by a
factor of zo/po
LAG CONTROLLER
• With the gain Kp excluded for the moment, the
transfer function of PID becomes:
•
Adding Kp to the equation, the transfer function of
PID becomes:
LEAD CONTROLLER
• The lead controller is basically added to
improve the transient response of the
system i.e. Ts and Tp mainly
• Not used here as it is not needed and the
desired parameters are already being
achieved
THANK YOU