Method for finding a solution to a linear constraint problem in a multi-mode powertrain system

Abstract

Method for operating a powertrain system comprising a multi-mode transmission designed to transmit torque between a power machine, torque machines and a final drive, the method comprising: Determining an objective function for a target component of interest; Identifying constraints for a plurality of independent and dependent variables; Evaluating a plurality of permutations of the objective function based on the independent variables and the dependent linear variables; Evaluate the objective function to determine maximum and minimum values ​​for the objective function for each of the permutations; Determining overall minimum and maximum values ​​for the objective function based on the maximum and minimum values ​​for the objective function for each of the permutations; and Controlling the operation of the powertrain system to which the target component of interest is assigned, based on the overall minimum and maximum values ​​for the objective function.

Description

TECHNICAL AREA

[0001] This disclosure relates to a method for operating a powertrain system comprising a multi-mode transmission.

[0002] EP 2 065 269 A2, for example, describes a method for controlling a hybrid transmission that serves to transfer power between an input element and a first and second torque machine and an output element in a fixed-gear operating condition, wherein the first and second torque machines are connected to an energy storage device. The method comprises: Determining an output torque instruction at the output element; determining motor torque limits for the first and second torque machines and determining power limits for the energy storage device; Iterative selection of candidate input torques that can be transferred to the input element and of associated output torques; determination of a second torque limit that is associated with the candidate input torque; Determine a third torque limit associated with the candidate input torque; and Determining a preferred input torque encompassing the candidate input torque that achieves the designated output torque at the output element and satisfies the motor torque limitations for the first and second torque machine, satisfies the power limitations for the energy storage device, and satisfies the second and third torque limitations associated with the candidate input torque when operating in the fixed-gear operating range condition. BACKGROUND

[0003] Powertrain systems can be designed to transmit torque from multiple torque-generating devices through a torque transmission device to an output element, which may be coupled to a final drive. Such powertrain systems include hybrid powertrain systems and extended-range electric vehicle systems. Control systems for operating such powertrain systems operate the torque-generating devices and employ torque transmission components in the transmission to transfer torque in response to operator-commanded output torque requests, taking into account fuel economy, emissions, drivability, and other factors. Exemplary torque-generating devices include internal combustion engines and non-combustion-based torque machines.Non-combustion torque machines can include electric machines that operate as motors or generators to produce a torque input to the transmission independently of a torque input from the internal combustion engine. These torque machines can convert the vehicle's kinetic energy, transmitted through the final drive, into electrical energy in a process known as recuperation, which can then be stored in an electrical energy storage device.A control system monitors various inputs from the vehicle and the operator and provides functional control of the hybrid powertrain, which includes controlling the transmission operating state and gear shifting, controlling the torque-generating devices, and regulating the electrical power exchange between the electrical energy storage device and the electric machines to manage transmission outputs that include torque and speed.

[0004] A well-known process for identifying extrema, i.e., minima and maxima, of an objective function subject to constraints involves applying linear programming, such as the simplex method. The set of evaluations required to identify the extrema relies on evaluating all combinations of constraints, which can consume a considerable amount of processor resources and limits the ability to quickly and repeatedly achieve an accurate result suitable for real-time powertrain control. SUMMARY

[0005] A powertrain system comprises an internal combustion engine, a multi-mode transmission having a plurality of torque motors, and a final drive. The inventive method for operating the powertrain system includes determining an objective function for a target component of interest within the powertrain system. Constraints are determined for a plurality of independent and dependent variables. Permutations of the objective function are evaluated based on the independent variables and the dependent linear variables. The objective function is evaluated to determine maximum and minimum values ​​for each permutation. Overall minimum and maximum values ​​for the objective function are determined based on the maximum and minimum values ​​for each permutation.The operation of the powertrain system, which is assigned to the target component of interest, is controlled on the basis of the overall minimum and maximum values ​​for the objective function. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Now, one or more embodiments will be described by way of example with reference to the accompanying drawings, in which: Fig. 1 a multi-mode powertrain system comprising an internal combustion engine, a transmission, a final drive and a controller, as illustrated in the disclosure; Fig. 2 a plurality of independent variables and constraints and dependent variables and constraints plotted in relation to the first and second independent variables X1 and X2, illustrated according to the disclosure; and Fig.3 illustrates a process that is applied to linear constraints comprising independent variables X1, X2 and X3, and constraints on dependent linear variables Y2, Y3, Y4, to determine extrema in relation to the linear constraints, as described in the disclosure. DETAILED DESCRIPTION

[0007] Now, with reference to the drawings, the illustrations of which are provided solely for the purpose of illustrating certain exemplary embodiments, it is stated that Fig.Figure 1 represents a non-restrictive powertrain system 100 comprising an internal combustion engine (power engine) 12, a multi-mode transmission (transmission) 10, a high-voltage electrical system 80, a final drive 90, and a controller 5. The transmission 10 is mechanically coupled to the power engine 12 and to a first and second torque machine 60 and 62, respectively, and is designed to transmit torque between the power engine 12, the torque machines 60 and 62, and the final drive 90. As illustrated, the first and second torque machines 60 and 62 are electric motors / generators.

[0008] The high-voltage electrical system 80 comprises an electrical energy storage device, e.g., a high-voltage battery (battery) 85, which is electrically coupled to a geared power converter control module (TPIM) 82 via a high-voltage electrical bus 84, and is equipped with suitable devices for monitoring the electrical current flow, including devices and systems for monitoring the electrical current and voltage. The battery 85 can be any suitable high-voltage electrical energy storage device, e.g., a high-voltage battery, and preferably comprises a monitoring system that provides a measure of the electrical power supplied to the high-voltage electrical bus 84, comprising voltage and electrical current.

[0009] The engine 12 can be any suitable internal combustion engine and comprises a multi-cylinder internal combustion engine that can be selectively operated in different states to transmit torque to the transmission 10 via an input element 14. It can be either a spark-ignition or a compression-ignition engine. The engine 12 includes a crankshaft coupled to the input element 14 of the transmission 10. A speed sensor 11 monitors the crank angle and speed of the input element 14. The power output of the engine 12, i.e., speed and engine torque, can differ from the input speed and torque to the transmission 10 due to the placement of torque-consuming components at the input element 14 between the engine 12 and the transmission 10, e.g., a torque management device.The power unit 12 is designed to perform auto-stop and auto-start operations during continuous powertrain operation in response to operating conditions. The controller 5 is designed to control actuators of the power unit 12 and thus control combustion parameters, including controlling the intake air flow rate, spark ignition timing, injected fuel quantity, fuel injection timing, EGR valve position to control the flow of recirculated exhaust gases, and intake and / or exhaust valve timing and phase positions on power units so equipped. Thus, the power unit speed can be controlled by controlling combustion parameters, including air flow torque and spark-induced torque. The power unit speed can also be controlled by controlling the engine torques of the first and second torque units 60 and 60, respectively.62 The reaction torque is controlled at the input element 14.

[0010] The illustrated transmission 10 is an electromechanical four-mode transmission 10 with combined power splitting, comprising three planetary gear sets 20, 30, and 40 and five engageable torque-transmitting devices, i.e., clutches C1 52, C2 54, C3 56, C4 58, and C5 50. Other embodiments of the transmission are considered. The transmission 10 is coupled to a first and second torque machine 60 and 62, respectively. The transmission 10 is configured to transmit torque between the power machine 12, the torque machines 60 and 62, and the output element 92 in response to an output torque request. In one embodiment, the first and second torque machines 60 and 62 are motors / generators that use electrical energy to generate and counteract torque. The planetary gear set 20 comprises a sun gear element 22, a ring gear element 26 and planet gears 24, which are coupled to a carrier element 25.The carrier element 25 rotatably mounts the planet gears 24, which are arranged in a meshing relationship with both the sun gear element 22 and the ring gear element 26, and is coupled to a rotatable shaft element 16. The planet gear set 30 comprises a sun gear element 32, a ring gear element 36, and planet gears 34, which are coupled to a carrier element 35. The planet gears 34 are arranged in a meshing relationship with both the sun gear element 32 and the ring gear element 36. The carrier element 35 is coupled to the rotatable shaft element 16. The planet gear set 40 comprises a sun gear element 42, a ring gear element 46, and planet gears 44, which are coupled to a carrier element 45. As shown, a first and second set of planet gears 44 are coupled to the carrier element 45. Thus, the planetary gear set 40 is a compound sun gear element-pinion gear-pinion gear-ring gear set.The carrier element 45 is rotatably coupled between couplings C1 52 and C2 54. The sun gear element 42 is rotatably coupled to the rotatable shaft element 16. The ring gear element 46 is rotatably coupled to the output element 92.

[0011] As used herein, couplings refer to torque transmission devices that can be selectively engaged in response to a control signal and that can be any suitable devices, including, for example, single or compound plate couplings or packs, one-way couplings, band couplings, and brakes. A hydraulic circuit 72 is designed to control the engagement states of each of the couplings with hydraulic pressurized fluid supplied by an electrically driven hydraulic pump 70, which is functionally controlled by the controller 5. Couplings C2 54 and C4 58 are hydraulically engaged rotary friction couplings. Couplings C1 52, C3 56, and C5 50 are hydraulically controlled brake devices that can be fixed to a gearbox 55.Each of the clutches C1 52, C2 54, C3 56, and C4 58 is hydraulically engaged using hydraulic pressure fluid, which in this embodiment is supplied by the hydraulic control circuit 72. The hydraulic circuit 72 is functionally controlled by the controller 5 to activate and deactivate the aforementioned clutches, to supply hydraulic fluid for cooling and lubricating components of the transmission, and to supply hydraulic fluid for cooling the first and second torque motors 60 and 62. Hydraulic pressure in the hydraulic circuit 72 can be determined by measurement using a pressure sensor(s), by estimation using onboard algorithms, or by other suitable methods.

[0012] The first and second torque machines 60 and 62 are three-phase AC motor / generator machines, each comprising a stator, a rotor, and a resolver. The motor stator for each of the torque machines 60 and 62 is fixed to an outer section of the gearbox 55 and comprises a stator core with helical electrical windings extending from it. The rotor for the first torque machine 60 is supported on a hub-plate gear, which is mechanically attached to a hollow shaft 18 coupled to the first planetary gear set 20. The rotor for the second torque machine 62 is fixed to a hollow shaft hub 19, which is mechanically attached to the second planetary gear set 30.Each resolver is connected, both signal-wise and functionally, to the gearbox power converter control module (TPIM) 82, and each detects and monitors the rotational position of the resolver rotor relative to the resolver stator, thereby monitoring the rotational position of the respective first and second torque machines 60 and 62. Additionally, the signals output by the resolvers can be used to determine the rotational speeds of the first and second torque machines 60 and 62.

[0013] The output element 92 of the transmission 10 is rotatably connected to the final drive 90 to supply output power to the final drive 90, which is transmitted to one or more vehicle wheels via a differential or transaxle assembly or other suitable device. The output power at the output element 92 is characterized in terms of output speed and output torque. A transmission output speed sensor 93 monitors the speed and direction of rotation of the output element 92. Each of the vehicle wheels is preferably equipped with a sensor configured to monitor the wheel speed and thus determine the vehicle speed and absolute and relative wheel speeds for brake control, traction control, and vehicle acceleration management.

[0014] The input torque from the power machine 12 and the motor torques from the first and second torque machines 60 and 62 are generated as a result of energy conversion from fuel or electrical potential stored in the electrical energy storage device (ESD) 85. The battery 85 is coupled to the TPIM 82 via the high-voltage DC electrical bus 84, which preferably includes a contactor that allows or prohibits the flow of electrical current between the battery 85 and the TPIM 82. The TPIM 82 preferably comprises a pair of power converters and respective motor control modules configured to receive torque commands and control the converter states accordingly, thus providing motor drive or recuperation functionality to comply with the motor torque commands.The power converters comprise complementary three-phase power electronics, each including a plurality of insulated-gate bipolar transistors for converting DC power from battery 85 into AC power to drive one of the first and second torque machines 60 and 62, respectively, by high-frequency switching. The insulated-gate bipolar transistors form a switching power supply configured to receive control commands. There is one pair of insulated-gate bipolar transistors for each phase of each of the three-phase electric machines. The states of the insulated-gate bipolar transistors are controlled to provide mechanical motor drive power generation or electrical energy recuperation functionality.The three-phase converters receive or supply direct current (DC) electrical energy via DC transmission conductors 27 and convert it into or from three-phase alternating current (AC) energy, which is routed to or from the first and second torque machines 60 and 62 for operation as motors or generators, respectively, via transmission conductors. The TPIM 82 transmits electrical energy to and from the first and second torque machines 60 and 62 through the power converters and respective motor control modules in response to the motor torque commands. Electrical current is transmitted to and from the battery 85 via the high-voltage electrical bus 84 to charge and discharge the battery 85.

[0015] Controller 5 is linked to various actuators and sensors in the powertrain system via a communication link 15, both signal-wise and functionally, to monitor and control the operation of the powertrain system. This includes synthesizing information and inputs and executing algorithms to control actuators and thus achieve control objectives related to fuel economy, emissions, performance, drivability, and the protection of components, including the batteries of battery 85 and the first and second torque motors 60 and 62. Controller 5 is a component of the vehicle's overall controller architecture and provides coordinated system control of the powertrain system.The controller 5 can comprise a distributed control module system containing individual control modules, including a monitoring control module, a power unit control module, a transmission control module, a battery pack control module, and the TPIM 82. A user interface 13 is preferably connected via signals to a plurality of devices through which a vehicle operator controls and directs the operation of the powertrain system. The devices preferably include an accelerator pedal 112, an operator brake pedal 113, a transmission range selector 114 (PRNDL), and a vehicle speed control system 116. The transmission range selector 114 can have a discrete number of operator-selectable positions that indicate the direction of the vehicle's intended movement by the operator and thus specify the preferred direction of rotation of the output element 92, either forward or reverse.It should be noted that a vehicle may, due to a rollback caused by its position, e.g., on a hill, move in a direction other than the specified direction of movement intended by the operator. The user interface 13 may comprise a single device, as shown, or alternatively, it may comprise multiple user interface devices directly connected to individual control modules.

[0016] The aforementioned control modules communicate with other control modules, sensors, and actuators via the communication link 15, which enables structured communication between the various control modules. The specific communication protocol is application-specific. The communication link 15 and suitable protocols ensure robust message transmission and interfaces for multiple control modules between the aforementioned control modules and other control modules that provide functionality such as anti-lock braking, traction control, and vehicle stability. Multiple communication buses can be used to improve communication speed and provide a degree of signal redundancy and integrity, including direct connections and serial peripheral interface (SPI) buses.Communication between individual control modules can also be achieved using a wireless connection, e.g., a short-range wireless communication bus. Individual devices can also be directly connected.

[0017] Control module, module, control, controller, control unit, processor and similar terms mean any of or various combinations of one or more of an application-specific integrated circuit(s) (ASIC), an electronic circuit, a central processing unit (preferably a microprocessor), and associated memory and storage (read-only memory, programmable read-only memory, random access memory, hard disk memory, etc.).The controller includes one or more software or firmware programs or routines, a combinational logic circuit, an input / output circuit and input / output devices, suitable signal conditioning and buffering circuitry, and other components to provide the described functionality. Software, firmware, programs, instructions, routines, code, algorithms, and similar terms mean any set of instructions executable by a controller, including calibrations and lookup tables. The control module has a set of control routines that are executed to provide the desired functions.Routines are executed, for example by a central processing unit, to monitor inputs from sensors and other networked control modules and to perform control and diagnostic routines to manage the operation of actuators. Routines can be executed at regular intervals, for example every 3, 125, 6, 25, 12.5, 25, and 100 milliseconds, during continuous operation of power machines and vehicles. Alternatively, routines can be executed in response to the occurrence of an event.

[0018] The powertrain 100 is designed to operate in one of a plurality of powertrain states, encompassing a plurality of transmission ranges and engine states, to generate torque and transmit it to the final drive 90. The engine states include an ON state, an OFF state, and a fuel-off-coupling (FCO) state. When the engine is in the OFF state, it is not supplied with fuel, does not ignite, and does not rotate. When the engine is in the ON state, it is supplied with fuel, ignites, and rotates. When the engine is in the FCO state, it rotates but is not supplied with fuel and does not ignite.The ON state of the engine can further include an all-cylinder state (ALLE), in which all cylinders are fueled and fire, and a cylinder deactivation state (DEAC), in which some cylinders are fueled and fire, and the remaining cylinders are not fueled and do not fire. The transmission ranges include multiple ranges of neutral, fixed gear, variable mode (EVT mode), electric vehicle (EV#), and transition (EV transition state and pseudogear#), achieved by selectively activating clutches C1, C2, C3, C4, and C5. A pseudogear range is a variable mode transmission range in which the torque delivered by the transmission 10 equals the input torque from the engine 12, taking into account torque losses associated with torque-consuming components at the input element 14.The pseudo-gear ranges are primarily used as intermediate gear ranges during shifts between the EVT mode ranges. Table 1 shows a plurality of gear ranges and engine states for operating the 100-series powertrain. Table 1 Area Power machine condition C1 C2 C3 C4 C5 Neutral 1 ON (ALL / DEAC / FCO) / OFF Neutral 2 ON (ALL / DEAC / FCO) / OFF x Neutral 3 ON (ALL / DEAC / FCO) / OFF x pseudoGang 1 ON (ALL / DEAC / FCO) / OFF x pseudoGang 2 ON (ALL / DEAC / FCO) / OFF x Neutral OUT OF x EVT mode 1 ON (ALL / DEAC / FCO) / OFF x x EVT mode 2 ON (ALL / DEAC / FCO) / OFF x x EVT mode 3 ON (ALL / DEAC / FCO) / OFF x x EVT mode 4 ON (ALL / DEAC / FCO) / OFF x x EV transition state 1 OUT OF x x EV transition state 2 OUT OF x x Gear 1 ONE(ALL / DEAC / FCO) x x x Gear 2 ONE(ALL / DEAC / FCO) x x x Gear 3 ONE(ALL / DEAC / FCO) x x x EV1 OUT OF x x x EV2 OUT OF x x x EV3 OUT OF x x x EV4 OUT OF x x x EV transition state 3 OUT OF x x x Neutral ON (ALL / DEAC / FCO) / OFF x x pseudoGang 3 ON (ALL / DEAC / FCO) / OFF x x Neutral OUT OF x x Neutral OUT OF x x

[0019] A control scheme is executed to identify extrema, i.e., maximum and minimum torques or accelerations, that a target component of interest can transport or generate while subject to constraints imposed by a powertrain system to control its operation, with such a powertrain system referring to Fig.The procedure is described in section 1. It involves generating a target component equation that expresses a relationship for a torque or rotational speed / acceleration of a component of interest, subject to linear constraints. These linear constraints can be transformed into equations representing lines.

[0020] Fig.Figure 2 comprises a graph 200, which represents a plurality of independent variables and constraints and dependent variables and constraints in relation to the first and second independent variables X1 and X2, respectively, where X1 is shown on the horizontal axis 201 and X2 is shown on the vertical axis 203. In one embodiment, X1 represents the rotational speed of the first torque machine 60, i.e., Na, and X2 represents the rotational speed of the second torque machine 62, i.e., Nb. Variable X1 has limits X1-min 202 and X1-max 204, and variable X2 has limits X2-min 202 and X2-max 204. A third independent variable X3 can be plotted in a third dimension.

[0021] An objective function can be determined in relation to the first, second, and third independent variables X1, X2, and X3. The objective component of interest, Y1, can be represented by an objective component equation, which has the following form: Y1=aX1+bX2+cX3+d where Y1 represents the target component of interest, e.g. a rotational speed / acceleration of one of the components of the powertrain system; a, b, c and d are known scalar values; X1, X2, and X3 are independent variables representing speed equations assigned to the independent variables with the highest priority in the system, e.g., speeds of the first and second torque machines 60 and 62, and the power machine 10. Independent variables X1, X2, and X3 are subject to the following constraints: X1_min≤X1≤X1_max; X2_min≤X2≤X2_max; and X3_min≤X3≤X3_max.

[0022] Additionally, there can be linear constraints that are dependent variables. In one embodiment, the relationship described in Eq. 1 is subject to dependent linear variables Y2, Y3, and Y4, as follows: Y2=a2*X1+b2*X2+c2*X3+D2 Y3=a3*X1+b3*X2+c3*X3+D3 Y4=a4*X1+b4*X2+c4*X3+D4 where the terms a2, a3, a4, b2, b3, b4, c2, c3 and c4 are scalar values ​​specific to the system.

[0023] The dependent linear variables Y2, Y3 and Y4 are subject to restrictions as follows: Y2_min≤Y2=a2*X1+b2*X2+c2*X3+D2≤Y2_max; Y3_min≤Y3=a3*X1+b3*X2+c3*X3+D3≤Y3_max; and Y4_min≤Y4=a4*X1+b4*X2+c4*X3+D4≤Y4_max.

[0024] Constraints are shown for the dependent linear variables, which include Y2_min 210, Y2_max 212, Y3_min 214, Y3_max 216, Y4_min 218, and Y4_max 220. The aforementioned constraints for the dependent linear variables Y2, Y3, and Y4 represent dependent component torque and / or acceleration constraints, characterized by linear component equations, each with minimum and maximum limits. X1, X2, and X3 represent three independent actuators, also characterized by minimum and maximum limits. Thus, a solution to find minimum and maximum values ​​for the target component of interest, Y1, can be visualized as intersecting pairs of lines, as shown in Fig.Figure 2 is shown. The minimum and maximum values ​​for the target component of interest Y1 225 are applied to determine limits for operating a system that is subject to the linear constraints imposed by various elements of the system.

[0025] Extrema for the target component of interest Y1 225, i.e., Y1_min and Y1_max, can be found at the intersections of the lines representing constraints on the dependent linear variables Y2, Y3, Y4 and the independent variables X1, X2, and X3, as shown in Fig.Figure 2 shows that the intersection points of the lines include points 230 to 257. Therefore, evaluating and selecting the extrema Y1_min and Y1_max can be computationally demanding because each evaluation of a new intersection point of a subset of planes is equivalent to a linear transformation, and yet another linear transformation is necessary to check whether the point in question violates any of the other restrictions.

[0026] Fig. Figure 3 schematically shows a process 300 applied to linear constraints encompassing independent variables X1, X2, and X3, and constraints on the dependent linear variables Y2, Y3, and Y4. The process 300 is executed to determine extrema, i.e., Y1_min and Y1_max, relative to these linear constraints. Table 2 serves as a key to... Fig.3 is specified, where the numbered blocks and the corresponding functions are executed as follows. Table 2 BLOCK BLOCK CONTENTS 302 Collect inputs - 1 objective function in the form of component equations - 3 component equations, each with minimum and maximum limits - 3 minimum and maximum actuator limits 304 All permutations evaluated? 305 Evaluate the next permutation 306 For the present permutation: Transform the objective function into the domain of the three active constraints of the present permutation, i.e., the three component equations. 307 Transformation results indicate whether the minimum or maximum of each of the three active constraints in this permutation must be chosen to maximize and minimize the target. 308 Value the transformed objective function at the maximizing and minimizing values ​​for the current permutation. 310 If the maximum value for the current permutation is less than RunningMax, then RunningMax = maximum value for the current permutation 312 If the minimum value for the current permutation is greater than RunningMin, then RunningMin = minimum value for the current permutation 320 Is RunningMax ≥ RunningMin? 322 The problem is unsolvable. 324 The problem is solvable: RunningMax = Max RunningMin = Min

[0027] Process 300 operates as follows. The inputs, comprising the aforementioned linear constraints on the independent variables X1, X2, and X3 and constraints on the dependent linear variables Y2, Y3, and Y4, are defined (302). The system identifies all permutations of the target component of interest Y1 based on the independent variables X1, X2, and X3 and the dependent linear variables Y2, Y3, and Y4, and then evaluates each permutation of the target component of interest Y1 in an iterative process. This includes determining whether all permutations of the target component of interest Y1 have been evaluated, or alternatively, whether an evaluation of any of the permutations of the target component of interest Y1 has resulted in a solution (304)(0). The permutations are forms of the equation for the target component of interest Y1 as follows. Y1=aX1+bX2+cX3+d

[0028] The permutations take into account the relationships between the independent variables X1, X2, and X3 and the dependent linear variables Y2, Y3, and Y4. Thus, exemplary permutations of the target component of interest, Y1, can take the following forms, where m, n, p, and r are generic constants that are determined specifically for each permutation and are therefore likely to be different for each permutation. Y1=mX1+nX2+pX3+r Y1=mX1+nX2+pY2+r Y1=mX1+nX2+pY3+r Y1=mX1+nX2+pY4+r Y1=mX1+nY2+pY3+r Y1=mX1+nY2+pY4+r Y1=mX1+nY3+pY4+r Y1=mX2+nY2+pY3+r Y1=mX2+nY2+pY4+r Y1=mX2+nY3+pY4+r Y1=mX3+nY2+pY3+r Y1=mX3+nY2+pY4+r Y1=mX3+nY3+pY4+r Y1=mY2+nY3+pY4+r

[0029] Each of Eqs. 5A–5N represents one of the permutations. The permutations represented by Eqs. 5A–5N are evaluated successively, which involves choosing one of the permutations represented by one of the preceding Eqs. 5A–5N as a present permutation (305). For the present permutation, the objective function is transformed into the domain of the three active constraints of the present permutation, i.e., the three component equations representing the chosen values ​​of the independent variables X1, X2, and X3 and the dependent linear variables Y2, Y3, and Y4 (306). The chosen constraints from the permutation are called active constraints.

[0030] The transformation results indicate whether the minimum or maximum of each of the three active constraints in the permutation must be chosen to maximize and minimize the objective function (307). The transformed objective function is evaluated at the maximizing and minimizing values ​​for the current permutation; that is, the transformed objective function is evaluated at the minimum and maximum values ​​of the active constraints (308). If a maximum value for the current permutation is less than a current maximum value (RunningMax), then the current maximum value is set equal to the maximum value for the current permutation (310). If a minimum value for the current permutation is greater than a current minimum value (RunningMin), then the current minimum value is set equal to the minimum value for the current permutation (312), and this iteration, which includes the evaluation of the current permutation, ends.

[0031] Once all permutations have been evaluated (304)(1), it is determined whether the current maximum value is less than the current minimum value (320). If this is the case (320)(0), the problem is considered unsolvable, i.e., there is no solution that satisfies all the constraints (322). If not (320)(1), the problem is solvable, and the current maximum value is applied as the maximum value for the objective function Y1, and the current minimum value is applied as the minimum value for the objective function Y1 (324).

[0032] Process 300 is executed to accurately and rapidly determine the maximum and minimum rotational speeds (or torques or accelerations) that a component can withstand, given known physical limits for other components exhibiting rotational speeds, torques, or accelerations related to those of the target component. Process 300 is applied to minimize the number of permutations while determining accurate minimum and maximum values ​​for the objective function. Such operation reduces the computational load compared to other algorithms that can be used to calculate maximum and minimum component rotational speeds subject to other known maximum and minimum component rotational speeds, where all components can be mathematically represented as functions of the same three independent variables.Examples of components can include engine speeds, engine torques, clutch speeds, clutch torques, clutch accelerations, power unit speeds, power unit torques, power unit accelerations, output shaft speed, and output torque. This is in reference to the... Fig. 2 and Fig. The three described methods can yield a result with 28 function evaluations and 13 linear transformations, whereas an implementation of the simplex method may require 448 function evaluations and 52 linear transformations to achieve a similar result for the same problem set. Thus, resource utilization is improved.

Claims

[1] Method for operating a powertrain system comprising a multi-mode transmission configured to transmit torque between a power machine, torque machines and a final drive, the method comprising: Determining an objective function for a target component of interest; Identifying constraints for a plurality of independent and dependent variables; Evaluating a plurality of permutations of the objective function based on the independent variables and the dependent linear variables; Evaluate the objective function to determine maximum and minimum values ​​for the objective function for each of the permutations; Determining overall minimum and maximum values ​​for the objective function based on the maximum and minimum values ​​for the objective function for each of the permutations; and Controlling the operation of the powertrain system to which the target component of interest is assigned, based on the overall minimum and maximum values ​​for the objective function. [2] Method according to claim 1, wherein the evaluation comprises the plurality of permutations of the objective function with reference to the independent variables and the dependent variables: For each permutation of the objective function, transform the objective function into a domain that includes active restrictions of the permutation, where the active restrictions include chosen independent and dependent variables. [3] The method of claim 1, wherein the evaluation of the objective function to determine maximum and minimum values ​​for the objective function for each of the permutations comprises: Transforming the objective function into a domain that includes active restrictions on the permutation; and Evaluating the transformed objective function at the minimum and maximum values ​​of the active constraints for the current permutation. [4] The method of claim 3, further comprising setting a present maximum value equal to the maximum value for the present permutation if the maximum value for the present permutation is less than the present maximum value. [5] The method of claim 3, further comprising setting a present minimum value equal to the minimum value for the present permutation if the minimum value for the present permutation is greater than the present minimum value. [6] The method of claim 1, further comprising determining that a solution of the objective function for the target component of interest is not feasible if the minimum value for the objective function is greater than the maximum value for the objective function, based on the maximum and minimum values ​​for the objective function for all permutations. [7] Method according to claim 1, wherein determining the objective function for a target component of interest comprises determining an objective function for a rotational speed or an acceleration of a component of the powertrain system. [8] Method according to claim 7, wherein determining the objective function for an objective component of interest comprises determining an objective component equation according to the following relationship: Y1=aX1+bX2+cX3+d where Y1 represents an equation for the target component of interest, X1, X2 and X3 represent equations assigned to independent variables, and a, b, c and d are known scalar values. [9] Method according to claim 8, wherein X1 and X2 are the torque machines and X3 is the power machine. [10] Method according to claim 1, wherein evaluating the plurality of permutations of the objective function with reference to the independent variables and the dependent variables comprises evaluating permutations of the objective function that are subject to the restrictions of the independent variables and to the restrictions for the dependent linear variables.

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