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# Cruise control simulation using matlab

http://ctms.engin.umich.edu/CTMS/index.php?example=CruiseControl&section=SystemAnalysis

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### Cruise control simulation using matlab

2. 2. CRUISE CONTROL
3. 3. CRUISE CONTROL Cruise control (speed control, auto-cruiseor tempomat) is a system that automaticallycontrols the speed of a motor vehicle. The systemtakes over the throttle of the car to maintain asteady speed as set by the driver.
4. 4. CRUISE CONTROL
5. 5. SYSTEM MODELLING feedback control system purpose is to maintain a constant vehiclespeed despite external disturbances, suchas changes in wind or road grade. accomplished byi. measuring the vehicle speedii. comparing it to the desired or reference speediii. automatically adjusting the throttle accordingto a control law
6. 6. PHYSICAL SETUP: FBDbv u Mass m Control force u Resistive forces bv Vehicle velocity v u = force generated at the road/tireinterface we will assume that :i. u can be controlled directlyii. the dynamics of thepowertrain, tires, etc are 0iii. bv, due to rolling resistance and winddrag varies linearly with the vehiclevelocity, v, and act in the directionopposite the vehicles motion
7. 7. FIRST ORDER EQUATIONWe are considering a first order mass-dampersystem.Summing forces in the x-direction and applyingNewtons 2nd law, we arrive at the followingsystem equation:m(dv/dt)+bv=uSince v is the required output:y = v
8. 8. TRANSFER FUNCTIONTaking the Laplace transform and assumingzero initial conditions, we find the transferfunction of the cruise control system to be:P(s) = V(s)/U(s)= 1/(ms+b)
9. 9. PID CONTROL
10. 10. PARAMETERS m vehicle mass 1000 kg b damping coefficient 50 N.s/m r reference speed 10 m/s Rise time < 5 s Overshoot < 10% Steady-state error < 2%
11. 11. BLOCK DIAGRAMC(s) P(s)Unity gain feedback controllerC(s) = Kp + Ki/s + Kd.s
12. 12. PROPORTIONALCONTROL The root-locus plot shows the locations ofall possible closed-loop poles when a singlegain is varied from zero to infinity. Only a proportional controller Kp will beconsidered to solve this problem. Theclosed-loop transfer function becomes:Y(s)/R(s) = Kp/(ms + ( b + Kp ) )
13. 13. PROPORTIONALCONTROL MATLAB command sgrid Used to display an acceptable region of theroot-locus plot Damping ratio (zeta) and the naturalfrequency (Wn) need to be determined
14. 14. PROPORTIONALCONTROL
15. 15. PROPORTIONALCONTROL We can then find a gain to place the closed-loop poles in the desired region byemploying the rlocfind command specific loop gain[Kp,poles]=rlocfind(P_cruise) In between the dotted lines (zeta > 0.6) andoutside the semi-ellipse (wn > 0.36)
16. 16. LAG CONTROLLER With the gain Kp being the only functionalgain and Ki and Kd being zero, the rise timeand the overshoot criteria have been met A steady-state error of more than 10%remains To reduce the steady-state error, a lagcontroller is added to the system
17. 17. LAG CONTROLLER To reduce the steady-state error, a lagcontroller will be added to the system. A pole and a zero, not too distant spacing-wise are introduced i.e:
18. 18. LAG CONTROLLER With the gain Kp being the only functionalgain and Ki and Kd being zero, the rise timeand the overshoot criteria have been met A steady-state error of more than 10%remains To reduce the steady-state error, a lagcontroller is added to the system the steady-state error will be reduced by afactor of zo/po
19. 19. LAG CONTROLLER With the gain Kp excluded for the moment, thetransfer function of PID becomes: Adding Kp to the equation, the transfer function ofPID becomes:
20. 20. LEAD CONTROLLER The lead controller is basically added toimprove the transient response of thesystem i.e. Ts and Tp mainly Not used here as it is not needed and thedesired parameters are already beingachieved