Method for generating torque in a steering system and steering system

Abstract

According to one or more embodiments of the technical solutions described herein, a method for generating torque in a steering system includes calculating, by a controller, a lateral velocity of a vehicle using a vehicle model that uses at least one of a vehicle velocity, a surface friction estimate, a tire angle, and at least one of a lateral acceleration and a measured yaw rate from a yaw rate sensor. The method also includes generating, by the controller, a torque command for providing an assist torque to a driver, the torque command being based on the calculated lateral velocity. The method also includes providing, by an electric motor, the assist torque, the assist torque being an amount of torque corresponding to the torque command.

Description

TECHNICAL FIELD

[0001] The present application relates generally to estimating (evaluating) rack force values in a steering system, and in particular to providing rack force estimates in real-time and independent of steering system signals. BACKGROUND

[0002] Electric power steering (EPS) systems contribute significantly to the (lateral) dynamic performance of vehicles using EPS by providing feedback to the driver in accordance with road disturbances, tire loads, and other forces experienced by the vehicle chassis. The response of the EPS system to driver input as well as external inputs, such as tire forces, affects the vehicle's yaw rate, roll rate, and lateral (Y) motion, as well as the hand-wheel rim force experienced by the driver. In addition, the EPS generates a compensating torque to mitigate some disturbances to help the driver drive more smoothly. Furthermore, the EPS generates an assist torque to reduce the effort required by the driver to maneuver the vehicle and overcome external forces. Thus, accurate effort communication and steering feel in all environmental conditions, such as icy surfaces and conditions beyond the tire limits, where undesirable yaw behavior is observed, such as oversteer, understeer, etc., greatly affect the overall performance of the vehicle. SUMMARY

[0003] According to one or more embodiments of the technical solution described herein, a method for generating torque in a steering system includes calculating, by a controller, a lateral velocity of a vehicle using a vehicle model that uses vehicle velocity, surface friction estimate, tire angle, and at least one of measured yaw rate from a yaw rate sensor and lateral acceleration. The method also includes generating, by the controller, a torque command for providing an assist torque to a driver, the torque command being based on the calculated lateral velocity. The method further includes providing, by an electric motor, the assist torque, the assist torque being a torque amount corresponding to the torque command.

[0004] According to one or more embodiments, a steering system includes an electric motor for generating torque, a lateral velocity estimation module, and an electric motor control system. The lateral velocity estimation module calculates a lateral velocity of a vehicle using a vehicle model that uses vehicle velocity, surface friction estimate, tire angle, and at least one of measured yaw rate from a sensor and lateral acceleration. The electric motor control system generates a torque command for providing an assist torque to a driver, the torque command being based on the calculated lateral velocity. Also, the electric motor provides the assist torque, the assist torque being a torque amount corresponding to the torque command.

[0005] According to one or more embodiments, a computer program product includes a storage device having computer executable instructions stored therein. The computer executable instructions, when executed by a controller, cause generation of a torque in a steering system. The generation of the torque includes calculating a lateral velocity of a vehicle using a vehicle model that uses a vehicle velocity, a surface friction estimate, a tire angle, and at least one of a measured yaw rate and a measured lateral acceleration from a sensor. Also, the generation of the torque includes generating a torque command for providing an assist torque to a driver, the torque command being based on the calculated lateral velocity. Also the generation of the torque includes providing the assist torque by an electric motor, the assist torque being an amount of torque corresponding to the torque command.

[0006] The above and other advantages and features of the present application will become more apparent from the following description of the preferred embodiments taken in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0007] The subject matter of the present application is particularly pointed out and distinctly claimed in the claims attached hereto, which are incorporated herein by reference, and the foregoing and other objects, features, and advantages of the present application will become more fully apparent from the following description, taken in conjunction with the accompanying drawings, in which:

[0008] Figure 1 is an exemplary embodiment of an electric steering system according to one or more embodiments;

[0009] Figure 2 depicts interaction of a vehicle with a road having a steering system according to an exemplary scenario;

[0010] Figure 3 depicts a block diagram of an operational flow for estimating rack force according to one or more embodiments of the present application;

[0011] Figure 4 shows an example variation of a tire drag with slip angle and surface friction; and

[0012] Figure 5 depicts a torque generated using an estimated rack force according to one or more embodiments of the present application. DETAILED DESCRIPTION

[0013] The present application will now be described with reference to the attached drawings, which are meant to be exemplary and not limiting, and specific embodiments are described in order to provide a thorough understanding of the present application. It will be apparent, however, that the present application can be practiced in a variety of ways and that the application is not limited to the embodiments described herein which are presented for the purpose of illustration only and explanation only and not limitation. The present application is not limited to the embodiments described herein which are presented for the purpose of illustration only and explanation only and not limitation.

[0014] As used herein, the terms module and sub-module refer to one or more processing circuits, such as an application specific integrated circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group) and memory that execute one or more software or firmware programs, a combinational logic circuit, and / or other suitable components that provide the described functionality. As can be appreciated, the sub-modules described below can be combined and / or further subdivided.

[0015] It is desirable for the steering system to perform a real-time estimation of rack force. Referring now to the drawings, in which specific embodiments will be described with reference to specific embodiments, it is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting, Figure 1 is an exemplary embodiment of an electric power steering system (EPS) 40 suitable for implementing the disclosed embodiments. The steering mechanism 36 is a rack and pinion system and includes a rack (not shown) within a housing 50 and a pinion gear (also not shown) positioned below a pinion housing 52. When an operator input, hereinafter denoted as a steering wheel 26 (e.g., hand wheel, etc.) is turned, an upper steering shaft 29 is turned and a lower steering shaft 51 connected to the upper steering shaft 29 by a universal joint 34 turns the pinion gear. Turning of the pinion gear moves the rack, which moves a plurality of tie rods 38 (only one shown) which in turn move a plurality of knuckles 39 (only one shown) of a steered wheel 44 (only one shown).

[0016] Electric power steering assist is provided by a control apparatus generally identified by reference numeral "24" and includes a controller 16 and an electric motor 19, which can be a permanent magnet synchronous motor, hereinafter denoted as motor 19. The controller 16 is powered by the vehicle power supply 10 through a line 12. The controller 16 receives a vehicle speed signal 14 representative of vehicle speed from a vehicle speed sensor 17. Steering angle is measured by a position sensor 32, which can be an optical encoder type sensor, a variable resistance type sensor, or any other suitable type of position sensor, and supplies a position signal 20 to the controller 16. Motor speed can be measured by a tachometer or any other means and transmitted as a motor speed signal 21 to the controller 16. Motor speed, denoted as ω m , can be measured, calculated, or a combination thereof. For example, motor speed ω m may be calculated as a change in motor position θ measured by the position sensor 32 over a prescribed time interval. For example, motor speed ω m may be calculated from the formula ω m= Δθ / Δt where Δt is the sample time and Δθ is the amount of position change during the sample interval. Alternatively, the motor speed can be derived from the motor position as the rate of change of position with respect to time. It will be understood that there are many well-known methods for performing the derivative function.

[0017] When the steering wheel 26 is turned, the torque sensor 28 senses the torque applied to the steering wheel 26 by the vehicle operator. The torque sensor 28 can include a torsion bar (not shown) and a variable resistance type sensor (also not shown) that outputs a variable torque signal 18 to the controller 16 in relation to the amount of twist on the torsion bar. While this is one type of torque sensor, any other suitable torque sensing device used with known signal processing techniques would be sufficient. In response to various inputs, the controller sends instructions 22 to the electric motor 19 that provides torque assist to the steering system through the worm 47 and worm gear 48 to provide torque assist to the vehicle steering.

[0018] It should be noted that while the disclosed embodiments are described by reference to electric motor control for electric power steering applications, it will be understood that these references are illustrative only and that the disclosed embodiments can be applied to any electric motor control application employing an electric power motor, such as steering, valve control, etc. Also, the references and descriptions herein can be used for many forms of parameter sensors, including but not limited to torque, position, speed, etc. It should also be noted that references herein to electric machines include but are not limited to electric motors, and for brevity and simplicity only, reference will be made hereinafter to but not limited to electric motors.

[0019] In the depicted control system 24, the controller 16 uses torque, position, and speed, among others, to compute command(s) to deliver the desired output power. The controller 16 is provided in association with various system and motor control system sensors. The controller 16 receives signals from the various system sensors, quantifies the received information, and provides output command signal(s) in response thereto, for example, to the motor 19. The controller 16 is configured to generate corresponding voltage(s) from an inverter (not shown), which can be selectively incorporated with the controller 16 and will be referred to herein as the controller 16, in order to produce the desired torque or position when supplied to the motor 19. In one or more examples, the controller 24 operates as a current regulator in a feedback control mode to generate the command 22. Alternatively, in one or more examples, the controller 24 operates in a feedforward control mode to generate the command 22. Because these voltages are related to the position and speed of the motor 19 and the desired torque, the position and / or speed of the rotor and the torque applied by the operator are to be determined. A position encoder is connected to the steering shaft 51 in order to detect the angular position Θ. The encoder can sense the rotational position based on optical detection, magnetic field changes, or other methodologies. Typical position sensors include potentiometers, resolvers, synchros, encoders, and the like, as well as combinations including at least one of the foregoing. The position encoder outputs a position signal 20 that is representative of the angular position of the steering shaft 51 and, by extension, the angular position of the motor 19.

[0020] The desired torque can be determined by one or more torque sensors 28 that deliver a torque signal 18 representative of the applied torque. One or more example embodiments include such torque sensors 28 and torque signals 18 from the torque sensors that can be responsive to a compliant torque bar, a T-bar, a spring, or similar devices (not shown) configured to provide a response representative of the applied torque.

[0021] In one or more examples, temperature sensor(s) 23 are positioned at the motor 19. Preferably, the temperature sensors 23 are configured to directly measure the temperature of the sensing portion of the motor 19. The temperature sensors 23 transmit temperature signals 25 to the controller 16 to facilitate the processing and compensation specified herein. Typical temperature sensors include thermocouples, thermistors, thermostats, and the like, as well as combinations including at least one of the foregoing sensors, which provide a calibratable signal proportional to a particular temperature when properly placed.

[0022] Position signal 20, speed signal 21, and torque signal(s) 18, among others, are provided to controller 16. Controller 16 processes all of the input signals to produce values corresponding to each signal so that rotor position values, motor speed values, and torque values are available for processing in the algorithms specified herein. Measurement signals such as the above-described signals are also commonly linearized, compensated, and filtered as needed collectively to enhance the characteristics of the desired signals or to eliminate undesired characteristics. For example, the signals can be linearized to improve processing speed or to address a large dynamic range of the signals. In addition, compensation and filtering based on frequency or time can be employed to eliminate noise or to avoid undesirable spectral characteristics.

[0023] To perform the specified functions and desired processing and thus calculations (e.g., identification of motor parameters, control algorithm(s), etc.), controller 16 can include, but is not limited to, processor(s), computer(s), DSP(s), memory, storage, register(s), timer(s), interrupter(s), communication interface(s), and input / output signal interface, among others, as well as combinations including at least one of the foregoing. For example, controller 16 can include input signal processing and filtering to enable accurate sampling and conversion or acquisition of such signals from the communication interface. Additional features of controller 16 and certain processing therein are discussed in detail later herein.

[0024] As described herein, it is desirable for the steering system 12 to perform a rack force estimation in real-time to assist in providing an assist torque to the driver. In addition, the rack force estimation can be used to at least partially mitigate external forces acting on the steering system 12, such as by compensating for tire load, road disturbances, etc., by generating a counteracting torque, thereby providing a smoother ride for the driver.

[0025] Typically, steering tuning engineers tune the steering system using algorithms that depend on the measured driver torque, handwheel angle, and steering rate to achieve the desired steering performance. In this case, a gain table and filter are applied directly to the measured driver torque to achieve the base assist torque, which is the main portion of the final motor torque in most driving conditions. There is an increasing trend to structure the EPS algorithm in a way that the desired driver torque assist is defined using the state of the vehicle (e.g., using the estimated rack force). In this structure, the tuning can be performed in a way that the handwheel effort is directly based on the estimated rack force. This assist command generation structure is applicable to steering systems with closed loop handwheel torque control, steer-by-wire (SbW) systems, and even to traditional steering systems.

[0026] A technical challenge in using this technique in the steering system 12 is estimating the rack force. Typically, known techniques for calculating rack force estimation using open loop vehicle models are tuned for dry road conditions and can have a mismatch in certain tire limit conditions. Alternatively, known techniques using observer based rack force estimation utilize EPS signals for estimation. This approach can accurately estimate the rack force in different conditions (dry, wet, icy roads) and successfully communicate road disturbances (texture, potholes, friction variations, etc.) to the driver, however, for driver effort calculation leading to a smoother steering feel, a vehicle model based approach is preferred.

[0027] Vehicle models, such as the well-known bicycle model, can be used to understand vehicle dynamics and various states of the vehicle, including lateral velocity, slip angle, and lateral acceleration, among others. While vehicle models provide such information, they have a lower bandwidth due to their open loop nature. Further, vehicle models are not valid in the nonlinear region of the tire and are sensitive to environmental conditions. Thus, a vehicle model based approach becomes a technical challenge in estimating the rack force using a vehicle model based approach.

[0028] The technical solutions described herein address such technical challenges by facilitating the steering system 12 to use a closed loop vehicle model based observer that estimates various vehicle states in real time. The observer utilizes a vehicle model, such as the bicycle model, along with a yaw rate measurement to estimate the lateral velocity, which in turn is used to calculate the slip angle. Thereafter, the slip angle is used to estimate the lateral acceleration and force, which are then used to determine the rack force. While the rack force estimation can be used to determine the driver effort curve and thereby provide the desired steering feel performance, the various vehicle state estimations can further be used for multiple other purposes, including understeer-oversteer detection (lateral velocity), auxiliary mitigation hand wheel torque loss (lateral acceleration), continuous friction estimation, and other such steering system functions. Further, the closed loop observer estimation of the rack force, which includes nonlinearity, also helps in forming a uniform rack force on center due to the bicycle model validity in the linear range of the tire. Further, these technical solutions help in accurate rack force estimation in the nonlinear tire range. The technical solutions described herein are effective at higher vehicle speeds (above a predetermined threshold, such as above 20 MPH, 40 MPH, etc.) and use surface friction information that can be obtained using existing friction estimation techniques.

[0029] Figure 2Interactions of a vehicle with a road having a steering system are depicted according to exemplary scenarios. As depicted, the vehicle 10 experiences external inputs from the road 7 on which the vehicle 10 is traveling, such as tire forces. In addition, the driver 5 provides input forces, such as engine throttle, brakes, steering angle, etc. Thus, one or more forces / parameters are generated via the vehicle and its subcomponents, such as the steering system 12, and the driver 5 receives these forces / parameters as feedback. For example, the driver 5 experiences motion in the X, Y, and Z directions; yaw, pitch, and roll motions; feedback from the hand wheel 26; and other types of feedback such as suspension, etc.

[0030] Figure 3 A block diagram of an operational flow for estimating rack force is depicted according to one or more embodiments of the application. A vehicle model, such as a bicycle model, is used to estimate rack force using a closed loop rack force observer. In one or more examples, the controller 24 executes a method for estimating rack force. Alternatively or additionally, a rack force estimation module implements a method that provides the estimated rack force to the controller and / or other components for further functionality.

[0031] The method uses a state observer based on a vehicle model, such as a bicycle model, to estimate the lateral velocity V of the vehicle 10 at 120. Inputs to the state observer include the measured yaw rate r, surface friction coefficient μ, and (front) tire angle δ f In one or more examples, the tire angle can be obtained from the motor angle θ at 110 using a kinematic model of the tire with appropriate lag compensation. The motor angle can be determined using a position sensor for the motor 19 or any other manner.

[0032] The state equation for the plant used to construct the state observer is as follows:

[0033]

[0034]

[0035] y = Cx

[0036]

[0037] Here, m is the vehicle mass, I zz is the z-axis mass moment of inertia about the vehicle CG, C αf and C αris the front-to-rear lateral stiffness, a and b are the distances of the front and rear axles from the CG along the x-axis, and U is the vehicle speed. These values are either known values that are dynamically measured using one or more corresponding sensors of the particular vehicle 10, and / or dynamically calculated using one or more sensor measurements. The state observer outputs include lateral velocity V and yaw rate (r), where the yaw rate is measured by a sensor.

[0038] In one or more examples, instead of the yaw rate, the lateral acceleration measured by a sensor can be used.

[0039] In one or more examples, the lateral velocity V is estimated using an alternative observer structure based on a modified bicycle model. In this case, the state equations of the device used to construct the observer are as follows:

[0040]

[0041] where, is the tire velocity, which is the derivative of the tire angle, and is modeled as an additional input in the augmented model, and can be calculated by differentiating the tire angle signal. Note that the only real input to the system is the tire angle. However, for the purpose of observer design using an augmented state matrix that includes lateral acceleration as an additional system state, the tire velocity can be modeled as an additional input. Furthermore, the observer structure can be further modified by simplifying assumptions (e.g., setting the tire velocity to zero, etc.).

[0042] The measurements used in the observer calculation can include the yaw rate (r) or the lateral acceleration (a y ) or a combination of both; these values are either measured by corresponding sensors, or calculated using steering system measurement signals as described herein. Depending on the measured values used in the state equation calculation, the output matrix for the observer can be any of the following sets:

[0043] y = Cx

[0044]

[0045] y = Cx

[0046] or

[0047]

[0048] In the above calculations, m is the vehicle mass, I zz is the z-axis mass moment of inertia about the vehicle center of gravity (CG), C αf and C αris the front and rear cornering stiffness, a and b are the distances of the front and rear axles from the CG along the x-axis, and U is the vehicle speed. In addition, the inputs to the observer include the measured lateral acceleration a y , (and / or) the measured yaw rate (which can be optional), the surface friction coefficient μ and the front tire angle δ f . The tire angle can be obtained from the motor angle θ using a kinematic model of the tire and appropriate hysteresis compensation.

[0049] The state observer with gain matrix L can be constructed as follows:

[0050]

[0051] The transfer matrix of the observer is obtained by taking the Laplace transform of the above equations. It should be noted that the observer gain selection can be made by any well-known methods, including pole placement, LQG, etc. Alternatively or additionally, the observer gain can also be determined to achieve a specific transfer function of the lateral velocity estimate as a function of the tire angle and / or the yaw rate. Thus, the lateral velocity V is continuously estimated using a closed loop control.

[0052] The lateral velocity estimate is then used at 130 together with the tire angle to obtain the front slip angle a f and the rear slip angle a r , respectively. In one or more examples, the slip angles can be determined using the following expressions.

[0053]

[0054]

[0055] In addition, the slip angle estimates are used at 140 to compute the lateral tire forces Fy. While linear tire models can be used, they are generally insufficient to represent the full tire force versus slip angle curve (which is substantially non-linear, especially at higher slip angles above a predetermined threshold). Non-linear tire models that take into account the surface friction (which can be received from other estimation algorithms) include empirical models or physics-based models, such as the Fiala tire model shown below.

[0056]

[0057] In one or more examples, the front tire force F yf and the rear tire force F yr may be computed by using the front and rear cornering stiffness C αf and C αr and a f and a ris calculated. Additionally, the slip angle a s1 and the maximum lateral tire force (a function of the friction μ) is represented as follows.

[0058]

[0059] I f = μN where N represents the vertical load on the axle.

[0060] The rack force estimate is further calculated at 150. The rack force can be estimated as the product of the front axle lateral force and the tire drag distance, which is the distance between the geometric center of the tire contact patch and the resultant force due to the sideslip. In one or more examples, the tire drag distance is modeled using an empirical model or a physics-based model, such as the Fiala model shown below.

[0061]

[0062] Here, s y = tan a and Additionally, since the tire drag distance varies significantly with surface friction, the model is modified to account for this. The variation of the tire drag distance with the slip angle and surface friction is shown in Figure 4 It should be appreciated that the model shown for varying the tire drag distance with the slip angle and surface friction is one example, and other models can be used in other examples.

[0063] The rack force is calculated as the product of the front axle lateral force F yf and the tire drag distance t p , as shown below:

[0064] T r = t p F yf

[0065] The results of the estimated rack force according to one or more embodiments of the present application provide an accurate estimate of the rack force for all vehicle states and when compared to actual data collected from in-car maneuvers. Thus, the technical solution described herein provides a rack force estimate that is independent of the steering system signals. Additionally, in some embodiments, the use of an estimated nonlinear model of one or more signals used to estimate the rack force facilitates accurate determination of system state estimates over a wider operating region of the vehicle and steering system (including linear and nonlinear regions of the tires) compared to linear models.

[0066] According to one or more embodiments of the present application, the estimated rack force value is used by the steering system 12 for one or more operations.

[0067] Figure 5Torque generated using estimated rack force is depicted in accordance with one or more embodiments of the present application. In the depicted example, rack force is estimated at 510 using one or more embodiments described herein. At 520, the rack force is used to generate a reference torque command (T ref ) in accordance with one or more embodiments. In one or more examples, the reference torque command is generated based on a look-up table that includes one or more reference curves that provide a desired reference torque generated for an estimated rack force value. The reference torque command is used by the steering system 12 to generate an assist torque at the hand wheel using the electric motor 19.

[0068] Further, in one or more examples, the reference torque command is modified at 530 using a hand wheel torque (T bar ) signal measured at the hand wheel 26. In one or more examples, the measured hand wheel torque is subtracted from the reference torque value at 540, and a resultant torque error is used by a closed loop hand wheel torque control system to generate a torque command for generating an assist torque by an electric motor control system (not shown) for the driver 5. The torque command can be applied to the electric motor 19 in the form of a current / voltage command to generate the assist torque. The electric motor control system 550 converts the torque command to a corresponding voltage / current command applied to the electric motor 19. In one or more examples, the electric motor control system is operated by the controller 24.

[0069] Accordingly, the technical solutions described herein facilitate a closed loop observer to utilize a vehicle model and signals to provide a high bandwidth estimate of rack force using a bicycle model and measured yaw rate and other vehicle signals. The estimate also provides an estimate of additional vehicle states such as lateral velocity, slip angle, and lateral force, etc. Accordingly, the technical solutions herein provide a rack force estimate that is independent of steering system signals. By using a non-linear model to estimate different signals, the technical solutions described herein provide the result of an effective system state estimation over the entire operating region of the vehicle and steering system (linear and non-linear regions). Accordingly, the rack force estimate is provided using a closed loop observer that is more accurate than typical techniques used, and also has a higher bandwidth and without the enhanced tuning required for typical rack force estimates. The technical solutions described herein improve the rack force estimate used in typical steering systems.

[0070] While the application has been described in detail with respect to limited embodiments, it will be appreciated that the application is not limited to these embodiments. On the contrary, the application is intended to encompass any and all variations, modifications and equivalents, which fall within the scope of the application. Furthermore, although embodiments of the application have been described, it is to be understood that the scope of the application can include only some of the described embodiments, or a combination of some or all of the described embodiments. Accordingly, the application is not to be seen as being limited by the foregoing description.

Claims

1. A method for generating torque in a steering system, the method comprising: calculating, by a controller, a rack force estimate for the steering system using a nonlinear vehicle model, the nonlinear vehicle model using a lateral velocity estimate, the lateral velocity estimate being based on at least one of a vehicle velocity, a surface friction estimate, a tire lateral rotation angle, a tire lateral rotation velocity, and both a measured yaw rate from a yaw rate sensor and a lateral acceleration; wherein the rack force estimate is calculated using a closed loop state observer, the lateral velocity estimate is estimated using a closed loop state observer and a closed loop calculation based on a modified nonlinear bicycle model, the tire lateral rotation velocity is a derivative of the tire lateral rotation angle, and a device for constructing the closed loop state observer is defined at least according to: where V is the lateral velocity, r is the yaw angular velocity, m is the vehicle mass, I zz is the z-axis mass moment of inertia about the vehicle center of gravity (CG), C αf and C αr are the front and rear cornering stiffness, a and b are the distances of the front and rear axles from the vehicle center of gravity (CG) along the x-axis, U is the vehicle speed, is the tire velocity as the derivative of the tire angle; calculating at least a front slip angle and a rear slip angle using the lateral velocity estimate; updating the rack force estimate based on a product of a front axle lateral force and a tire drag value associated with a tire drag model, the tire drag model using at least one of the front slip angle and the rear slip angle, wherein the tire drag model is modified based on the surface friction estimate, determining the tire lateral rotation angle using a motion model of the tire associated with a motor angle based on the tire lateral rotation angle, wherein the motion model is adjusted to compensate for at least a corresponding hysteresis, and wherein the motor angle is determined based on an angular position of a steering shaft of the steering system received from a position encoder; generating, by the controller, a torque command for providing an assist torque to a driver, the torque command being based on the rack force estimate; and providing, by a motor, the assist torque, the assist torque being an amount of torque corresponding to the torque command.

2. The method of claim 1, further comprising: calculating, by the controller, a tire lateral rotation angle of a front tire based on a position of the motor.

3. A steering system comprising: a motor for generating torque; and a controller for: calculating a vehicle rack force estimate using a nonlinear vehicle model, the nonlinear vehicle model using a lateral velocity estimate, the lateral velocity estimate being based on at least one of a vehicle velocity, a surface friction estimate, a tire lateral rotation angle, a tire lateral rotation velocity, and a measured yaw rate from a sensor and a lateral acceleration, wherein the rack force estimate is calculated using a closed loop state observer, the lateral velocity estimate is estimated using a closed loop state observer and a closed loop calculation based on a modified nonlinear bicycle model, the tire lateral rotation velocity is a derivative of the tire lateral rotation angle, and a device for constructing the closed loop state observer is defined at least according to: where V is the lateral velocity, r is the yaw angular velocity, m is the vehicle mass, I zz is the z-axis mass moment of inertia about the vehicle center of gravity (CG), C αf and C αr are the front and rear cornering stiffness, a and b are the distances of the front and rear axles from the vehicle center of gravity (CG) along the x-axis, U is the vehicle speed, is the tire velocity as the derivative of the tire angle; calculating at least a front slip angle and a rear slip angle using the lateral velocity estimate; updating the rack force estimate based on a product of a front axle lateral force and a tire drag value associated with a tire drag model using at least one of the front slip angle and the rear slip angle, wherein the tire drag model is modified based on the surface friction estimate, determining a tire lateral rotation angle using a motion model of the tire associated with the motor angle based on the position encoder, wherein the motion model is adjusted to at least compensate for a corresponding hysteresis, and wherein the motor angle is determined based on an angular position of a steering shaft of the steering system received from a position encoder; generating torque instructions for providing an assist torque to the driver, the torque instructions based on the rack force estimate; and the motor providing the assist torque as an amount of torque corresponding to the torque instructions.

4. The steering system of claim 3, wherein, the controller calculating a tire lateral rotation angle of the front tire based on a position of the motor.

5. A computer program product comprising a storage device having computer executable instructions stored therein which, when executed by a controller, cause generation of a torque in a steering system, said generation comprising: calculating a rack force estimate of the steering system using a nonlinear vehicle model using a lateral velocity estimate, the lateral velocity estimate based on a vehicle velocity, a surface friction estimate, a tire lateral rotation angle, a tire lateral rotation velocity, and at least one of a measured yaw rate and a lateral acceleration from a sensor; wherein the rack force estimate is calculated using a closed loop state observer, the lateral velocity estimate is estimated using a closed loop state observer and a closed loop calculation based on a modified nonlinear bicycle model, the tire lateral rotation velocity is a derivative of the tire lateral rotation angle, and the device for constructing the closed loop state observer is defined at least according to: where V is the lateral velocity, r is the yaw angular velocity, m is the vehicle mass, I zz is the z-axis mass moment of inertia about the vehicle center of gravity (CG), C αf and C αr are the front and rear cornering stiffness, a and b are the distances of the front and rear axles from the vehicle center of gravity (CG) along the x-axis, U is the vehicle speed, is the tire velocity as the derivative of the tire angle; calculating at least a front slip angle and a rear slip angle using the lateral velocity estimate; updating the rack force estimate based on a product of a front axle lateral force and a tire drag value associated with a tire drag model using at least one of the front slip angle and the rear slip angle, wherein the tire drag model is modified based on the surface friction estimate, determining a tire lateral rotation angle using a motion model of the tire associated with the motor angle based on the position encoder, wherein the motion model is adjusted to at least compensate for a corresponding hysteresis, and wherein the motor angle is determined based on an angular position of a steering shaft of the steering system received from a position encoder; generating torque instructions for providing an assist torque to the driver, the torque instructions based on the rack force estimate; and the motor providing the assist torque as an amount of torque corresponding to the torque instructions.

6. The computer program product of claim 5, wherein, the generating the torque further comprises: calculating a tire lateral rotation angle of the front tire based on a position of the motor.

5. A computer program product comprising a storage device having computer executable instructions stored therein which, when executed by a controller, cause generation of a torque in a steering system, said generation comprising: calculating a rack force estimate of the steering system using a nonlinear vehicle model using a lateral velocity estimate, the lateral velocity estimate based on a vehicle velocity, a surface friction estimate, a tire lateral rotation angle, a tire lateral rotation velocity, and at least one of a measured yaw rate and a lateral acceleration from a sensor; wherein the rack force estimate is calculated using a closed loop state observer, the lateral velocity estimate is estimated using a closed loop state observer and a closed loop calculation based on a modified nonlinear bicycle model, the tire lateral rotation velocity is a derivative of the tire lateral rotation angle, and the device for constructing the closed loop state observer is defined at least according to: calculating at least a front slip angle and a rear slip angle using the lateral velocity estimate; updating the rack force estimate based on a product of a front axle lateral force and a tire drag value associated with a tire drag model using at least one of the front slip angle and the rear slip angle, wherein the tire drag model is modified based on the surface friction estimate, determining a tire lateral rotation angle using a motion model of the tire associated with the motor angle based on the position encoder, wherein the motion model is adjusted to at least compensate for a corresponding hysteresis, and wherein the motor angle is determined based on an angular position of a steering shaft of the steering system received from a position encoder; generating torque instructions for providing an assist torque to the driver, the torque instructions based on the rack force estimate; and the motor providing the assist torque as an amount of torque corresponding to the torque instructions. the generating the torque further comprises: calculating a tire lateral rotation angle of the front tire based on a position of the motor.

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