Modeling and simulation of a vehicle with automatic transmission

6. Controller: TCU

Shifting gears in an automatic transmission is done according to a certain schedule, designed according to certain criteria: fuel economy, dynamic performance or comfort. The most modern automatic transmissions are adaptive, which means that the shift scheduling is modified according to the driving speed of the car and the driving style of the driver (economy vs. sport).

A shift scheduler consists of static shift lines (maps) and dynamic corrections. The shift map gives the right gear for a particular vehicle speed and throttle (accelerator pedal) position. The dynamic corrections are modifying the static gear calculation function mainly of the rate of accelerator pedal position and vehicle state (acceleration vs. deceleration).

6.1 Shift lines (maps)

For a given vehicle speed and accelerator pedal (throttle) position, there can be only one gear engaged. The shift lines, also called shift maps, define in which gear the transmission should be, for a particular vehicle speed and accelerator pedal position.

For our example, we are going to have 7 forward gears, which means that will have 6 shift lines for up shifting and another 6 shift lines for down shifting.

Image: Upshift lines	Image: Downshift lines
Image: Shift lines

The upshift line represent the maximum vehicle speed, for a given acceleration pedal (throttle) position, in a given gear. If the line is crossed, the transmission will shift into an upper gear (e.g. 1 to 2). For downshifting, the logic is the same, only that the shift line is the minimum speed in the current gear. When this limit is passed, the transmission downshifts in a lower gear (e.g. 2 to 1).

Upshift lines data:

Upshift lines [kph]		Gear [-]
		1	2	3	4	5	6	7
Accelerator pedal (throttle) position [%]	0	12	21	32	45	64	84	350
	21	12	21	32	45	64	86	350
	21.01	12	21	32	46	64	86	350
	21.02	12	21	32	47	65	86	350
	23	12	21	34	49	68	86	350
	25	12	21	36	52	72	91	350
	28	12	22	39	57	78	99	350
	33	14	25	44	63	87	109	350
	34	14	25	45	66	90	114	350
	34.01	15	26	45	67	92	115	350
	38	16	30	52	76	104	131	350
	72	44	75	118	165	227	281	350
	74	45	77	120	169	232	287	350
	76	47	80	123	174	238	294	350
	82	52	86	132	186	255	315	350
	84	54	88	134	190	260	320	350
	85	55	89	135	192	263	320	350
	87	56	91	135	192	263	320	350
	89	58	91	135	192	263	320	350
	100	58	91	135	192	263	320	350

Downshift lines data:

Downshift lines [kph]		Gear [-]
		1	2	3	4	5	6	7
Accelerator pedal (throttle) position [%]	0	0	10	16	24	37	50	68
	20	0	10	16	24	37	50	68
	21	0	10	16	24	37	50	68
	23	0	10	16	24	38	51	69
	25	0	10	16	25	39	52	70
	32	0	11	17	27	42	57	73
	35	0	11	18	28	43	59	75
	35.01	0	11	18	29	44	59	77
	37	0	11	19	29	45	62	81
	38	0	11	19	30	46	64	83
	54	0	11	24	42	68	91	125
	56	0	11	25	44	70	95	129
	74	0	13	30	58	91	131	188
	78	0	13	31	60	95	138	202
	80	0	13	32	62	97	144	211
	81	0	13	32	64	100	147	215
	86	0	13	35	73	113	161	215
	94	0	13	35	73	113	161	215
	94.01	0	17	45	82	126	192	270
	100	0	17	45	82	126	192	270

The upshift and downshift lines are integrated into the Xcos block diagram using the 2-D interpolation blocks.

Inputs

Name	Value	Description
AccrPedlPosn_prc	–	Acceleration pedal position [%]
GearNr_z	–	Current gear [-]

Parameters

Name	Value	Description
GbxGearNr_z_X	(table)	Gear number array (axis) [-]
AccrPedlPosnTrnsUpShift_prc_Y	(table)	Upshift accelerator pedal position array (axis) [%]
AccrPedlPosnTrnsDownShift_prc_Y	(table)	Downshift accelerator pedal position array (axis) [%]
VehVUpShiftLim_kph_Z	(table)	Upshift vehicle speed limit for current gear (map) [kph]
VehVDownShiftLim_kph_Z	(table)	Downshift vehicle speed limit for current gear (map) [kph]

Outputs

Name	Value	Description
VehUpShiftLim_kph	–	Upshift vehicle speed limit for current gear [kph]
VehDownShiftLim_kph	–	Downshift vehicle speed limit for current gear [kph]

6.2 Shift scheduler (dynamic corrections)

In order to have more consistent gear changes we need to apply some corrections on the target gear coming from the shift maps. These correction are meant to improve the driveability of the vehicle and reduce the fuel consumption of the engine.

6.2.1 Minimum Time in Gear Correction

The purpose of minimum time in gear is to avoid having successive upshifts or downshifts. Since in this simulation, the gear change is instant (because there no model of the actuation system), we need to keep the current gear for a minimum time.

If there is a gear change detected, a Counter/Timer is started from an initial time. If the Timer hasn’t expired yet (reached 0), we do not allow another gear shift, even if the shift lines speed limits are crossed by the current vehicle speed.

The time delay (minimum time in gear) can be calibrated differently for upshifts or downshifts.

Inputs

Name	Value	Description
GearNr_z	–	Current gear [-]
GearNrRaw_z	–	Current gear (raw) [-]

Parameters

Name	Value	Description
TrnsUpGearMinT_s_C	2	Upshift minimum time in gear [s]
TrnsDownGearMinT_s_C	1	Downshift minimum time in gear [s]

Outputs

Name	Value	Description
GearUpShiftDly_B	–	Upshift delay shift correction active [-]
GearDownShiftDly_B	–	Downshift delay shift correction active [-]

6.2.2 Engine Braking Correction

The purpose of this correction is to keep the transmission in the current gear, when the driver is fully releasing the accelerator pedal. Without this correction, if the vehicle speed is 100 kph and the accelerator pedal (throttle) position is 50 %, the current gear is 3^rd gear. If there is a full lift from the accelerator pedal 0 %, the transmission will shift to 7^th gear. This behaviour is not desirable.

Inputs

Name	Value	Description
VehV_kph	–	Vehicle speed [kph]
AccrPedlPosn_prc	–	Accelerator pedal position [%]

Parameters

Name	Value	Description
AccrPedlPosnMaxEngBrk_prc_C	1	Maximum accelerator pedal position for engine braking shift correction [%]
VehVMaxEngBrk_kph_C	10	Minimum vehicle speed for engine braking shift correction [kph]

Outputs

Name	Value	Description
GearShiftStopEngBrk_B	–	Engine braking shift correction active [-]

6.2.3 Tip In-Out Corrections

The purpose of this correction is to avoid gear shifts when the driver suddenly presses or releases the accelerator pedal. The rapid press on the acceleration pedal is called a tip-in event, while a sudden release of the accelerator pedal is called a tip-out event.

The gradient (rate of change) of the accelerator pedal is compared with two calibrate-able thresholds, one for tip-in event and the other for tip-out events. When these limits are exceeded, a flag is raised which blocks the gear shift.

The tip-in correction presented in this example is simplified for an easier understanding of the concept. In reality this correction needs to take into account the power reserve of the engine. If the power reserve of the engine is not sufficient to provide significant vehicle acceleration, a accelerator pedal tip-in should allow a downshift to take place.

The tip-out correction makes sense as it is, because a sudden release of the accelerator pedal means that the driver wants to slow down only and not to change gears. Therefore the current gear must be kept to allow the engine to brake (overrun).

Inputs

Name	Value	Description
AccrPedlPosn_prc	–	Accelerator pedal position [%]

Parameters

Name	Value	Description
AccrPedlMinGrdt_prcps_C	-10	Minimum accelerator pedal gradient threshold for shift inhibit [%/s]
AccrPedlMaxGrdt_prcps_C	10	Maximum accelerator pedal gradient threshold for shift inhibit [%/s]

Outputs

Name	Value	Description
GearShiftStopTipOut_B	–	Accelerator pedal tip-out gear shift correction active [-]
GearShiftStopTipIn_B	–	Accelerator pedal tip-in gear shift correction active [-]

The values of the minimum and maximum pedal gradients are set to a small value to be able to visualise them during simulation. In reality the actual values can be 5-10 times higher.

6.2.4 Gear Calculation

The gear calculation takes into account the shift lines gear decision and all the dynamic corrections. If there is no correction active and the current vehicle speed is above/below the shift line speed limit, the current gear is incremented (upshift) or decremented (downshift).

This algorithm is relatively simple because all the gear changes are done sequentially. In reality the gears can be skipped, especially during a downshift. If there is a heavy braking event, a modern transmission can do for example a 6-4 downshift.

The current gear has a sample time delay. This is needed in order to avoid the algebraic loop with the shift line speed limit calculation.

Inputs

Name	Value	Description
VehV_kph	–	Vehicle speed [kph]
VehUpShiftLim_kph	–	Upshift vehicle speed limit for current gear [kph]
VehDownShiftLim_kph	–	Downshift vehicle speed limit for current gear [kph]
GearUpShiftDly_B	–	Upshift delay shift correction active [-]
GearDownShiftDly_B	–	Downshift delay shift correction active [-]
GearShiftStopEngBrk_B	–	Engine braking shift correction active [-]
GearShiftStopTipOut_B	–	Accelerator pedal tip-out gear shift correction active [-]
GearShiftStopTipIn_B	–	Accelerator pedal tip-in gear shift correction active [-]

Outputs

Name	Value	Description
GearNr_z	–	Current gear [-]
GearNrRaw_z	–	Current gear (raw) [-]