System constraints method of controlling operation of an electro-mechanical transmission with an additional constraint range

A method for controlling an electro-mechanical transmission mechanically coupled to first and second electric machines to transmit power to an output member includes determining motor torque constraints and battery power constraints. A preferred output torque to an output member is determined that is achievable within the motor torque constraints, within a range for an additional torque input and based upon the battery power constraints.

TECHNICAL FIELD

This disclosure pertains to control systems for electromechanical transmissions.

BACKGROUND

Known hybrid powertrain architectures can include multiple torque-generative devices, including internal combustion engines and non-combustion machines, e.g., electric machines, which transmit torque through a transmission device to an output member. One exemplary hybrid powertrain includes a two-mode, compound-split, electromechanical transmission which utilizes an input member for receiving tractive torque from a prime mover power source, preferably an internal combustion engine, and an output member. The output member can be operatively connected to a driveline for a motor vehicle for transmitting tractive torque thereto. Machines, operative as motors or generators, can generate torque inputs to the transmission independently of a torque input from the internal combustion engine. The machines may transform vehicle kinetic energy transmitted through the vehicle driveline to energy that is storable in an energy storage device. A control system monitors various inputs from the vehicle and the operator and provides operational control of the hybrid powertrain, including controlling transmission operating state and gear shifting, controlling the torque-generative devices, and regulating the power interchange among the energy storage device and the machines to manage outputs of the transmission, including torque and rotational speed.

SUMMARY

A powertrain includes an electro-mechanical transmission mechanically-operatively coupled to an internal combustion engine and first and second electric machines to transmit power to an output member. A method for controlling the electromechanical transmission includes determining motor torque constraints for the first and second electric machines, and determining battery power constraints for an electrical energy storage device. A range for an additional torque input to the electro-mechanical transmission is determined. A preferred output torque to the output member of the electromechanical transmission is determined that is achievable within the motor torque constraints and within the range of the additional torque input and is based upon the battery power constraints.

DETAILED DESCRIPTION

Referring now to the drawings, wherein the showings are for the purpose of illustrating certain exemplary embodiments only and not for the purpose of limiting the same,FIGS. 1 and 2depict an exemplary electro-mechanical hybrid powertrain. The exemplary electromechanical hybrid powertrain in accordance with the present disclosure is depicted inFIG. 1, comprising a two-mode, compound-split, electromechanical hybrid transmission10operatively connected to an engine14and first and second electric machines (‘MG-A’)56and (‘MG-B’)72. The engine14and first and second electric machines56and72each generate power which can be transferred to the transmission10. The power generated by the engine14and the first and second electric machines56and72and transferred to the transmission10is described in terms of input and motor torques, referred to herein as TI, TA, and TBrespectively, and speed, referred to herein as NI, NA, and NB, respectively.

The exemplary engine14comprises a multi-cylinder internal combustion engine selectively operative in several states to transfer torque to the transmission10via an input shaft12, and can be either a spark-ignition or a compression-ignition engine. The engine14includes a crankshaft (not shown) operatively coupled to the input shaft12of the transmission10. A rotational speed sensor11monitors rotational speed of the input shaft12. Power output from the engine14, comprising rotational speed and engine torque, can differ from the input speed NIand the input torque TIto the transmission10due to placement of torque-consuming components on the input shaft12between the engine14and the transmission10, e.g., a hydraulic pump (not shown) and/or a torque management device (not shown).

The exemplary transmission10comprises three planetary-gear sets24,26and28, and four selectively engageable torque-transferring devices, i.e., clutches C170, C262, C373, and C475. As used herein, clutches refer to any type of friction torque transfer device including single or compound plate clutches or packs, band clutches, and brakes, for example. A hydraulic control circuit42, preferably controlled by a transmission control module (hereafter ‘TCM’)17, is operative to control clutch states. Clutches C262and C475preferably comprise hydraulically-applied rotating friction clutches. Clutches C170and C373preferably comprise hydraulically-controlled stationary devices that can be selectively grounded to a transmission case68. Each of the clutches C170, C262, C373, and C475is preferably hydraulically applied, selectively receiving pressurized hydraulic fluid via the hydraulic control circuit42.

The first and second electric machines56and72preferably comprise three-phase AC machines, each including a stator (not shown) and a rotor (not shown), and respective resolvers80and82. The motor stator for each machine is grounded to an outer portion of the transmission case68, and includes a stator core with coiled electrical windings extending therefrom. The rotor for the first electric machine56is supported on a hub plate gear that is operatively attached to shaft60via the second planetary gear set26. The rotor for the second electric machine72is fixedly attached to a sleeve shaft hub66.

Each of the resolvers80and82preferably comprises a variable reluctance device including a resolver stator (not shown) and a resolver rotor (not shown). The resolvers80and82are appropriately positioned and assembled on respective ones of the first and second electric machines56and72. Stators of respective ones of the resolvers80and82are operatively connected to one of the stators for the first and second electric machines56and72. The resolver rotors are operatively connected to the rotor for the corresponding first and second electric machines56and72. Each of the resolvers80and82is signally and operatively connected to a transmission power inverter control module (hereafter ‘TPIM’)19, and each senses and monitors rotational position of the resolver rotor relative to the resolver stator, thus monitoring rotational position of respective ones of first and second electric machines56and72. Additionally, the signals output from the resolvers80and82are interpreted to provide the rotational speeds for first and second electric machines56and72, i.e., NAand NB, respectively.

The transmission10includes an output member64, e.g. a shaft, which is operably connected to a driveline90for a vehicle (not shown), to provide output power to the driveline90that is transferred to vehicle wheels93, one of which is shown inFIG. 1. The output power at the output member64is characterized in terms of an output rotational speed NOand an output torque TO. A transmission output speed sensor84monitors rotational speed and rotational direction of the output member64. Each of the vehicle wheels93is preferably equipped with a sensor94adapted to monitor wheel speed, the output of which is monitored by a control module of a distributed control module system described with respect toFIG. 2, to determine vehicle speed, and absolute and relative wheel speeds for braking control, traction control, and vehicle acceleration management.

The input torque from the engine14and the motor torques from the first and second electric machines56and72(TI, TA, and TBrespectively) are generated as a result of energy conversion from fuel or electrical potential stored in an electrical energy storage device (hereafter ‘ESD’)74. The ESD74is high voltage DC-coupled to the TPIM19via DC transfer conductors27. The transfer conductors27include a contactor switch38. When the contactor switch38is closed, under normal operation, electric current can flow between the ESD74and the TPIM19. When the contactor switch38is opened electric current flow between the ESD74and the TPIM19is interrupted. The TPIM19transmits electrical power to and from the first electric machine56by transfer conductors29, and the TPIM19similarly transmits electrical power to and from the second electric machine72by transfer conductors31to meet the torque commands for the first and second electric machines56and72in response to the motor torques TAand TB. Electrical current is transmitted to and from the ESD74in accordance with whether the ESD74is being charged or discharged.

The TPIM19includes the pair of power inverters (not shown) and respective motor control modules (not shown) configured to receive the torque commands and control inverter states therefrom for providing motor drive or regeneration functionality to meet the commanded motor torques TAand TB. The power inverters comprise known complementary three-phase power electronics devices, and each includes a plurality of insulated gate bipolar transistors (not shown) for converting DC power from the ESD74to AC power for powering respective ones of the first and second electric machines56and72, by switching at high frequencies. The insulated gate bipolar transistors form a switch mode power supply configured to receive control commands. There is typically one pair of insulated gate bipolar transistors for each phase of each of the three-phase electric machines. States of the insulated gate bipolar transistors are controlled to provide motor drive mechanical power generation or electric power regeneration functionality. The three-phase inverters receive or supply DC electric power via DC transfer conductors27and transform it to or from three-phase AC power, which is conducted to or from the first and second electric machines56and72for operation as motors or generators via transfer conductors29and31respectively.

FIG. 2is a schematic block diagram of the distributed control module system. The elements described hereinafter comprise a subset of an overall vehicle control architecture, and provide coordinated system control of the exemplary hybrid powertrain described inFIG. 1. The distributed control module system synthesizes pertinent information and inputs, and executes algorithms to control various actuators to meet control objectives, including objectives related to fuel economy, emissions, performance, drivability, and protection of hardware, including batteries of ESD74and the first and second electric machines56and72. The distributed control module system includes an engine control module (hereafter ‘ECM’)23, the TCM17, a battery pack control module (hereafter ‘BPCM’)21, and the TPIM19. A hybrid control module (hereafter ‘HCP’)5provides supervisory control and coordination of the ECM23, the TCM17, the BPCM21, and the TPIM19. A user interface (‘UI’)13is signally connected to a plurality of devices through which a vehicle operator controls or directs operation of the electromechanical hybrid powertrain. The devices include an accelerator pedal113(‘AP’), an operator brake pedal112(‘BP’), a transmission gear selector114(‘PRNDL’), and a vehicle speed cruise control (not shown). The transmission gear selector114may have a discrete number of operator-selectable positions, including the rotational direction of the output member64to enable one of a forward and a reverse direction.

The aforementioned control modules communicate with other control modules, sensors, and actuators via a local area network (hereafter ‘LAN’) bus6. The LAN bus6allows for structured communication of states of operating parameters and actuator command signals between the various control modules. The specific communication protocol utilized is application-specific. The LAN bus6and appropriate protocols provide for robust messaging and multi-control module interfacing between the aforementioned control modules, and other control modules providing functionality including e.g., antilock braking, traction control, and vehicle stability. Multiple communications buses may be used to improve communications speed and provide some level of signal redundancy and integrity. Communication between individual control modules can also be effected using a direct link, e.g., a serial peripheral interface (‘SPI’) bus (not shown).

The HCP5provides supervisory control of the hybrid powertrain, serving to coordinate operation of the ECM23, TCM17, TPIM19, and BPCM21. Based upon various input signals from the user interface13and the hybrid powertrain, including the ESD74, the HCP5determines an operator torque request, an output torque command, an engine input torque command, clutch torque(s) for the applied torque-transfer clutches C170, C262, C373, C475of the transmission10, and the motor torques TAand TBfor the first and second electric machines56and72. The TCM17is operatively connected to the hydraulic control circuit42and provides various functions including monitoring various pressure sensing devices (not shown) and generating and communicating control signals to various solenoids (not shown) thereby controlling pressure switches and control valves contained within the hydraulic control circuit42.

The ECM23is operatively connected to the engine14, and functions to acquire data from sensors and control actuators of the engine14over a plurality of discrete lines, shown for simplicity as an aggregate bi-directional interface cable35. The ECM23receives the engine input torque command from the HCP5. The ECM23determines the actual engine input torque, TI, provided to the transmission10at that point in time based upon monitored engine speed and load, which is communicated to the HCP5. The ECM23monitors input from the rotational speed sensor11to determine the engine input speed to the input shaft12, which translates to the transmission input speed, NI. The ECM23monitors inputs from sensors (not shown) to determine states of other engine operating parameters including, e.g., a manifold pressure, engine coolant temperature, ambient air temperature, and ambient pressure. The engine load can be determined, for example, from the manifold pressure, or alternatively, from monitoring operator input to the accelerator pedal113. The ECM23generates and communicates command signals to control engine actuators, including, e.g., fuel injectors, ignition modules, and throttle control modules, none of which are shown.

The TCM17is operatively connected to the transmission10and monitors inputs from sensors (not shown) to determine states of transmission operating parameters. The TCM17generates and communicates command signals to control the transmission10, including controlling the hydraulic circuit42. Inputs from the TCM17to the HCP5include estimated clutch torques for each of the clutches, i.e., C170, C262, C373, and C475, and rotational output speed, NO, of the output member64. Other actuators and sensors may be used to provide additional information from the TCM17to the HCP5for control purposes. The TCM17monitors inputs from pressure switches (not shown) and selectively actuates pressure control solenoids (not shown) and shift solenoids (not shown) of the hydraulic circuit42to selectively actuate the various clutches C170, C262, C373, and C475to achieve various transmission operating range states, as described hereinbelow.

The BPCM21is signally connected to sensors (not shown) to monitor the ESD74, including states of electrical current and voltage parameters, to provide information indicative of parametric states of the batteries of the ESD74to the HCP5. The parametric states of the batteries preferably include battery state-of-charge, battery voltage, battery temperature, and available battery power, referred to as a range PBAT—MINto PBAT—MAX.

A brake control module (hereafter ‘BrCM’)22is operatively connected to friction brakes (not shown) on each of the vehicle wheels93. The BrCM22monitors the operator input to the brake pedal112and generates control signals to control the friction brakes and sends a control signal to the HCP5to operate the first and second electric machines56and72based thereon.

Each of the control modules ECM23, TCM17, TPIM19, BPCM21, and BrCM22is preferably a general-purpose digital computer comprising a microprocessor or central processing unit, storage mediums comprising read only memory (‘ROM’), random access memory (‘RAM’), electrically programmable read only memory (‘EPROM’), a high speed clock, analog to digital (‘A/D’) and digital to analog (‘D/A’) circuitry, and input/output circuitry and devices (‘I/O’) and appropriate signal conditioning and buffer circuitry. Each of the control modules has a set of control algorithms, comprising resident program instructions and calibrations stored in one of the storage mediums and executed to provide the respective functions of each computer. Information transfer between the control modules is preferably accomplished using the LAN bus6and serial peripheral interface buses. The control algorithms are executed during preset loop cycles such that each algorithm is executed at least once each loop cycle. Algorithms stored in the non-volatile memory devices are executed by one of the central processing units to monitor inputs from the sensing devices and execute control and diagnostic routines to control operation of the actuators, using preset calibrations. Loop cycles are executed at regular intervals, for example each 3.125, 6.25, 12.5, 25 and 100 milliseconds during ongoing operation of the hybrid powertrain. Alternatively, algorithms may be executed in response to the occurrence of an event.

The exemplary hybrid powertrain selectively operates in one of several operating range states that can be described in terms of an engine state comprising one of an engine-on state (‘ON’) and an engine-off state (‘OFF’), and a transmission state comprising a plurality of fixed gears and continuously variable operating modes, described with reference to Table 1, below.

Each of the transmission operating range states is described in the table and indicates which of the specific clutches C170, C262, C373, and C475are applied for each of the operating range states. A first continuously variable mode, i.e., EVT Mode1, or M1, is selected by applying clutch C170only in order to “ground” the outer gear member of the third planetary gear set28. The engine state can be one of ON (‘M1_Eng_On’) or OFF (‘M1_Eng_Off’). A second continuously variable mode, i.e., EVT Mode2, or M2, is selected by applying clutch C262only to connect the shaft60to the carrier of the third planetary gear set28. The engine state can be one of ON (‘M2_Eng_On’) or OFF (‘M2_Eng_Off’). For purposes of this description, when the engine state is OFF, the engine input speed is equal to zero revolutions per minute (‘RPM’), i.e., the engine crankshaft is not rotating. A fixed gear operation provides a fixed ratio operation of input-to-output speed of the transmission10, i.e., NI/NO. A first fixed gear operation (‘G1’) is selected by applying clutches C170and C475. A second fixed gear operation (‘G2’) is selected by applying clutches Cl70and C262. A third fixed gear operation (‘G3’) is selected by applying clutches C262and C475. A fourth fixed gear operation (‘G4’) is selected by applying clutches C262and C373. The fixed ratio operation of input-to-output speed increases with increased fixed gear operation due to decreased gear ratios in the planetary gears24,26, and28. The rotational speeds of the first and second electric machines56and72, NAand NBrespectively, are dependent on internal rotation of the mechanism as defined by the clutching and are proportional to the input speed measured at the input shaft12.

In response to operator input via the accelerator pedal113and brake pedal112as captured by the user interface13, the HCP5and one or more of the other control modules determine torque commands to control the torque generative devices comprising the engine14and first and second electric machines56and72to meet the operator torque request at the output member64and transferred to the driveline90. Based upon input signals from the user interface13and the hybrid powertrain including the ESD74, the HCP5determines the operator torque request, a commanded output torque between the transmission10and the driveline90, an input torque from the engine14, clutch torques for the torque-transfer clutches C170, C262, C373, C475of the transmission10; and the motor torques for the first and second electric machines56and72, respectively, as is described hereinbelow. The commanded output torque can be a tractive torque wherein torque flow originates in the engine14and the first and second electric machines56and72and is transferred through the transmission10to the driveline90, and can be a reactive torque wherein torque flow originates in the vehicle wheels93of the driveline90and is transferred through the transmission10to first and second electric machines56and72and the engine14.

Final vehicle acceleration can be affected by other factors including, e.g., road load, road grade, and vehicle mass. The operating range state is determined for the transmission10based upon a variety of operating characteristics of the hybrid powertrain. This includes the operator torque request communicated through the accelerator pedal113and brake pedal112to the user interface13as previously described. The operating range state may be predicated on a hybrid powertrain torque demand caused by a command to operate the first and second electric machines56and72in an electrical energy generating mode or in a torque generating mode. The operating range state can be determined by an optimization algorithm or routine which determines optimum system efficiency based upon operator demand for power, battery state of charge, and energy efficiencies of the engine14and the first and second electric machines56and72. The control system manages torque inputs from the engine14and the first and second electric machines56and72based upon an outcome of the executed optimization routine, and system efficiencies are optimized thereby, to manage fuel economy and battery charging. Furthermore, operation can be determined based upon a fault in a component or system. The HCP5monitors the torque-generative devices, and determines the power output from the transmission10required in response to the desired output torque at output member64to meet the operator torque request. As should be apparent from the description above, the ESD74and the first and second electric machines56and72are electrically-operatively coupled for power flow therebetween. Furthermore, the engine14, the first and second electric machines56and72, and the electromechanical transmission10are mechanically-operatively coupled to transfer power therebetween to generate a power flow to the output member64.

Operation of the engine14and transmission10is constrained by power, torque and speed limits of the engine14, the first and second electric machines56and72, the ESD74and the clutches C170, C262, C373, and C475. The operating constraints on the engine14and transmission10can be translated to a set of system constraint equations executed as one or more algorithms in one of the control modules, e.g., the HCP5.

Referring again toFIG. 1, in overall operation, the transmission10operates in one of the operating range states through selective actuation of one or two of the torque-transfer clutches. Torque constraints for each of the engine14and the first and second electric machines56and72and speed constraints for each of the engine14, the first and second electric machines56and72, and the output shaft64of the transmission10are determined. Battery power constraints for the ESD74are determined, and are applied to further limit the motor torque constraints for the first and second electrical machines56and72. The preferred operating region for the powertrain is determined using the system constraint equation, based upon the battery power constraints, the motor torque constraints, and the speed constraints. The preferred operating region comprises a range of permissible operating torques or speeds for the engine14and the first and second electric machines56and72.

By deriving and simultaneously solving dynamics equations of the transmission10, the torque limit, in this embodiment the output torque TO, can be determined using the following linear equations:
TM1=TAtoTM1*TA+TBtoTM1*TB+Misc—TM1[1]
TM2=TAtoTM2*TA+TBtoTM2*TB+Misc—TM2[2]
TM3=TAtoTM3*TA+TBtoTM3*TB+Misc—TM3[3]
wherein, in this embodiment,TM1represents the output torque TOat output member64,TM2represents the input torque TIat input shaft12,TM3represents the reactive clutch torque(s) for the applied torque-transfer clutches C170, C262, C373, C475of the transmission10,TAtoTM1, TAtoTM2, TAtoTM3are contributing factors of TAto TM1, TM2, TM3, respectively,TBtoTM1, TBtoTM2, TBtoTM3are contributing factors of TBto TM1, TM2, TM3, respectively,Misc_TM1, Misc_TM2, and Misc_TM3are constants which contribute to TM1, TM2, TM3by NI—DOT, NO—DOT, and NC—DOT(time-rate changes in the input speed, output speed and clutch slip speed) respectively, andTAand TBare the motor torques from the first and second electric machines56and72.
The torque parameters TM1, TM2, TM3can be any three independent parameters, depending upon the application.

The engine14and transmission10and the first and second electric machines56and72have speed constraints, torque constraints, and battery power constraints due to mechanical and system limitations.

The speed constraints can include engine speed constraints of NI=0 (engine off state), and NIranging from 600 rpm (idle) to 6000 rpm for the engine14. The speed constraints for the first and second electric machines56and72can be as follows:
−10,500 rpm≦NA≦+10,500 rpm, and
−10,500 rpm≦NB≦+10,500 rpm.

The torque constraints include engine torque constraints including TI—MIN<TI<TI—MAX, and motor torque constraints for the first and second electric machines including TA—MIN<TA<TA—MAXand TB—MIN<TB<TB—MAX. The motor torque constraints TA—MAXand TA—MINcomprise torque limits for the first electric machine56when working as a torque-generative motor and an electrical generator, respectively. The motor torque constraints TB—MAXand TB—MINcomprise torque limits for the second electric machine72when working as a torque-generative motor and an electrical generator, respectively. The maximum and minimum motor torque constraints TA—MAX, TA—MIN, TB—MAX, TB—MINare preferably obtained from data sets stored in tabular format within one of the memory devices of one of the control modules. Such data sets are empirically derived from conventional dynamometer testing of the combined motor and power electronics (e.g., power inverter) at various temperature and voltage conditions.

Battery power constraints comprise the available battery power within the range of PBAT—MINto PBAT—MAX, wherein PBAT—MINis maximum allowable battery charging power and PBAT—MAXis the maximum allowable battery discharging power. Battery power is defined as positive when discharging and negative when charging.

Minimum and maximum values for TM1are determined within the speed constraints, the motor torque constraints, clutch torque constraints, and the battery power constraints during ongoing operation, in order to control operation of the engine14, the first and second electric machines56and72, also referred to hereinafter as Motor A56and Motor B72, and the transmission10to meet the operator torque request and the commanded output torque.

An operating range, comprising a torque output range is determinable based upon the battery power constraints of the ESD74. Calculation of battery power usage, PBATis as follows:
PBAT=PA,ELEC+PB,ELEC+PDC—LOAD[4]
wherein PA,ELECcomprises electrical power from Motor A56,PB,ELECcomprises electrical power from Motor B72, andPDC—LOADcomprises known DC load, including accessory loads.

Substituting equations for PA,ELECand PB,ELEC, yields the following:
PBAT=(PA,MECH+PA,LOSS)+(PB,MECH+PB,LOSS)+PDC—LOAD[5]
wherein PA,MECHcomprises mechanical power from Motor A56,PA,LOSScomprises power losses from Motor A56,PB,MECHcomprises mechanical power from Motor B72, andPB,LOSScomprises power losses from Motor B72.

Eq. 5 can be restated as Eq. 6, below, wherein speeds, NAand NB, and torques, TAand TB, are substituted for powers PAand PB. This includes an assumption that motor and inverter losses can be mathematically modeled as a quadratic equation based upon torque as follows:

This can be restated as Eq. 7 as follows.

This reduces to Eq. 8 as follows.

This reduces to Eq. 10 as follows.

The motor torques TAand TBcan be transformed to TXand TYas follows:

Eq. 11 can thus be further reduced as follows.
PBAT=(TX2+TY2)+C[13]
PBAT=R2+C[14]

Eq. 12 specifies the transformation of motor torque TAto TXand the transformation of motor torque TBto TY. Thus, a new coordinate system referred to as TX/TYspace is defined, and Eq. 13 comprises battery power, PBAT, transformed into TX/TYspace. Therefore, the battery power range between maximum and minimum battery power PBAT—MAXand PBAT—MINcan be calculated and graphed as radii RMaxand RMinwith a center at locus (0, 0) in the transformed space TX/TY, designated by the letter K as shown with reference toFIG. 3, wherein:
RMin=SQRT(PBAT—MIN−C), and
RMax=SQRT(PBAT—MAX−C).

The minimum and maximum battery powers, PBAT—MINand PBAT—MAX, are preferably correlated to battery physics, e.g. state of charge, temperature, voltage and usage (amp-hour/hour). The parameter C, above, is defined as the absolute minimum possible battery power at given motor speeds, NAand NB, within the motor torque limits. Physically, when TA=0 and TB=0 the output power from the first and second electric machines56and72is zero. Physically TX=0 and TY=0 corresponds to a maximum charging power for the ESD74. The positive sign (‘+’) is defined as discharging power from the ESD74, and the negative sign (‘−’) is defined as charging power into the ESD74. RMaxdefines a maximum battery power, typically a discharging power, and RMindefines a maximum battery charging power.

The forgoing transformations to the TX/TYspace are shown inFIG. 3, with representations of the battery power constraints as concentric circles having radii of RMinand RMax(‘Battery Power Constraints’) and linear representations of the motor torque constraints (‘Motor Torque Constraints’) circumscribing an allowable operating region. Analytically, the transformed vector [TXTY] determined in Eq. 12 is solved simultaneously with the vector defined in Eq. 13 comprising the minimum and maximum battery powers identified by RMinand RMaxto identify a range of allowable torques in the TX/TYspace which are made up of motor torques TAand TBconstrained by the minimum and maximum battery powers PBAT—MINto PBAT—MAX. The range of allowable torques in the TX/TYspace is shown with reference toFIG. 3, wherein points A, B, C, D, and E represent the bounds, and lines and radii are defined.

A constant torque line can be defined in the TX/TYspace, and depicted inFIG. 3(‘TM1=C1’), comprising the limit torque TM1, described in Eq. 1, above. The limit torque TM1comprises the output torque TOin this embodiment, Eqs. 1, 2, and 3 restated in the TX/TYspace are as follows.
TM1=TAtoTM1*(TX−A2)/A1+TBtoTM1*(TY−B2l )/B1+Misc—TM1[15]
TM2=TAtoTM2*(TX−A2)/A1+TBtoTM2*(TY−B2)/B1+Misc—TM2[16]
TM3=TAtoTM3*(TX−A2)/A1+TBtoTM3*(TY−B2)/B1+Misc—TM3[17]

The speed constraints, motor torque constraints, and battery power constraints can be determined during ongoing operation and expressed in linear equations which are transformed to TX/TYspace. Eq. 21 comprises a limit torque function describing the output torque constraint TM1, e.g., TO.

The torque limit of the transmission10, in this embodiment the output torque TO, can be determined by using Eq. 21 subject to the TM2and TM3constraints defined by Eqs. 22 and 23 to determine a transformed maximum or minimum limit torque in the TX/TYspace, comprising one of TM1—XYMax and TM1—XYMin, e.g., maximum and minimum output torques TO—Maxand TO—Minthat have been transformed. Subsequently the transformed maximum or minimum limit torque in the TX/TYspace can be retransformed out of the TX/TYspace to determine maximum or minimum limit torques TM1—Max and TM1—Min for managing control and operation of the transmission14and the first and second electric machines56and72.

FIG. 4shows motor torque constraints comprising the minimum and maximum motor torques for TAand TBtransformed to TX/TYspace (‘Tx_Min’, ‘Tx_Max’, ‘Ty_Min’, ‘Ty_Max’). Battery power constraints are transformed to the TX/TYspace (‘R_Min’, ‘R_Max’) and have a center locus point K comprising (Kx, Ky)=(0,0). Constraints comprising maximum and minimum limits for an additional constraint torque are depicted (‘Tm2=Tm2_High_Lmt’ and ‘Tm2=Tm2_Low_Lmt’), and comprise the range of input torques TIat input shaft12transformed to TX/TYspace in this embodiment and can be mathematically represented by the line TM2—XYdescribed with reference to Eq. 22, above. The lines TM2—XYdescribed in Eq. 22 includes the TM2—Intercept having two different values corresponding to the maximum limit and the minimum limit for the engine input torque TI. Alternatively, the second input torque TM2—XYcan comprise a range of clutch torques or another torque input.

The operating range of the output torque TOshown as the lines representing the maximum limit (‘Tm1=−Tx+Ty (max)’) and the minimum limit (‘Tm1=−Tx+Ty (min)’).

A constant torque line (‘Tm1’) representing line TM1—XYhas a positive slope of a/b of the general form in Eq. 24:
Tm1=a*Tx+b*Ty+C[24]
wherein a<0 and b>0 and C is a constant term. In the ensuing descriptions, the line TM1—XYhas a positive slope of 1:1 for purposes of illustration. The x-intercept C of Eq. 24 can change to be one of a minimum or a maximum torque. Thus, the operating range of output torque TOis shown as the lines representing the maximum limit (‘Tm1=−Tx+Ty (max)’) and the minimum limit (‘Tm1=−Tx+Ty (min)’).

FIG. 5depicts a process for determining one of the maximum and minimum output torques TO—Maxand TO—Minbased upon the speed constraints, motor torque constraints, and battery power constraints and constrained within the range of the additional torque input comprising Tm2. The process includes determining whether the preferred solution is a maximum value for the output, i.e., TM1—XYMax as indicated by setting a flag Tm1_Max_Flag, or alternatively whether the preferred solution is a minimum value for the output, i.e., TM1—Min as indicated by not setting the flag Tm1_Max_Flag. A maximum (or minimum) value for the first torque Tm1is calculated based upon the motor torque constraints and battery power constraints in TX/TYspace, comprising one of TM1—XYMax and TM1—XYMin, and depicted as point P (or point Q) and having coordinates of (Tx, Ty) onFIG. 4(502). A value for the second input torque TM2—XY(‘Tm2_Value’) is calculated using Eq. 22 (504). It is determined whether the value for the second input torque TM2—XY(‘Tm2_Value’) is within the operating range of the second input torque, shown as the lines representing the high limit (‘Tm2_High Lmt’) and the low limit (‘Tm2_Low_Lmt’) (506). When it is determined that the value for the second input torque TM2—XY(‘Tm2_Value’) is within the operating range of the second input torque, the maximum (or minimum) value for the first torque Tm1depicted as point P (or point Q) and having the coordinates of (Tx, Ty) is accepted as the valid answer (518). The (Tx, Ty) point represents the preferred solution for controlling operation that can be retransformed to motor torques (TA, TB) to control operation of the first and second electric machines56and72.

When it is determined that the value for the second input torque TM2—XY(‘Tm2_Value’) is less than the operating range of the second input torque, shown as the line representing the low limit (‘Tm2_Low_Lmt’) as shown inFIG. 4(508), the second torque Tm2is set to the low limit, i.e., Tm2=Tm2_min is set equal to the line Tm2=Tm2_Low_Lmt (510), and a search is conducted to determine a minimum (or maximum) value for the first torque Tm1that is within the motor torque constraints and the battery power constraints and at the low limit (‘Tm2_Low_Lmt’) (514). In any case, the solution comprises the minimum (or maximum) value for the first torque Tm1that is within the motor torque constraints and the battery power constraints and the constraints of the second torque Tm2(520).

When it is determined that the value for the second input torque TM2—XY(‘Tm2_Value’) is greater than the operating range of the second input torque, shown as the line representing the high limit (‘Tm2_High_Lmt’) (508,512), a search is conducted to determine a maximum (or minimum) value for the first torque Tm1that is within the motor torque constraints and the battery power constraints and at the high limit (‘Tm2_High_Lmt’) (516). In any case, the solution comprises the minimum (or maximum) value for the first torque Tm1that is within the motor torque constraints and the battery power constraints and the constraints of the second torque Tm2(520).

The preferred solution for this set of constraints (520) is the solution that has the lesser Tm1point, i.e., the lesser output torque constraint TM1, when maximizing the output torque or the solution that has the greater Tm1point, when minimizing the output torque. The solution set preferably comprises a (Tx, Ty) point representing a preferred solution for controlling operation that can be retransformed to motor torques (TA, TB) to control operation of the first and second electric machines56and72.

The embodiment described hereinabove is based upon the line TM1—XYhaving a positive slope of a/b of the general form in Eq. 24 (as above):
Tm1=a*Tx+b*Ty+C[24]
wherein a<0 and b>0 and C is a constant term, with a slope of a/b=1:1 for purposes of illustration with the x-intercept C being changeable. The description is applicable to combinations of a>0, b<0, and the slope of a/b being less than 1:1 and being greater than 1:1.