A State-Space Representation Model and Learning Algorithm for ...

difference between the desired and actual vehicle speed, ∆V,namely,S = { si| si= ( gear, ∆V)}.(23)The actions, α, correspond to the gas pedal position andcan take values from the feasible set A, defined asA = As (i) = [0,0.7], where i= 1, 2,..., N, N=| S | . (24)To incorporate uncertainty the vehicle is simulated in agreat range of different road grades from 0° to 10°.Consequently, at state s i∈S and executing a control action(gas pedal position), the system transits to another statesj∈S with a conditional probably ps (j| si, α ( si)), since theacceleration capability of a vehicle varies at different roadgrades. As a consequence of this state transition the systemreceives a numerical reward (difference between the desiredand actual vehicle speed).4.2 Simulation ResultsAfter completing four simulations of each road grade, the PODcruise controller realizes the control policy (gas pedal position)to maintain the vehicle’s speed at the desired set point. Thevehicle model was initiated from zero speed. The driver model,following the driving cycle, accelerated the vehicle up to40mph and at 10sec activated the POD cruise controller. Thedesired and actual vehicle speeds for three different road gradesas well as the gas pedal rates of the POD controller areillustrated in Figure 6. The small discrepancy between thedesired and actual vehicle speed before the cruise controlleractivation is due to the steady-state error of the driver’s model.However, since the desired driving cycle set the vehicle’s speedto be at 40mph, when the POD cruise controller is activatedhelps to correct this error and, afterwards, maintains thevehicle’s actual speed at the set point. The accelerator pedalposition is at different values because in the case of road grades2º and 6º the selected transmission gear is 2, shown in Figure 7,while in case of road grade 10º the selected transmission gear is1. So, at different selected gears, the accelerator pedal varies tomaintain constant vehicle’s speed. In Figure 8, the performanceof POD cruise controller is evaluated in a severe drivingscenario where the road grade changes from 0° to 10°, whilethe POD cruise controller is active. In this scenario, the POD isactivated again at 10sec when the road grade is 0°, and at 14sec the road grade becomes 10°. The engine speed and theselected transmission gear for this scenario are shown in Figure9. While the vehicle is cruising at constant speed and the roadgrade changes from 0º to 10º, the vehicle’s speed startsdecreasing after some time. Once this occurs, the self-learningcruise controller senses the discrepancy between the desiredand actual vehicle speed and commands the accelerator pedalso as to correct the error. Consequently, there is a small timedelay in the acceleration pedal command, illustrated in Figure8, which depends on vehicle inertia.Vehicle Velocity [mph]Accelerator PedalCruise Control with POD4030Driving Cycle20Grade 2 oGrade 6 o10Grade 10 o00 5 10 15 2010.500 5 10 15 20Time [sec]Figure 6. Vehicle speed and accelerator pedal rate for differentroad grades by self-learning cruise control with POD.Engine Speed [RPM]30002000Cruise Control with POD1000Grade 2 o00 5 10 Grade 15 6 o 20Grade 10 o3Transmission Gear2100 5 10 15 20Time [sec]Figure 7. Engine speed and transmission gear selection fordifferent road grades by self-learning cruise control with POD.Vehicle Velocity [mph]Accelerator PedalCruise Control with PODAt 14 sec the road grade increases from 0 o to 10 o4030Driving Cycle20Vehicle Speed1000 5 10 15 2010.500 5 10 15 20Time [sec]Figure 8. Vehicle speed and accelerator pedal rate for a roadgrade increase from 0° to 10°.8 Copyright © 2007 by ASME