A method for calibrating feedback gain of an LQI controller

Abstract

A method for calibrating feedback gains of an LQI controller implemented in an electronic control unit (25) operatively connected for controlling operation of a physical electrical or electromechanical device (26) of a dynamic physical system (28), in particular a vehicle powertrain system (4), wherein the method for calibrating the LQI controller comprises: obtaining values of various physical parameters of the dynamic physical system (28); substituting the obtained values of the physical parameters into a predetermined equation for calculating numerical values of individual terms of a P matrix, wherein the P matrix is a solution of an algebraic Riccati equation, and wherein the predetermined equation includes the physical parameters of the system (28); and calculating new feedback gains of the LQI controller based on a matrix equation based on an arbitrary chosen positive value of r, wherein the terms of the K matrix correspond to the feedback gains.

Description

Technical Field

[0001] This disclosure relates to a method for calibrating the feedback gain of a linear quadratic integrator (LQI) controller. This disclosure also relates to a dynamic physical system including an LQI controller.

[0002] The methods and systems according to this disclosure can be deployed in many types of implementations across a wide range of technical fields where low steady-state errors are required.

[0003] Furthermore, even though the methods and systems described in this disclosure are primarily concerned with hybrid electric powertrain systems for automobiles, the methods and systems are not limited to this particular embodiment, but can instead be used, installed, or implemented in many other types of embodiments having controllable devices (such as motors, actuators, generators, etc.). Background Technology

[0004] In the field of feedback controllers used to control almost any type of dynamic physical system with controllable devices, LQI controllers based on a state-space model representing the physical system are a well-known design.

[0005] LQI controller calibration is typically required during the initial startup of a physical system, and sometimes it is also related to the replacement or maintenance of system hardware (such as actuators, motors, clutches, etc.), as such replacement / maintenance may cause changes in the values ​​of relevant system parameters (such as inertia, damping constant, spring constant, friction, actuator speed, and acceleration). LQI controller calibration may also be desirable in cases of temporary and / or rapid changes in relevant control parameters, such as changes in ambient temperature, weather conditions, lighting conditions, road conditions, air quality, or a change in driver with different driving habits.

[0006] However, LQI controller calibration is often problematic for various reasons. For example, calibration using a trial-and-error approach by manually tuning the LQI controller can be complex and time-consuming, and may lead to performance degradation. Furthermore, in technical implementations with relatively limited memory and processing power, computer-aided calibration involving extensive matrix calculations may not be desirable.

[0007] Therefore, it is desirable to provide an improved LQI controller calibration. Summary of the Invention

[0008] The purpose of this disclosure is to provide a method and system to avoid the problems mentioned above. This purpose is achieved at least in part by the features of the independent claim. The dependent claims contain further improvements to the method and system.

[0009] According to a first aspect of this disclosure, a method is provided for calibrating the feedback gain of an LQI controller, the LQI controller being implemented in an electronic control unit operatively connected to the operation of a physical electrical or electromechanical device for controlling a dynamic physical system (particularly a vehicle powertrain), wherein the LQI controller is based on an augmented state-space model having the following form:

[0010]

[0011] B aug =[B 0] T C aug =[C 0]

[0012] The augmented state-space model is based on the following state-space model representing a dynamic physical system:

[0013]

[0014] y = Cx

[0015] Where x is the control system state vector, ε is the control system tracking error, u is the control system input, ref is the control system target reference value, y is the control system output, and A, B, and C represent matrices derived from the mathematical model of the dynamic physical system. The method for calibrating the LQI controller includes: obtaining values ​​of various physical parameters of the dynamic physical system; substituting the obtained physical parameter values ​​into a predetermined equation for calculating the values ​​of each term of the P matrix, where the P matrix is ​​a solution to the algebraic Riccati equation, and wherein the predetermined equation includes the physical parameters of the dynamic physical system; and based on the matrix equation... The new feedback gain of the LQI controller is calculated based on any chosen positive value of r, where each term of the K matrix corresponds to the feedback gain.

[0016] According to a second aspect of this disclosure, a dynamic physical system, particularly a vehicle powertrain system, is provided, comprising: physical electrical or electromechanical equipment; and an electronic control unit operatively connected to the physical electrical or electromechanical equipment, wherein the electronic control unit includes an LQI controller configured to control the operation of the physical electrical or electromechanical equipment, wherein the LQI controller is based on an augmented state-space model representing the dynamic physical system, wherein the augmented state-space model may have the following form:

[0017]

[0018] B aug =[B 0] T C aug =[C 0],

[0019] The augmented state-space model is based on the following state-space model representing the physical system:

[0020]

[0021] y = Cx,

[0022] Where x is the control system state vector, ε is the control system tracking error, u is the control system input, ref is the control system target reference value, y is the control system output, and A, B, and C represent matrices derived from the mathematical model of the dynamic physical system. The electronic control unit also includes a data storage device containing predetermined equations for calculating the values ​​of each term of the P matrix, where the P matrix is ​​a solution to an algebraic Riccati equation, and where the predetermined equations include the physical parameters of the system. The feedback gain of the LQI controller is configured to be calibrated by: obtaining values ​​of various physical parameters of the dynamic physical system; substituting the obtained physical parameter values ​​into the predetermined equations for calculating the values ​​of each term of the P matrix; and based on the matrix equations... The new feedback gain of the LQI controller is calculated based on any chosen positive value of r, where each term of the K matrix corresponds to the feedback gain.

[0023] In this way, LQI controller calibration can be performed with significantly less processing power because matrix calculations can be largely omitted, and the obtained parameter values ​​can be directly substituted into the equations used to calculate the terms of the P matrix. This allows for the rapid and simplified calculation of the P matrix, and subsequently the calculation of the new feedback gain, without first calculating, for example, a numerical version of the A matrix and transforming that matrix into a controllable canonical form. Therefore, the method for calibrating an LQI controller according to this disclosure is particularly advantageous in technical implementations with relatively limited memory and processing power (such as, for example, vehicle implementations).

[0024] For example, if vehicle cruise control is implemented via an LQI controller, this algebraic method can be used to determine the feedback gain of the LQI controller based solely on the vehicle's physical parameters and the functional requirements of the cruise control system. This allows for relatively straightforward recalibration of the LQI controller based on changes in environmental conditions, such as the estimated road friction coefficient. Specifically, parameters defining the functional requirements of cruise control, such as, for example, the maximum permissible vehicle acceleration, may need to be adjusted to account for changes in the road friction coefficient. This is achieved by simply calculating the new feedback gain of the LQI controller using the algebraic method defined above, where one or more physical parameters defining the functional requirements of the cruise control system are adjusted to reflect the newly estimated road friction coefficient.

[0025] In other words, the predetermined equations used to calculate the values ​​of each item in the P matrix include defining the physical parameters of the vehicle system and the functional requirements of the cruise control system, and the method involves: substituting updated values ​​of the physical parameters into the predetermined equations used to calculate the values ​​of each item in the P matrix; and based on the matrix equations... Calculate the new feedback gain of the LQI controller.

[0026] This can be performed by the vehicle computer without the need for trial-and-error tuning of the feedback gain, nor is it necessary to recalculate the algebraic Riccati equations, since the equations used to derive the individual terms of the P matrix are predetermined and include the relevant physical parameters that define the vehicle system and functional requirements.

[0027] Further advantages can be achieved by implementing one or more features of the dependent claims.

[0028] In some example embodiments, the P matrix is ​​a diagonal matrix of the following form:

[0029]

[0030] In some example embodiments, which can be combined with any one or more of the above embodiments, each equation used to compute terms of the P matrix is ​​a function of constants, available physical parameters of the dynamic physical system, other terms of the P matrix, and terms of the Q matrix. In other words, the derived equations of the P matrix can be computed based solely on the physical parameters of the physical system.

[0031] In some example embodiments, which can be combined with any one or more of the above embodiments, the physical parameters of the dynamic physical system are obtained manually by a user who is measuring, detecting, or estimating the values ​​of the physical parameters of the dynamic physical system, and / or by an electronic control unit that automatically measures, detects, or estimates the values ​​of the physical parameters of the dynamic physical system. Therefore, the calibration process may require some manual input unless the system autonomously determines the updated values ​​of the relevant physical parameters.

[0032] In some example embodiments, which can be combined with any one or more of the above embodiments, the step of calculating the feedback gain of the LQI controller does not involve matrix calculations of the numerical representation of matrix A of the dynamic physical system. This reduces the computational load on the CPU used to perform the calibration.

[0033] In some example embodiments that can be combined with any one or more of the above embodiments, the method further includes a setup phase of the LQI controller performed prior to the calibration of the feedback gain K, wherein the setup phase includes: determining terms of matrices A, B, and C in the form of equations expressed as 1s, 0s, and physical constants of the system, while omitting the step of transforming matrices A, B, and C into a controllable canonical form; determining a feedback control system with a linear quadratic integral (LQI) controller, the LQI controller outputting a system input u that minimizes the standard J, wherein... Where Q is a matrix and r is a scalar, and the LQI feedback controller includes the feedback gain; determine the characteristic equation of the control system; determine the transfer function of the control system, and subsequently determine the location of the poles of the transfer function; and use the algebraic Riccati equations: Derive the equations for each term in the Q and P matrices. The setup phase is typically performed only once and can be, for example, during the design phase of the physical system.

[0034] In some example embodiments that can be combined with any one or more of the above embodiments, the characteristic equation of the closed-loop control system has the following form:

[0035]

[0036] In some example embodiments, which can be combined with any one or more of the above embodiments, the equations for the terms of the P matrix are also derived based on the coefficients and constant terms of the characteristic polynomial of the closed-loop system in conjunction with the denominator of the transfer function. Therefore, the transfer function can be used to find the algebraic solution to the equations for the P matrix.

[0037] In some example embodiments that can be combined with any one or more of the above embodiments, the method further includes: determining the location of the poles of the transfer function by performing an inverse Laplace transform on the denominator of the transfer function and inputting the values ​​of any point of the step response of the transfer function G(s), thereby enabling the calculation of the natural frequency ω. n This gives the location of the poles of the transfer function. The location of the poles is typically needed to compute the equations for the terms of the P matrix.

[0038] In some example embodiments, which can be combined with any one or more of the above embodiments, the transfer function includes a damping ratio ζ, and wherein the damping ratio ζ is chosen to be equal to about 1.0, or exactly 1.0. A critically damped system is generally a good choice because it eliminates overshoot, thereby simplifying the control of the controllable device.

[0039] In some example embodiments that can be combined with any one or more of the above embodiments, the transfer function includes an inherent frequency w. n .

[0040] In some example embodiments that can be combined with any one or more of the above embodiments, the Q matrix is ​​a diagonal weight matrix of the following form:

[0041] In some example embodiments that can be combined with any one or more of the above embodiments, the step of transforming matrices A, B, and C into controllable canonical form is omitted so that the terms of matrices A, B, and C retain their original expressions as functions of detectable system parameters, such that the equations for calculating the terms of matrix P can be expressed as functions of detectable system parameters, thereby enabling easy calculation of new feedback gains, suitable for implementation in low-computational-consumption systems (such as, in particular, vehicle systems).

[0042] In some example embodiments that can be combined with any one or more of the above embodiments, the physical electrical or electromechanical equipment of the dynamic physical system is an actuator, motor, pump, light source or RF source or electric device.

[0043] In some example embodiments, which can be combined with any one or more of the above embodiments, the dynamic physical system is a vehicle system, specifically a vehicle powertrain, and more specifically a vehicle powertrain having a first motor operatively connected to a first portion of a jaw clutch, wherein an electronic control unit controls the rotational speed of the first portion of the jaw clutch for synchronization with the speed of a second portion of the jaw clutch, such that the first and second portions of the jaw clutch can switch smoothly and noiselessly from a disengaged state to an engaged state. Implementing an LQI controller for the jaw clutch to switch drive modes between series-parallel hybrid drive modes is advantageous because low steady-state error is required to ensure smooth and noiseless engagement, and because the engagement process is less time-sensitive.

[0044] In some example embodiments, which can be combined with any one or more of the above embodiments, the predetermined equations for calculating the values ​​of the individual terms of the P matrix include at least one parameter defining the functional requirements of the physical system. Therefore, according to this disclosure, the algebraic method for determining the feedback gain of the LQI controller based on the vehicle's physical parameters and the system's functional requirements not only guarantees stability but also guarantees that the control requirements are met.

[0045] In some example embodiments, which can be combined with any one or more of the above embodiments, the vehicle powertrain is implemented in a hybrid electric vehicle having an internal combustion engine driven by a first electric motor and a second electric motor driven by a second portion of a jaw clutch, wherein switching between the first and second portions of the jaw clutch from a disengaged state to an engaged state causes the hybrid electric vehicle to switch from series operation to parallel operation. Implementing an LQI controller for the jaw clutch to switch drive modes between series and parallel hybrid drive modes is advantageous because low steady-state error is required to ensure smooth and noiseless engagement, and because the engagement process is less time-sensitive.

[0046] In some example embodiments that can be combined with any one or more of the above embodiments, the physical parameters of the dynamic physical system are configured to be obtained manually by a user who is measuring, detecting or estimating the values ​​of the physical parameters of the dynamic physical system, and / or by an electronic control unit that automatically measures, detects or estimates the values ​​of the physical parameters of the dynamic physical system.

[0047] In some example embodiments that can be combined with any one or more of the above embodiments, the data memory further includes 1s, 0s, and terms in the form of matrices A, B, and C in the form of equations expressing the physical constants of the system, wherein matrices A, B, and C have not yet been transformed into controllable canonical form, wherein the LQI controller is configured to output a control system input u that minimizes the standard J, wherein Here, Q is a matrix and r is a scalar, where the equations of the terms of matrix Q are stored in a data memory.

[0048] In some example embodiments that can be combined with any one or more of the above embodiments, matrices A, B, and C stored in the data memory have not been transformed into controllable canonical form, and the terms of matrices A, B, and C thus retain their original expressions as functions of detectable system parameters, such that the equations for calculating the terms of matrix P can be expressed as functions of detectable system parameters, thereby enabling easy calculation of new feedback gains, suitable for implementation in low-computational-consumption systems (such as, in particular, vehicle systems).

[0049] In some example embodiments that can be combined with any one or more of the above embodiments, the predetermined equations for calculating the values ​​of the individual terms of the P matrix further include at least one parameter defining the functional requirements of the physical system, wherein the feedback gain of the LQI controller is configured to be calibrated by: obtaining values ​​of various physical parameters of the dynamic physical system and the value of at least one parameter defining the functional requirements of the physical system; substituting the obtained values ​​of the physical parameters and functional requirements into the predetermined equations for calculating the values ​​of the individual terms of the P matrix; and subsequently based on the matrix equations... The new feedback gain of the LQI controller is calculated. Therefore, according to this disclosure, the algebraic method for determining the feedback gain of the LQI controller based on the vehicle's physical parameters and the system's functional requirements not only guarantees stability but also guarantees that the control requirements are met.

[0050] This disclosure also relates to a hybrid electric vehicle having a vehicle powertrain system, comprising: a jaw clutch having a first portion and a second portion; an internal combustion engine droopingly connected to a first electric motor operatively connected to the first portion of the jaw clutch; a second electric motor droopingly connected to the second portion of the jaw clutch; and a dynamic physical system as described above.

[0051] In some example embodiments, which can be combined with any one or more of the above embodiments, the switching of the first and second portions of the jaw clutch from a disengaged state to an engaged state is configured to switch the operation of the hybrid electric vehicle from series operation to parallel operation.

[0052] Other features and advantages of the invention will become apparent when examined in light of the appended claims and the following description. Those skilled in the art will recognize that different features of this disclosure can be combined to create embodiments other than those explicitly described above and below, without departing from the scope of this disclosure. Attached Figure Description

[0053] The methods and systems according to this disclosure will now be described in detail with reference to the accompanying drawings.

[0054] Figure 1A A side view of a vehicle with a hybrid electric drive system is shown schematically.

[0055] Figure 1B The layout of an example embodiment of a hybrid electric drive system is schematically shown.

[0056] Figure 2 The graphs showing the changes in speed and torque over time during the speed synchronization phase are shown.

[0057] Figures 3A to 3C show schematic diagrams of exemplary embodiments of a jaw clutch including a jaw clutch actuation mechanism.

[0058] Figures 4A to 4D show four different stages of tooth engagement.

[0059] Figure 5 The noise results of a laboratory test of clutch engagement are shown.

[0060] Figure 6A and Figure 6B The effect of drag torque on the tooth motion path during engagement is shown.

[0061] Figure 7 A two-degree-of-freedom (2DOF) torsion system is schematically illustrated.

[0062] Figure 8 A linear state feedback control system is shown.

[0063] Figure 9 The graph shows the speed change over time during the speed synchronization phase.

[0064] Figure 10 A linear state feedback control system with an LQI controller is shown.

[0065] Figure 11 The step response of a fourth-order system is shown.

[0066] Figure 12 The step response of a critically damped fourth-order system is shown.

[0067] Figure 13 The rotational speed status during the speed synchronization phase is shown.

[0068] Figure 14 The controller performance that meets the functional requirements is shown.

[0069] Figure 15 The controller performance is shown for different functional requirements.

[0070] Figure 16 The vibration isolation of the controller under different functional requirements is shown, where the thick dashed line represents when tsynch = 2 sec and the thin dashed line represents when tsynch = 1 sec.

[0071] Figure 17A and Figure 17B The main steps of a method according to two embodiments of this disclosure are illustrated schematically.

[0072] Figure 18 A general system according to this disclosure is illustrated schematically. Detailed Implementation

[0073] The various aspects of this disclosure will now be described in conjunction with the accompanying drawings, in order to illustrate and not limit the disclosure, wherein like reference numerals denote like elements, and variations of the described aspects are not limited to the embodiments specifically shown, but are applicable to other variations of the disclosure.

[0074] This disclosure relates to a method for calibrating an LQI controller, the method being provided for implementing a feedback control strategy to minimize one or more operating parameters of a physical system and a corresponding dynamic physical system including the LQI controller.

[0075] Typically, the advantages of LQI controllers are that they provide robust state feedback design and, due to the integral component, there is no steady-state error. This makes LQI controllers very useful, for example, in applications where steady-state error is unacceptable.

[0076] Therefore, the LQI calibration process disclosed herein can be implemented in many different types of physical systems in many different technical fields, such as, but not limited to, vehicles, avionics equipment, ships, power generators, etc.

[0077] One specific implementation of the LQI controller is used to control the speed synchronization of the jaw clutch before engagement, in order to provide a smooth and noiseless clutch engagement process.

[0078] The calibration of the LQI controller minimizes mechanical noise during engagement of the jaw clutch. Jaw clutches are used in various technical implementations to achieve selective torque transfer between the first and second portions of the jaw clutch.

[0079] The engagement of a dog clutch can occur, for example, during automatic shifting in a stepped transmission (e.g., an automatic single or dual clutch transmission or an automatic manual transmission (AMT)). Alternatively or additionally, the engagement of a dog clutch can occur when switching a conventional dog clutch from a disengaged state to an engaged state. A conventional dog clutch, as used herein, refers to a dog clutch having a first clutch portion rotatably fixed to a first shaft and a second clutch portion rotatably fixed to a second shaft separated from but aligned with the first shaft. Engagement of a dog clutch can be achieved by axially sliding an outer clutch engagement sleeve to selectively set the first and second clutch portions to a rotatably connected state. Alternatively, engagement of a dog clutch can be achieved, for example, by axially sliding the first clutch portion relative to the first shaft to selectively set the first and second clutch portions to a rotatably connected state.

[0080] Using a relatively simple and robust jaw clutch for selective torque transfer between the power source and the power-consuming device provides a low-cost overall design, and the calibration process of the LQI controller that controls the clutch engagement process can provide virtually interference-free, low-noise engagement with almost no wear, thus providing longer service life, reduced maintenance, and increased user satisfaction.

[0081] The method for calibrating the LQI controller and the corresponding dynamic physical system including the LQI controller will be described in more detail below in an exemplary embodiment of a jaw clutch in the powertrain of a hybrid electric vehicle. However, the methods and systems according to this disclosure are not limited to this particular exemplary embodiment, but can be implemented alternatively in various technical systems.

[0082] In order to set up the jaw clutch and vehicle powertrain according to this exemplary embodiment in the context, Figure 1A A car 1 with a powertrain 4 is schematically shown. The powertrain 4 includes a propulsion power source 2, such as an internal combustion engine and an electric motor, which is driven to the drive wheels 3 of the car 1 via a transmission.

[0083] refer to Figure 1B A more detailed description of the example powertrain 4 of the hybrid electric vehicle 1 is provided. The powertrain 4 of the hybrid electric vehicle includes an internal combustion engine (ICE) 5 drivenly connected to a first electric motor P1, which is arranged to charge a high-voltage battery 7, such as... Figure 1B As indicated by charging arrow 9. The powertrain 4 also includes a second motor P2, which is powered by the battery 7 and driven to the wheels 3 via a transmission 8 for converting the rotational speed of the second motor P2 into a suitable wheel speed. The second motor P2 is powered by electricity from the battery 7. Figure 1B The discharge arrow 10 indicates the direction.

[0084] For efficiency during driving, at high speeds, the ICE 5 can be driven to engage with the wheels 3 via a dog clutch 6, thereby switching the vehicle from series hybrid mode to parallel hybrid mode.

[0085] like Figure 1B As schematically shown, the internal combustion engine 5 can be connected to a first electric motor P1 via a dual-mass flywheel (DMF) 11. The first electric motor P1 is connected to a first portion 6a of a jaw clutch 6, and a second portion 6b of the jaw clutch 6 is connected to a second electric motor P2. A battery 7 supplies power to the second electric motor P2. Depending on the vehicle size, the power level of the second electric motor P2 can be, for example, in the range of 50kW to 300kW, particularly in the range of 100kW to 150kW. An ICE (Integrated Circuit Vehicle) can have a similar power range.

[0086] Experimental results show that if the speed difference between the two sides of the jaw clutch 6, namely the first part 6a and the second part 6b, is below a certain level, there will be no clonk noise during engagement. In this exemplary embodiment of the present disclosure, the designed state feedback linear quadratic integral (LQI) controller provides a synchronous torque request to the first motor P1, thereby matching the speed of the first part 6a of the jaw clutch 6 with the speed of the second part 6b of the jaw clutch 6 under the interference of the combustion torque from the internal combustion engine 5.

[0087] Typically, LQI controllers are tuned through trial and error or through extensive computationally intensive matrix calculations. However, this disclosure proposes an algebraic method in which the feedback gain of the LQI controller is calculated solely based on the system's physical parameters, the time required for speed synchronization, and an acceptable value for the speed difference derived from experimental results. This approach minimizes the need for manual tuning and allows for the provision of controller gain for transmissions of any size and version by modifying only parameter values ​​and functional requirements.

[0088] When driving, vehicle 1 can operate in different driving modes. For example, according to Figure 1B The powertrain system of the example hybrid electric vehicle shown can operate in the following drive modes:

[0089] 1. Pure electric

[0090] 2. Series hybrid power

[0091] 3. Parallel hybrid power

[0092] In pure electric drive mode, ICE 5 is off, the jaw clutch 6 is engaged, and the second motor P2 provides drive torque to wheels 3. The discharge power flow from battery 7 to the second motor P2 is indicated by arrow 10.

[0093] When the state of charge of battery 7 is low, the powertrain 4 of vehicle 1 can switch to series hybrid drive mode. Then, the first motor P1 can draw power from battery 7 to temporarily operate as an engine starter motor. Once ICE 5 is running, ICE 5 can be used, for example, as a range extender, and battery 7 is charged by the electrical energy supplied and generated by the first motor P1.

[0094] Furthermore, when the vehicle speed exceeds a certain value v1, for efficiency, the powertrain 4 of vehicle 1 can be set to parallel hybrid drive mode. In parallel hybrid drive mode, the jaw clutch 6 is engaged, thereby drivingly connecting the ICE 5 to the wheels 3. Switching the drive mode from pure electric or series hybrid drive mode to parallel hybrid drive mode involves three distinct stages.

[0095] 1. Speed ​​synchronization

[0096] 2. Engagement of the jaw clutch

[0097] 3. Ramp up torque

[0098] In the first stage of "speed synchronization", the first motor P1 is controlled. Figure 1B The rotational speed ω of the main side 6a of the toothed clutch 6 p To match the rotational speed ω of the driven side 6b of the jaw clutch 6. s At the end of stage 1, the speed difference between the primary side 6a and the secondary side 6b of the jaw clutch 6, i.e., ω p and ω s The speed difference between the two phases determined the noise level generated during phase 2, “dog clutch engagement.” The experimental results presented in this disclosure demonstrate the limitation on the speed difference at the end of phase 1, which would result in noiseless dog clutch engagement.

[0099] To minimize the speed difference during engagement of the jaw clutch, the torque request to the first motor P1 is calculated by a feedback controller designed later in this disclosure. Figure 1B As can be seen, the main side 6a of the jaw clutch 6 consists of two inertial components, namely, the ICE and the first motor P1 connected by an elastic coupling in the dual-mass flywheel 11. This disclosure provides an algebraic method for calculating the weighting matrix of the LQI controller based on the algebraic Riccati equations, while clearly defining the weighting matrix based on the physical parameters of the two inertial systems, the required speed synchronization time, and the speed difference constraint at the end of speed synchronization. This novel method minimizes the need for manual tuning of the controller while satisfying stability and noise suppression requirements.

[0100] Figure 2 This illustrates the first two phases of mode switching during vehicle acceleration. Before time point t1, the vehicle speed is less than a specific value v. init The first motor P1 operates in generator mode and applies a constant braking torque to the engine. At time t1, the vehicle speed is equal to v. initAnd the speed synchronization phase begins. During the speed synchronization phase, the braking torque of the first motor P1 is temporarily increased until the desired engine speed is reached at time t2, which allows the primary and secondary sides of the jaw clutch 6 to engage smoothly and without noise. The braking torque during the speed synchronization phase is calculated by the feedback controller explained later in this disclosure.

[0101] Speed ​​synchronization between the master and slave sides can be achieved alternatively by simply cutting off the fuel of the ICE 5 and reducing the speed of the master side 6a of the jaw clutch 6 under friction, but using the braking torque from the first motor P1 to achieve speed synchronization is more controllable.

[0102] Speed ​​synchronization time t synch Assume that at time t2, the velocity ω of the driven side 6b of the jaw clutch 6 is... s The hybrid electric powertrain accurately predicts that at time t2, the vehicle speed equals v1. This is based on the vehicle acceleration a. veh Synchronization time t synch The duration, the vehicle speed v1 at time point t2, and the vehicle speed v at time point t1. init It can be calculated using the following formula:

[0103] v init =v1-a veh t synch (1)

[0104] In this disclosure

[0105] t synch =2sec (2)

[0106] Since speed synchronization is not as time-sensitive for this particular type of transmission, two seconds is a reasonable choice. Once the speed synchronization phase is complete, the second phase, "dog clutch engagement," begins. If the speeds are perfectly matched, there will be minimal noise and wear in the transmission.

[0107] Speed ​​difference ω diff Defined as

[0108] ω diff =ω p -ω s (3)

[0109] To minimize noise and wear, ω is used before the jaw clutch engages. diff It must be within certain limits, as discussed in the later parts of this disclosure.

[0110] After the jaw clutch engages, the torque at wheel 3 will be the sum of the torques from ICE 5, the first motor P1, and the second motor P2. To maintain smooth acceleration of the vehicle during drive mode switching, it may be desirable to manage the torque from all sources to meet the torque requirements for constant acceleration throughout the drive mode switching process.

[0111] From the above, we can conclude that the first stage of drive mode switching, namely speed synchronization, is not as time-critical. Based on the power available for speed synchronization from the first motor P1, the synchronization time t... synch This will change, thus altering the speed v when speed synchronization should begin. init Unlike the transmissions in conventional powertrain systems, where drive mode switching and speed synchronization are time-critical issues for meeting torque demands, the controller design in this disclosure focuses on speed synchronization and the engagement of a noiseless and wear-free jaw clutch.

[0112] Figure 3A shows a schematic diagram of an exemplary embodiment of the actuation mechanism 12 of the jaw clutch 6. In this exemplary embodiment, the main side 6a of the jaw clutch includes a sleeve 13 and a hub 14, which are shown in an enlarged view in Figure 3B. The hub 14 has externally axially extending teeth 16 that connect to internally axially extending teeth 17 of the sleeve 13 for enabling the sleeve 13 to move axially relative to the hub 14, which is rotatably fastened to the input shaft of the first motor P1 via a spline connection 15.

[0113] The disengagement side of the jaw clutch 6 is shown in an enlarged view in FIG. 3C, and the driven side 6b of the jaw clutch 6 includes external teeth 18, which are configured to engage internal teeth 17 of the sleeve 13 when the sleeve 13 is axially displaced toward the driven side of the jaw clutch 6 during engagement. A second motor P2 is connected to the driven side of the jaw clutch 6 via a transmission 8, as shown in FIG. 3A and 3C.

[0114] Referring to Figure 3A, the axial displacement of the sleeve 13 toward and away from the driven side of the jaw clutch 6 serves to position the jaw clutch 6 in an engaged or disengaged state, for example, by an electric shift motor that drives the linearly movable shift guide 21. The rotational-linear motion conversion between the shift motor and the shift guide can be achieved, for example, by the shift finger 22. Furthermore, the axial displacement of the sleeve 13 can be achieved by means of a shift fork 23, which is fastened to the shift guide 21 and engages the sleeve 13.

[0115] Figures 4A to 4D illustrate the forces and velocities involved on the master and slave teeth during the engagement process, with Figure 4A showing the disengaged jaw clutch, Figure 4B showing the jaw clutch during movement toward engagement, Figure 4C showing the jaw clutch during tooth impact, and Figure 4D showing the jaw clutch in the engaged state.

[0116] Figure 4A shows the relative positions of the teeth of the jaw clutch disengaged at the end of the speed synchronization phase. The main teeth (i.e., teeth 17 of sleeve 13) rotate at a speed ω. p Move, and from the tooth (i.e., from tooth 18 on side 6b) at a rotational speed ω. s move.

[0117] When the shift motor 20 rotates in the shifting direction indicated by the rotation arrow in Figure 3A, the shift fork 23 will move at an axial velocity The movable sleeve 13 is shown in Figure 4B. This can be achieved by assuming the tooth 18 is stationary and the main tooth 17 has a velocity difference ω defined by Equation 3. diff Rotation simplifies the speed difference.

[0118] Due to the principal side velocity ω p Controlled by a feedback controller and ω s Proportional to vehicle speed, therefore it can be assumed that during the short duration of the engagement phase, ω diff It will be constant.

[0119] When the primary tooth 17 is at time t imp After moving a certain distance, the master tooth 17 will contact the slave tooth 18, as shown in Figure 4C. According to t imp axial velocity and speed difference ω diff The impact force F perpendicular to the impact surface imp It will be generated on both types of teeth. The impact force will be related to ω. diff (t imp )and It is directly proportional to the noise and wear.

[0120] The impact force F shown in Figure 4C imp axial component F xi The resistance to engagement is overcome by the shift motor 21 shown in Figure 3A. Once the master tooth 17 has moved a certain distance and engaged with the slave tooth 18, at time t... end Then, the third stage of the drive mode switching, namely the "torque increase" stage, can begin.

[0121] At time t imp When teeth 17 and 18 collide, the tangential component of the impact force F yi This will affect the rotational speed ω of the teeth.p and ω s This effect can be seen through the angular acceleration α of the teeth. imp To measure. α during impact. imp It can be defined as:

[0122] α imp =constant F yi (4)

[0123] acceleration α imp The maximum value will be at time t imp place and by express.

[0124] During normal vehicle operation, ω diff (t synch The ω must be very close to zero before the jaw clutch engages. This is achieved through different ω values. diff (t synch Laboratory tests were conducted by engaging a jaw clutch at the specified value and measuring the maximum instantaneous angular acceleration and noise from the jaw clutch. The results are shown in... Figure 5 middle.

[0125] from Figure 5 It can be seen that if α imp Above a certain value, a clonk sound is heard during engagement. As shown in Equation 4, the higher the α... imp This means a higher impact force F imp Higher impact force F imp Another higher ω diff The result. From Figure 5 It can be seen that if ω diff (t synch If the rpm is between -20 and 5, there is most likely to be no clicking sound.

[0126] exist Figure 5 During the laboratory test shown, the main side velocity ω p Uncontrolled, therefore from time t synch to t end Rotational speed difference ω diff This is due to the drag torque in the transmission, rather than being constant.

[0127] Ideally, Figure 5 The pattern of points in the middle should be based on zero ω. diff Centered on, because α imp It is ω diff A function of the absolute value of .

[0128] Figure 6A and 6BThe axial movement of the main teeth is shown separately under conditions of no drag torque and with drag torque. For example... Figure 6A As shown, if there is no drag torque in the transmission, then ω diff (t synch ) will equal ω diff (t imp Therefore, the impact force will be the same, and with ω diff The direction is irrelevant. On the other hand, Figure 6B The effect of drag torque is shown, where the drag torque on the master or slave side can be represented by the directional drag torque.

[0129] The effect of directional drag torque will depend on ω diff The direction differs. For Figure 6B As shown in the drag torque diagram, ω diff (t imp Less than ω diff (t synch ), and ω diff Compared to the case in the upward direction, ω diff The downward direction results in a lower F. imp and α imp Therefore, if ω diff In the downward direction, the noise generated by the impact will be lower.

[0130] For the purposes of this disclosure, based on Figure 5 as well as Figure 6A and Figure 6B It is safe to assume that

[0131]

[0132] In order to reduce the main speed ω before the jaw clutch 6 can engage p To achieve the correct value, torque control is used with the first motor P1. However, due to the time-varying nature of the dual-mass flywheel 11 and the motor torque, this is not a simple control task. To ensure fast, accurate, and robust control of the main speed, a controller is designed in the following sections.

[0133] The components on the main side of the jaw clutch can be made of, for example Figure 7 The diagram illustrates a two-degree-of-freedom (2DOF) torsional system.

[0134] The torque from ICE 5 acts on one side of the dual-mass flywheel 11, and the torque from the first motor P1 acts on the other side of the dual-mass flywheel 11. In the middle are several inertial components, which can be grouped together into two inertial components connected via a torsion spring and a damper. These two inertial components are...

[0135] Jp =J Hub&Sleeve +J P1rotor +J DMF secondary

[0136] J e =J crankshaft +J Flywheel +J DMF primary (6)

[0137] The torsion spring and damper of the DMF are used in these two inertial elements J p and J e The applied torque T DMF for

[0138] T DMF =d(ω) p -ω e )+k(θ p -θ e (7)

[0139] Define Δθ such that

[0140] Δθ=θ p -θ e (8)

[0141] For inertial component J p and J e Applying Newton's second law, we obtain a set of two differential equations describing the system's velocity dynamics.

[0142]

[0143] Differentiating both sides of equation 8, we get

[0144]

[0145] Combining the differential equations in equations 9 and 10, by setting the disturbance T ICE =0, can obtain Figure 7 The linear time-invariant state-space model of the mechanical system in the figure makes

[0146]

[0147] y = Cx (11)

[0148] Where the state vector x is

[0149] x=[ω p Δθ ω e ] T (12)

[0150] as well as

[0151]

[0152] B = [1 / J] p 0 0] T =[b 0 0] T (14)

[0153] The constants a1 to a4 in Equation 13 and the constant b in Equation 14 are positive numbers and depend on the physical constants of the system.

[0154] The vector C in equation 11 will be

[0155] C = [1 0 0] (15)

[0156] Because only the first state ω is controlled during the speed synchronization phase. p That is, the speed of the main lateral teeth.

[0157] To synchronize the speed of the main side of the jaw clutch, the system input u will be the torque request from the first motor P1, therefore

[0158] u = T P1 (16)

[0159] A linear state feedback controller was chosen because it can be easily implemented in existing transmission control software. Figure 8 In the diagram, the controlled object model is shown on the right, and the state feedback controller is indicated on the left by a dashed line, where K is the linear state feedback gain.

[0160] pass Figure 8 The torque request of the first motor P1 in Equation 16 can be rewritten as follows:

[0161] u = -Kx (17)

[0162] In order to come from T ICE The velocity difference ω in equation 3 is affected by the interference. diff Minimize the first state ω of the system in Equation 12. p ω needs to be reached pref The target speed shown is as follows: Figure 9 As shown.

[0163] from Figure 9 It can be seen that at time t synch ω pref equal to ω s Therefore, if ω p Reaching ω pref Then at time t synch Then, the jaw clutch can be engaged without noise. To analyze speed control, an error ε can be introduced.

[0164] ε=ωpref -ω p (18)

[0165] Adding the integral of the error ε as an additional state to system (11) yields the integral action of feedback control, which eliminates the steady-state error. Using this new state, the augmented state-space model will be...

[0166]

[0167] in

[0168]

[0169] Using the integral state and reference ω pref Updated Figure 8 Feedback control systems in such systems Figure 10 As shown. Figure 10 A reference tracking integral control system is described.

[0170] pass Figure 10 The torque request u of the first motor P1 can be rewritten as

[0171]

[0172] State feedback can be chosen in many ways, but it is generally desirable to find the optimal controller gain under certain criteria. One way to find the optimal feedback control law of Equation 21 is by solving an infinite-time linear quadratic problem, thus obtaining an LQI controller. This type of controller outputs a control input u that minimizes the standard J, where

[0173]

[0174] By using this method, the resulting controller will be robust and inherently stable.

[0175] The matrix Q and scalar r in equation 22 can be defined as follows:

[0176]

[0177] The elements of matrix Q and r define the weights of the state and control inputs in the criterion to be minimized (22). When determining the LQI controller gain, the absolute values ​​of Q and r are not important. Instead, their relative values ​​determine the controller's feedback gain. For example, a relatively high value of q4 means that keeping the integral error ε small is more important than keeping other states or control variables small. A very high value of r means that keeping the control variable u small is more important than keeping the state error small.

[0178] For the LQI controller, the feedback gain K and K in Equation 21 are... IIt can be calculated using the following formula:

[0179]

[0180] Where P is a solution to the algebraic Riccati equation, i.e.

[0181]

[0182] And P is a symmetric matrix of the following form:

[0183]

[0184] The values ​​of Q and r in Equation 22 can be found, for example, experimentally, or calculated based on the characteristic equation of the closed-loop system. However, the characteristic equation has so far been based on the controllable canonical form of the system, rather than the augmented system shown in Equation 19.

[0185] The goal is to calculate the new feedback gain directly based on the physical system parameters, as this allows for quick and simple calibration of the LQI controller without requiring significant processing power. To maintain that the feedback gain value in Equation 24 depends on the system's physical parameters, matrices A, B, and C are not transformed into controllable canonical form, as this would require substituting the system's physical parameter values ​​at an early stage.

[0186] The core idea of ​​the method for controller calibration in the following parts of this disclosure is:

[0187] ● Minimize the need for manual tuning

[0188] ●Based on the physical properties and functional requirements of the system, this method can be used for transmissions of any size and version without changing anything other than the parameter values.

[0189] ● Ensure stability

[0190] ●Low steady-state error

[0191] ●Noise suppression

[0192] Figure 10 The characteristic equation of the closed-loop system in the figure can be written as:

[0193] det(sI-A aug +B aug K)=0 (27)

[0194] Substitute K from equation 24 into equation 27

[0195]

[0196] The roots of Equation 28 define the poles of the closed-loop system, and thus the system's time response. The system in Equation 19 is a fourth-order system, so four poles need to be determined. Once the system's poles are determined, the solution P of the algebraic Riccati equation can be calculated, and then the feedback gain in Equation 24 can be computed.

[0197] The transfer function of a fourth-order system is

[0198]

[0199] Where w n ζ is the natural frequency, and ζ is the damping ratio.

[0200] Figure 11 It shows a fixed natural frequency w. n The response of a fourth-order system with a variable damping ratio ζ.

[0201] from Figure 11 It can be seen that the critically damped response reaches its steady-state value in the shortest time. The underdamped response reaches the desired speed more quickly, but cannot stabilize at that speed, instead continuing to fluctuate and produce overshoot. Since the control problem in this disclosure involves speed synchronization, overshoot will cause noise, vibration, and acoustic roughness (NVH) problems; therefore, a critically damped system is chosen.

[0202] When ξ = 1 and input(ε) is a unit step size, the transfer function in equation 29 becomes

[0203]

[0204] Using partial fraction decomposition, equation 30 becomes...

[0205]

[0206] Inverse Laplace transform on both sides of equation 31

[0207]

[0208] Equation 32 can be obtained by using Figure 12 Let's find a solution. Figure 12 The step response of a critically damped fourth-order system is shown.

[0209] exist Figure 12 In the middle, if the step input is from Figure 9 ω pref The output will then be ω. p The error ε in Equation 18 can be used in conjunction with Equation 5 to define the error ε(t). synch If ε(t) synch Within the limits defined in Equation 5, then at time t synchThen the jaw clutch can be engaged without noise.

[0210] Equation 32 represents output or ω p Evolution over time. Regarding ω p The requirement is that at time t synch After that, ω p ω should be achieved within the error range defined in Equation 5. s (t synch Therefore, equation 32 can be rewritten as

[0211]

[0212] Since equation 33 has an unknown w n Therefore w n It can be solved, and the solution will have the following form:

[0213] w n =constant / t synch (34)

[0214] Equation 34 represents the location of the four poles of the transfer function in Equation 29, where all four poles are located in the same position.

[0215] In this step, w from equation 34 n The value of will be used in the denominator polynomial of the transfer function in Equation 29 to determine the elements in the P matrix.

[0216] By using s in equation 28 3 ,s 2 Comparing the coefficients and constant terms of s with the denominator polynomial of equation 29, we obtain the following system of equations, where p 11 ,p 12 ,p 13 and p 14 These are unknowns that must be calculated:

[0217]

[0218] The constants a1 to a4 in Equation 13 and the constant b in Equation 14 are positive numbers and depend on the physical constants of the system.

[0219] Since equation system 35 has four unknowns p 11 ,p 12 ,p 13 and p 14 The unique solution to each of the four equations, each containing an unknown, can be calculated by setting ξ = 1 and setting r to any positive number, such as 1.

[0220] Specifically, p 11Calculate directly based on the first row of equation 35, and p 14 The calculation is performed directly based on the last line of Equation 35. Subsequently, p is calculated directly based on the third line of Equation 35. 13 Finally, p is calculated directly based on the second line of equation 35. 12 .

[0221] After solving equation system 35, six remaining unknown elements will remain in the P matrix of equation 26, and the four elements of the Q matrix of equation 23 also need to be calculated. This requires 10 equations obtained from matrix equation 25, where the terms p of the P matrix... 22 ,p 23 ,p 24 ,p 33 ,p 34 and p 44 And the terms q1, q2, q3, and q4 of the Q matrix are unknowns that must be calculated:

[0222]

[0223] Similar to the above, the system of equations is solved by first calculating the equation with the fewest variables. For example, based on previously calculated p... 11 p 12 p 13 p 14 We directly calculate q1 based on the first line of equation system 36, directly calculate q4 based on the last line of equation system 36, and directly calculate p based on the seventh line of equation system 36. 34 .

[0224] After that, conventional matrix calculations can be used to solve for term p. 22 ,p 23 ,p 24 ,p 33 ,p 34 ,q2 and q3, for example, by replacing certain variables to eliminate variables, such that only a single equation with a single unknown variable remains, thereby enabling the computation of said unknown variable. The value of this computed variable can then be substituted into other equations used to compute the remaining variables.

[0225] After solving system of equations 36, the six remaining elements p of matrix P are... 22 ,p 23 ,p 24 ,p 33 ,p 34 and p 44 The four elements q1, q2, q3 and q4 of matrix Q have been calculated.

[0226] Once the solution P of the Riccati equation in Equation 26 has been calculated, the linear feedback gain K and K can be calculated using Equation 24. I The controller design is then completed, where the variable r is set to any previously selected positive number.

[0227] In summary, the feedback gain K and K in the controller design process I The P matrix depends on the arbitrary choice of positive r, as shown in Equation 24.

[0228] Since p is a symmetric matrix as shown in Equation 26, p has 10 unknowns instead of the 16 unknowns for an asymmetric matrix. The first row / column of p can be calculated by comparing the characteristic polynomial of the closed-loop system in Equation 28 with the denominator of the fourth-order transfer function in Equation 35.

[0229] Through the Figure 12 By choosing points and solving equation 32, the denominator can be obtained.

[0230] The remaining elements in matrix P and diagonal matrix Q can then be solved using the Riccati equation.

[0231] It is worth noting that the controller design process described in this disclosure will also work if matrix Q is not in diagonal form as shown in Equation 22. If, for example, the form of matrix Q resembles one of the equations in set 36, then matrix Q will be updated accordingly, and if the number of elements in matrix Q is four, the system will still have a unique solution.

[0232] The resulting controller will be stable because it is an LQI feedback controller with a damping ratio ξ set to a positive value, and the integral action guarantees low steady-state error. Since the poles are selected for the critically damped system, the response will reach the desired value in a short time without overshoot, thus avoiding the need for a polarity-changing torque from the first motor P1.

[0233] In the last equation of equation system 35, p 14 Substituting the value of into the last equation of equation system 36, we obtain the following equation:

[0234]

[0235] Equation 37 shows the relative value between the arbitrarily chosen positive weight r on the input u and the weight q4 on the integral error defined by equations 22 and 23. From Equation 37, it can be seen that the relative value depends on a4 and b, which are determined by equations 13 and 14, as well as w. n Define the physical parameters of the system, where w n It depends on the desired performance of the system and is derived from the functional requirements shown in Equation 33.

[0236] Therefore, in order to meet the functional requirements of a specific physical system, the relative weights between q4 and r must be defined as in Equation 37.

[0237] It can also be shown that the other weights q1, q2, and q3 relative to r will also depend only on the physical parameters in matrices A and B from equations 13 and 14, and on the use of Figure 12 Defined functional requirements.

[0238] Therefore, the LQI control implementation described in this disclosure provides a controller scheme in terms of physical parameters and functional requirements, thus eliminating the need for extensive controller simulations to tune the controller for the desired response. This saves a significant amount of transmission calibration work and also eliminates the risk of errors during the calibration process.

[0239] To demonstrate the performance of the controller designed using the proposed method, a 2DOF torsional system representing an ICE, a dual-mass flywheel, and a first motor P1 was simulated.

[0240] Figure 13 The angular velocity ω during the velocity synchronization phase is shown. p and ω e .

[0241] pass Figure 12 When the vehicle speed is below v init At that time, the main side of the ICE 5 and the jaw clutch 6a operated at 2000 rpm. Figure 13 At 0.5 seconds, when the vehicle speed becomes greater than v init At that time, speed synchronization begins, and the main speed decreases to 1500 rpm within 2 seconds, where 2 seconds is the time t defined by Equation 2. synch .

[0242] Figure 14 It shows the target velocity ω ref Control the main side speed ω p The magnified view shown by the dashed box illustrates time t. synch Since ε is less than 5 rpm, according to Equation 5, the following dog clutch engagement will be without clicking noise.

[0243] If the function requires t synch If the time in Equation 2 is changed from 2 seconds to 1 second, and the controller is redesigned, then the performance of the new controller will be... Figure 15 As shown in the image.

[0244] from Figure 15 It can be seen that the synchronization time requirement of 1 second is met, but the time t... synch Subsequent errors are not within the limits defined by Equation 5.

[0245] The reason can be seen by examining the result of q2 in Equation 23. Through Equations 22 and 12, the result q2 is the weight defined for the system's state Δθ. A high value of q2 implies that Δθ should be very small. According to Equation 8, a very small Δθ means that the vibration isolation between the engine and the main side of the jaw clutch will be poor. This can be compared with... Figure 16 The middle is marked as "ω" p The design shown by the thin dashed line “1 sec” is t. synch ω equals 1 second of controller p The magnitude of the fluctuation and the influence of Figure 16 The middle is marked as "ω" p The design indicated by the thick line “2sec” is t. synch ω equals 2 seconds of controller p The magnitude of the fluctuation can be used to determine this.

[0246] Figure 16 Vibration isolation of controllers with different functional requirements is shown, where the thick dashed line represents t. synch = 2sec, the thin dashed line represents t synch = 1 sec.

[0247] from Figure 16 It can be seen that, in the interference T ICE Under the influence of the two controllers, ω e The fluctuations are the same.

[0248] For a controller designed using the described method, t synch The value of q2 at 1 sec is t. synch = 170 times the value of q2 at 2sec, therefore with Figure 14 compared to, Figure 15 Mid-time t synch Subsequently, the vibration isolation effect was poor and failed to meet the error requirements.

[0249] For the specific problem of speed synchronization in the hybrid powertrain system described in this exemplary embodiment of the present disclosure, a long synchronization time is not a problem because speed synchronization is not so time-sensitive. Therefore, by... Figure 2 Decrease v init t can be calculated according to equation 1. synch Increase to a level that meets noise requirements, for example, t synch It equals 2 seconds.

[0250] Alternatively, the off-diagonal form of Q in Equation 23 can be computed using an iterative method with the desired closed-loop poles. The desired closed-loop poles can be obtained from the method described above.

[0251] The above has been referenced Figures 1A to 16Furthermore, the calibration method and corresponding dynamic physical system of this disclosure have been described in detail within the context of a specific implementation of the clutch engagement process of a jaw clutch. However, as mentioned earlier herein, the calibration method and corresponding dynamic physical system of this disclosure are not limited to this exemplary embodiment, but can also be advantageously used in other technical implementations having a controller for controlling a controllable device.

[0252] Therefore, refer to Figure 17A This disclosure relates to a general method for calibrating the feedback gain K of an LQI controller implemented in an electronic control unit operatively connected to the operation of a physical electrical or electromechanical device for controlling a dynamic physical system (particularly a vehicle powertrain), wherein the LQI controller is based on an augmented state-space model having the following form:

[0253]

[0254] B aug =[B 0] T C aug =[C 0]

[0255] The augmented state-space model is based on the following state-space model representing the physical system:

[0256]

[0257] y = Cx

[0258] Where x is the control system state vector, ε is the control system tracking error, u is the control system input, ref is the control system target reference value, y is the control system output, and A, B, and C represent matrices derived from the mathematical model of the dynamic physical system. The method for calibrating the LQI controller includes a first step S100 of obtaining values ​​of various physical parameters of the dynamic system. The method further includes a second step S200: substituting the obtained physical parameter values ​​into a predetermined equation for calculating the values ​​of each item in the P matrix, where the P matrix is ​​a solution to an algebraic Riccati equation, and where the predetermined equation includes the physical parameters of the system. Finally, the method includes a third step S300: based on the matrix equation... Calculate the new feedback gain of the LQI controller based on any positive value of r, where each term of the K matrix corresponds to the feedback gain.

[0259] Therefore, the LQI controller can be calibrated simply by applying the new feedback gain.

[0260] Depending on the type of system and controllable device, physical parameters can be any type of parameter associated with the physical system, such as inertia, damping constant, spring constant, weight, friction, conductivity, viscosity, etc.

[0261] In addition, the method may also include the step of calculating the values ​​of each item in the B matrix, since calculating the feedback gain also requires the values ​​of the items in the B matrix.

[0262] In some example embodiments, the P matrix is ​​a diagonal matrix of the following form:

[0263]

[0264] In some example embodiments, each equation used to compute terms of the P matrix is ​​a function of constants, available physical parameters of the dynamic system, other terms of the P matrix, and terms of the Q matrix.

[0265] In some example embodiments, the physical parameters of the dynamic system are obtained manually by a user who is measuring, detecting, or estimating the values ​​of the physical parameters of the dynamic system; and / or by an electronic control unit that automatically measures, detects, or estimates the values ​​of the physical parameters of the dynamic system.

[0266] In some example embodiments, the step of calculating the feedback gain K of the LQI controller does not involve matrix calculations of the numerical representation of the matrix A of the dynamic physical system.

[0267] In some exemplary embodiments, the method further includes a setup phase for the LQI controller. The setup phase is typically performed in conjunction with the design of the LQI controller for the physical system, and it occurs prior to the calibration of the feedback gain K. (See reference...) Figure 17B The setup phase may include a first step S10: determining the terms of matrices A, B, and C in the form of equations expressing 1s, 0s, and physical constants of the system, while omitting the step of transforming matrices A, B, and C into controllable canonical form. A second step S20: determining a feedback control system with a linear quadratic integral (LQI) controller whose output minimizes the standard j, where... Where Q is a matrix, r is a scalar, and the LQI feedback controller includes the feedback gain. The setup phase may further include: a third step S30, determining the characteristic equation of the control system; a fourth step S40, determining the transfer function of the control system; a fifth step S50, determining the location of the poles of the transfer function; and a sixth step S60, using the algebraic Riccati equations: Derive the equations for each term in the Q and P matrices.

[0268] Setting a matrix to controllable canonical form means transforming, for example, matrix A, such that each of the coefficients in the denominator of the transfer function of the closed-loop system, i.e., the coefficients of the characteristic polynomial, appears in reverse order in the bottom row of matrix A and is inverted.

[0269] In some example embodiments, the characteristic equation of the closed-loop control system has the following form:

[0270] In some example embodiments, the equations for the terms of the P matrix are also derived based on the coefficients and constant terms of the characteristic polynomial of the closed-loop system in combination with the denominator of the transfer function.

[0271] In some example embodiments, the method further includes determining the location of the poles of the transfer function by performing an inverse Laplace transform on the denominator of the transfer function and inputting the values ​​at any point of the step response of the transfer function G(s), thereby enabling the calculation of the natural frequency ω. n It gives the location of the poles of the transfer function.

[0272] In some exemplary embodiments, the transfer function includes a damping ratio ζ, and wherein the damping ratio ζ is selected to be equal to about 1.0, or exactly 1.0.

[0273] In some example embodiments, the Q matrix is ​​a diagonal weight matrix of the following form:

[0274] In some example embodiments, omitting the step of transforming one or more of matrices A, B, and C into controllable canonical form allows the terms of matrices A, B, and C to retain their original expressions as functions of detectable system parameters, so that the equations used to compute the terms of matrix P can be expressed as functions of detectable system parameters, thereby enabling easy computation of new feedback gains, suitable for implementation in low-computational-consumption systems, such as, in particular, vehicle systems.

[0275] Additionally, refer to Figure 18 This disclosure also relates to a general dynamic physical system 28, particularly a vehicle powertrain system, the dynamic physical system 28 including physical electrical or electromechanical devices 26, such as motors, actuators, etc. The dynamic physical system 28 also includes an electronic control unit 25 operatively connected to the physical electrical or electromechanical devices 26, wherein the electronic control unit 25 includes a CPU 29 adapted to execute code for implementing an LQI controller configured to control the operation of the physical electrical or electromechanical devices 26, wherein the LQI controller is based on an augmented state-space model representing the dynamic physical system, wherein the augmented state-space model may have the following form:

[0276]

[0277] B aug =[B 0] T C aug =[C 0]

[0278] The augmented state-space model is based on the following state-space model representing the physical system:

[0279]

[0280] y = Cx

[0281] Where x is the control system state vector, ε is the control system tracking error, u is the control system input, ref is the control system target reference value, y is the control system output, and A, B, and C represent matrices derived from the mathematical model of the dynamic physical system. The electronic control unit 25 also includes a data memory 27 containing predetermined equations for calculating the values ​​of the individual terms of the P matrix, where the P matrix is ​​a solution to an algebraic Riccati equation, and where the predetermined equations include the physical parameters of the system. The feedback gain of the LQI controller is configured to be calibrated by: obtaining values ​​of various physical parameters of the dynamic system; substituting the obtained values ​​of the physical parameters into the predetermined equations for calculating the values ​​of the individual terms of the P matrix; and based on the matrix equations… The new feedback gain of the LQI controller is calculated based on any chosen positive value of r, where each term of the K matrix corresponds to the feedback gain.

[0282] In some example embodiments, the physical electrical or electromechanical equipment 26 of the dynamic physical system is an actuator, motor, pump, light source or RF source or electric device.

[0283] In some example embodiments, the dynamic physical system 28 is a vehicle system, particularly a vehicle powertrain, and more specifically a vehicle powertrain having a first motor P1 operably connected to a first portion 6a of a jaw clutch 6, wherein an electronic control unit 25 controls the rotational speed of the first portion 6a of the jaw clutch 6 to synchronize the speed with that of the second portion 6b of the jaw clutch 6, such that the first portion 6a and the second portion 6b of the jaw clutch can switch from a disengaged state to an engaged state in a smooth and noiseless manner.

[0284] In some exemplary embodiments, the vehicle powertrain is implemented in a hybrid electric vehicle having an internal combustion engine 5 drivenly connected to a first motor P1 and a second motor P2 drivenly connected to a second portion 6b of a jaw clutch 6, wherein switching from a disengaged state to an engaged state of the jaw clutch causes the hybrid electric vehicle to switch from series operation to parallel operation.

[0285] This disclosure also relates to a hybrid electric vehicle, wherein the switching of the first and second portions of the jaw clutch from a disengaged state to an engaged state is configured to switch the operation of the hybrid electric vehicle from series operation to parallel operation.

[0286] This disclosure has been presented above with reference to specific embodiments. However, other embodiments besides those described above are also possible and are within the scope of this disclosure.

[0287] Specifically, the method for calibrating the feedback gain K of an LQI controller according to this disclosure can be applied to LQI controllers used to control almost any type of technical system, especially systems that require noise suppression, such as control systems with measurement and process noise about one or more control parameters.

[0288] In other words, the calibration method is applicable to all types of technical systems, such as, but not limited to, road vehicles, avionics equipment, ships, rail vehicles, maglev trains, power generators, and industrial manufacturing processes. Regarding vehicles, the calibration method can be applied, for example, to LQI controllers, vehicle speed controllers, vehicle stability controllers, vehicle motor controllers, vehicle battery thermal controllers, vehicle battery charging controllers, vehicle DC / DC controllers, vehicle suspension controllers, vehicle autonomous driving controllers, and vehicle platooning controllers arranged to control vehicle clutches.

[0289] Method steps different from the above-described method steps, which are performed by hardware or software, may be provided within the scope of this disclosure.

[0290] The methods disclosed herein can be implemented in a general-purpose computer, processor, or processor core. Suitable processors include, for example, general-purpose processors, special-purpose processors, conventional processors, digital signal processors (DSPs), multiple microprocessors, one or more microprocessors associated with a DSP core, controllers, microcontrollers, application-specific integrated circuits (ASICs), field-programmable gate array (FPGA) circuits, any other type of integrated circuit (IC), and / or state machines.

[0291] The methods or flowcharts provided herein can be implemented in a computer program, software, or firmware incorporated in a computer-readable storage medium for execution by a general-purpose computer or processor. Examples of computer-readable storage media include read-only memory (ROM), random access memory (RAM), registers, cache memory, semiconductor storage devices, magnetic media such as internal hard disks and removable disks, magneto-optical media, and optical media such as CD-ROMs and DVDs.

[0292] Therefore, according to an exemplary embodiment, a non-transitory computer-readable storage medium is provided that stores one or more programs configured to be executed by one or more processors of a dynamic physical system 28 having an LQI controller, the one or more programs including instructions for performing the methods described according to any of the above embodiments. Alternatively, according to another exemplary embodiment, a cloud computing system may be configured to perform any of the method aspects presented herein. The cloud computing system may include distributed cloud computing resources that jointly perform the method aspects presented herein under the control of one or more computer program products. Furthermore, the processor may be connected to one or more communication interfaces and / or sensor interfaces for receiving and / or transmitting data with external entities, such as sensors deployed on the surface of a vehicle, an off-site server, or a cloud-based server.

[0293] The processor of the dynamic physical system 28 may be or include any number of hardware components for performing data or signal processing or for executing computer code stored in memory. The system may have associated memory, which may be one or more devices for storing data and / or computer code for performing or facilitating the various methods described herein. The memory may include volatile or non-volatile memory. The memory may include database components, object code components, script components, or any other type of information structure for supporting the various activities described herein. According to exemplary embodiments, any distributed or local memory device may be used with the systems and methods of this specification. According to exemplary embodiments, the memory may be communicatively connected to the processor (e.g., via circuitry or any other wired, wireless, or network connection) and includes computer code for performing one or more processes described herein.

[0294] It should be understood that the above description is exemplary in nature only and is not intended to limit this disclosure, its application, or use. While specific examples have been described in the specification and shown in the accompanying drawings, those skilled in the art will understand that various changes can be made and its elements can be substituted with equivalents without departing from the scope of this disclosure as defined in the claims. Furthermore, modifications can be made to adapt particular situations or materials to the teachings of this disclosure without departing from the basic scope of this disclosure.

[0295] Therefore, this disclosure is not intended to be limited to the specific examples described in the illustrations and specification, which are currently contemplated as the best way to implement the teachings of this disclosure, but rather the scope of this disclosure will include any embodiments consistent with the foregoing description and the appended claims. Reference numerals used in the claims should not be considered as limiting the scope of the content protected by the claims, and their sole function is to facilitate the understanding of the claims.

[0296] Figure Labels

[0297] 1. Cars

[0298] 2. Propulsion power source

[0299] 3. Wheels

[0300] 4. Powertrain System

[0301] 5. Internal combustion engine

[0302] 6. Jaw clutch

[0303] 7. Battery

[0304] 8. Transmission

[0305] 9. Charging current

[0306] 10. Discharge current

[0307] 11. Dual-mass flywheel

[0308] 12. Actuation mechanism

[0309] 13. Sleeve

[0310] 14. Wheel hub

[0311] 15. Spline connection

[0312] 16. Wheel hub teeth

[0313] 17. The teeth of the sleeve

[0314] 18. Lateral teeth

[0315] 19. Gearbox gears

[0316] 20. Gear shifter motor

[0317] 21. Gear shifter guide rail

[0318] 22. Gear shifting finger

[0319] 23. Shift fork

[0320] 24. Setup Phase

[0321] 25. Electronic control unit

[0322] 26. Physically controllable equipment

[0323] 27. Data storage device

[0324] 28. Physical System

[0325] 29. CPU

[0326] P1. First motor

[0327] P2. Second motor

Claims

1. A method for calibrating the feedback gain K of a linear quadratic integral LQI controller, the LQI controller being implemented in an electronic control unit (25) operatively connected to control the operation of physical electrical or electromechanical equipment (26) of a dynamic physical system (28), wherein the LQI controller is based on an augmented state-space model having the following form: ， ， The augmented state-space model is based on the following state-space model representing the dynamic physical system: in It is the state vector of the control system. It is the tracking error of the control system. It is the control system input. It is the target reference value of the control system. These are the outputs of the control system, and A, B, and C represent matrices derived from the mathematical model of the dynamic physical system. The method for calibrating the LQI controller includes: Obtain the values ​​of various physical parameters of the dynamic physical system (28); The obtained values ​​of the physical parameters are substituted into a predetermined equation for calculating the values ​​of each term of the P matrix, wherein the P matrix is ​​a solution to an algebraic Riccati equation, and wherein the predetermined equation includes the physical parameters of the dynamic physical system (28) and at least one parameter defining the functional requirements of the dynamic physical system (28); and Based on matrix equations ,based on For any chosen positive value, calculate the new feedback gain of the LQI controller, where each term of the K matrix corresponds to the feedback gain.

2. The method according to claim 1, wherein, Each equation used to compute terms of the P matrix is ​​a function of constants, available physical parameters of the dynamic physical system (28), other terms of the P matrix, and terms of the Q matrix.

3. The method according to any one of claims 1 to 2, wherein: Manually, and / or by a user who is detecting or estimating the values ​​of the physical parameters of the dynamic physical system (28), and / or The electronic control unit (25) automatically detects or estimates the values ​​of the physical parameters of the dynamic physical system (28). To obtain the physical parameters of the dynamic physical system (28).

4. The method according to any one of claims 1 to 2, further comprising a setup phase of the LQI controller performed before calibrating the feedback gain K, wherein the setup phase includes: The terms of matrices A, B, and C are determined in the form of equations expressing 1, 0, and the physical constants of the dynamic physical system, while omitting the step of transforming matrices A, B, and C into controllable canonical form. Determine a feedback control system having the LQI controller, wherein the LQI controller output enables the standard Minimize the system input u, where in It is a matrix. It is a scalar, and the LQI feedback controller includes the feedback gain. Determine the characteristic equation of the feedback control system. The transfer function of the feedback control system is determined, and then the locations of the poles of the transfer function are determined. Using the algebraic Riccati equation: Derive the equations for each term in the Q and P matrices.

5. The method according to claim 4, wherein the equations for the terms of the P matrix are further derived based on the coefficients and constant terms of the characteristic polynomial of the closed-loop system in combination with the denominator of the transfer function.

6. The method according to any one of claims 1 to 2 further comprises: The location of the poles of the transfer function can be determined by performing an inverse Laplace transform on the denominator of the transfer function and inputting the values ​​of any point in the step response of the transfer function G(s), thereby enabling the calculation of the natural frequency. It gives the location of the poles of the transfer function.

7. The method according to claim 4, wherein, Omitting the step of transforming matrices A, B, and C into controllable canonical form allows the terms of matrices A, B, and C to retain their original expressions as functions of detectable system parameters, so that the equations used to compute the terms of the P matrix can be expressed as functions of the detectable system parameters, thereby enabling easy computation of the new feedback gain.

8. The method according to any one of claims 1 to 2, wherein, The dynamic physical system (28) is a vehicle powertrain system having a first motor (P1) operably connected to a first part (6a) of a dog clutch (6), wherein the electronic control unit (25) controls the rotational speed of the first part (6a) of the dog clutch (6) to synchronize the speed with that of the second part (6b) of the dog clutch (6), such that the first part (6a) and the second part (6b) of the dog clutch can switch from a disengaged state to an engaged state in a smooth and noiseless manner.

9. A dynamic physical system (28), comprising: Physical electrical or mechanical equipment (26), and An electronic control unit (25) is operatively connected to the physical electrical or electromechanical equipment (26). The electronic control unit (25) includes an LQI controller configured to control the operation of the physical electrical or electromechanical equipment (26), wherein the LQI controller is based on an augmented state-space model having the following form: ， ， The augmented state-space model is based on the following state-space model representing the dynamic physical system: in It is the state vector of the control system. It is the tracking error of the control system. It is the control system input. It is the target reference value of the control system. It is the output of the control system, and A, B, and C represent matrices derived from the mathematical model of the dynamic physical system (28). The electronic control unit (25) further includes a data storage (27) containing predetermined equations for calculating the values ​​of the terms of the P matrix, wherein the P matrix is ​​a solution to an algebraic Riccati equation, and wherein the predetermined equations include physical parameters of the dynamic physical system (28) and at least one parameter defining the functional requirements of the dynamic physical system (28). The feedback gain of the LQI controller is configured to be calibrated by the following operation: Obtain the values ​​of various physical parameters of the dynamic physical system (28); The obtained physical parameter values ​​are substituted into the predetermined equation used to calculate the values ​​of each item in the P matrix; as well as Based on matrix equations ,based on For any chosen positive value, calculate the new feedback gain of the LQI controller, where each term of the K matrix corresponds to the feedback gain.

10. The dynamic physical system (28) according to claim 9, wherein, Each equation used to compute terms of the P matrix is ​​a function of constants, available physical parameters of the dynamic physical system (28), other terms of the P matrix, and terms of the Q matrix.

11. The dynamic physical system (28) according to any one of claims 9 to 10, The data storage (27) further includes terms of matrices A, B, and C in the form of equations expressing the physical constants of the dynamic physical system (28), wherein matrices A, B, and C have not yet been transformed into controllable canonical form. The LQI controller is configured to output standard Minimize the control system input u, where And among them It is a matrix, and It is a scalar. The equations for the terms of the Q matrix are stored in the data memory (27).

12. The dynamic physical system (28) according to any one of claims 9 to 10, wherein the matrices A, B and C stored in the data memory (27) have not been transformed into controllable canonical form, and the terms of the matrices A, B and C thus retain their original expressions as functions of detectable system parameters, such that the equations for calculating the terms of the P matrix can be expressed as functions of detectable system parameters, thereby enabling easy calculation of new feedback gains.

13. The dynamic physical system (28) according to any one of claims 9 to 10, wherein, The physical electrical or electromechanical equipment (26) of the dynamic physical system (28) is a motor, pump, light source or RF source.

14. The dynamic physical system (28) according to any one of claims 9 to 10, wherein, The dynamic physical system (28) is a vehicle powertrain system having a first motor (P1) operably connected to a first part (6a) of a dog clutch (6), wherein the electronic control unit (25) is configured to control the rotational speed of the first part (6a) of the dog clutch (6) to synchronize the speed with that of the second part (6b) of the dog clutch (6), such that the first part (6a) and the second part (6b) of the dog clutch can switch from a disengaged state to an engaged state in a smooth and noiseless manner.

15. The dynamic physical system (28) according to any one of claims 9 to 10, The feedback gain of the LQI controller is configured to be calibrated by the following operation: Obtain the values ​​of various physical parameters of the dynamic physical system (28) and the value of at least one parameter that defines the functional requirements of the dynamic physical system; The obtained values ​​of the physical parameters and functional requirements are substituted into the predetermined equations used to calculate the values ​​of each item in the P matrix; And subsequently Based on matrix equations Calculate the new feedback gain of the LQI controller.

16. A hybrid electric vehicle having a vehicle powertrain system, comprising: A jaw clutch (6) having a first part (6a) and a second part (6b), An internal combustion engine (5) is driven to a first electric motor (P1), which is operatively connected to the first portion (6a) of the jaw clutch (6). The second motor (P2) is drivably connected to the second part (6b) of the jaw clutch (6), and The dynamic physical system (28) according to any one of claims 9 to 15.

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