CN111090237A - Robust feedforward controller and high-frequency gain compensator optimization method - Google Patents
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Abstract
The invention discloses a robust feedforward controller and high-frequency gain compensator optimization method, which comprises the following steps: establishing an EPS system mathematical model to obtain system transfer characteristics; establishing a torque control loop control strategy, and obtaining a transfer function which has obvious influence on the steering feeling of a driver through a system mathematical model and a basic control strategy; the method comprises the following steps of taking the change of a torque sensor signal as main disturbance of the EPS system, using a second-order feedforward controller to carry out disturbance compensation on a torque control loop, taking the change of the EPS system transfer characteristic caused by the main disturbance as the uncertainty of the system, and establishing an internal model control structure; establishing a design target of the robust feedforward controller by using a robust control theory, and solving an optimal algorithm to obtain a robust second-order feedforward controller; and a high-frequency gain compensator is added to improve the control effect of the second-order feedforward controller in a high frequency band. The invention not only can conveniently acquire the parameters of the robust controller, but also can more simply and conveniently adjust the controller.
Description
Technical Field
The invention relates to the technical field of control of electric power steering systems, in particular to a robust feedforward controller and a high-frequency gain compensator optimization method for restraining torque fluctuation of an electric power steering system.
Background
An Electric Power Steering System (hereinafter abbreviated as an EPS System) is an on-demand System, and a motor works when Steering is needed, so that the fuel consumption of an automobile can be improved by using the Electric Power Steering System, and the Electric Power Steering System is more energy-saving and environment-friendly. In addition, the electric power steering system has higher safety and better driving comfort, meanwhile, the electronic integration degree is higher, and the electric power steering system is easy to realize the variable power and other advanced driving functions and is easier to further develop on the basis of the EPS system. Therefore, the EPS system becomes a necessary trend for the development of the future automobile steering technology.
The key technology of the EPS system is the design of a control strategy which takes road sensing tracking as core content. The key of the road feel tracking technology is that the voltage of the motor is controlled to enable the power-assisted torque actually generated by the motor to track a power-assisted curve designed by power-assisted matching, and when the motor is controlled, the adverse effect of torque fluctuation of an EPS system on the hand feel of a driver needs to be inhibited.
Aiming at the problem of inhibiting torque fluctuation when an EPS system is steered, Kevin M McLaughlin et al of TRW company in America proposes a control method of modular control, a self-adaptive torque filter, a hybrid filter and the like, and divides an EPS control strategy into three control loops, namely a torque control loop, a motor control loop and a current control loop, and a modular control idea reduces the complexity and the coupling degree of the control system and is convenient for control parameter debugging and system maintenance; the adaptive torque filter can compensate the system, reduce the influence of the change of the power-assisted gain on the relative stability of the system and improve the steering hand feeling; the design of the hybrid filter can separate the torque signals of different frequency ranges of the system, so that the torque signals of different frequency ranges can be respectively processed, and the comfort of the steering system is improved. In japan, seiko koku corporation, teletoshiba has proposed an electric power steering control device including a feedforward control unit, a feedback control unit, and a response control unit, which is capable of stabilizing a vibration mode of a second-order system composed of a steering wheel inertia and a motor inertia without degrading responsiveness and improving system stability by combining a pole shift and a zero pole offset with respect to a characteristic of the second-order inertial system composed of a steering wheel inertia and a motor inertia to set the characteristic, and by improving the degree of freedom of setting the characteristic in the vicinity of the center.
However, the control strategy applied by the enterprise at present can meet the requirements of the EPS system on dynamic property and steady state property through the experience of engineers and continuous calibration particularly in the aspect of parameter debugging of the controller, but lacks the theoretical support of the forward development of the system. A large amount of manpower and material resources are consumed in the early parameter adjusting process or the parameter adjusting process after the power-assisted curve is modified. Research of scientific research institutions rarely considers the problem of system engineering implementation, and although the model-based controller design method provided by the scientific research institutions can calculate the parameters of the controller through the modern control theory, the problems that the controller is not well designed or the order of the controller is high and difficult to implement in engineering due to the fact that the model is not accurate enough generally exist.
Disclosure of Invention
The invention provides a robust feedforward controller and a high-frequency gain compensator optimization method, which are used for inhibiting the moment fluctuation of an EPS system, and aims to design a controller which is easy to realize in engineering, can obtain parameters in a positive direction and can inhibit the moment fluctuation of the EPS system.
In order to achieve the purpose of inhibiting the moment fluctuation of the EPS system, the technical scheme adopted by the invention comprises the following steps:
a robust feedforward controller and high-frequency gain compensator optimization method comprises the following steps:
step 1: build up torque T by hand forcehMotor assisting torque TmAnd ground moment of resistance TloadFor inputting, a torque sensor signal T is acquired by a torque sensor on a torsion bar at the joint of a pipe column on the pipe column and the intermediate shaftseAn output mathematical model of the electric power steering system;
step 2: obtained by laplace transform arrangement of differential equations: with motor assisting torque TmFor input, the torque sensor signal TseAs a transfer function G of the outputms(s); by hand force moment ThFor inputting, torque sensor signals TseAs a transfer function G of the outpuths(s); ground resisting moment T for vehicle by ground actionloadFor inputting, torque sensor signals TseAs a transfer function G of the outputls(s)；
And step 3: establishing a torque sensor signal TseFor input, target moment TcmdFor the control strategy of the output torque control loop, the motor assisting torque TmUsing torque control loop and torque sensor signal TseThe transfer function H which has obvious influence on the steering feeling of a driver is obtained through a mathematical model of the power-assisted steering system and a torque control loophs(s)；
And 4, step 4: will torque sensor signal TseAs the main disturbance of the EPS system, the torque control loop utilizes a second order feedforward controller Qff(s) performing disturbance compensation;
and 5: considering the change of the EPS system transfer characteristic caused by the main disturbance as the uncertainty of the system, a nominal system transfer function G containing an estimation is establishedeq(j ω) and transfer function G of nominal measurable disturbance to process outputd_eq(j ω) an internal model control structure; establishing a design target of the robust feedforward controller by using a robust control theory, and solving an optimal algorithm to obtain a robust second-order feedforward controller;
step 6: by adding a high frequency gain compensator Hhfg(s) adjusting the control effect of the controller in the high frequency band.
Further, in step 3, the torque control loop comprises a power-assisted curve and a feed-forward controller, wherein the power-assisted curve determines the power-assisted torque T of the motor at a certain vehicle speedmAnd torque sensor signal TseThe function mapping relation of the motor is that the power-assisted torque is equal to the power-assisted gain a (T)se) Multiplying by the torque sensor signal Tse：
Tm(s)＝a(Tse)·Tse(s)。
Further, in step 3, the transfer function Hhs(s) the expression is:
further, the design goal of the robust feedforward controller in the step 5 is:
where w(s) is a frequency weighting function that sets a frequency range where the expected control performance is attenuated as little as possible.
Further, the frequency weighting function w(s) is frequency weighted according to the following equation:
W(s)＝(0.3s+1)/s。
further, the equivalent transfer function H of the high frequency gain compensator in the step 6hfg(s) is:
Hhfg(s)＝LG·Hlp(s)+HG·(1-Hlp(s))
where LG is the low frequency gain, HG is the high frequency gain, the transfer function H of the low pass filterlp(s) is:
cut-off frequency omega of low-pass filterlpIs the EPS system resonance peak frequency.
Compared with the prior art, the invention has the beneficial effects that:
the method can guide forward solving of the parameters of the second-order feedforward controller for compensating main disturbance (torque sensor signal change) of the EPS system. Through system uncertainty analysis, a robust feedforward controller design target is provided by applying a robust control theory, and a robust second-order feedforward controller can be obtained by applying an optimal algorithm. Finally, the control effect of the second-order feedforward controller in a high frequency band is improved by adding a high-frequency gain compensator. The method of the invention not only can guide the parameter acquisition of the robust controller which can effectively restrain the torque fluctuation of the electric power steering system, but also can more simply and conveniently adjust the control effect of the controller in different frequency ranges.
Drawings
Fig. 1 is a diagram of an internal model control structure of an EPS system.
Fig. 2 is a schematic EPS system dynamics modeling diagram.
Fig. 3 is a diagram of a torque control loop.
Fig. 4 is a schematic diagram of a series high-frequency gain compensator.
Fig. 5 is a schematic diagram of the structure of the high frequency gain compensator.
FIG. 6 is a Bode diagram of the equivalent transfer function of the feedforward control loop.
Fig. 7 is a bode plot of the open loop transfer function under boost gain.
Fig. 8 is a unit step response graph.
FIG. 9 is a schematic diagram of a bench test input regime.
FIG. 10 is a time domain plot of the results of the torque response experiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer and clearer, the present invention is further described in detail below by referring to the accompanying drawings and examples.
A robust feedforward controller and high-frequency gain compensator optimization method comprises the following steps:
step 1: build up torque T by hand forcehMotor assisting torque TmAnd ground moment of resistance TloadFor input, the joint of the upper pipe column and the middle shaft of the pipe columnTorque sensor signal T acquired by torque sensor on torsion barseAn output mathematical model of the electric power steering system;
step 2: obtained by laplace transform arrangement of differential equations: with motor assisting torque TmFor input, the torque sensor signal TseAs a transfer function G of the outputms(s); by hand force moment ThFor inputting, torque sensor signals TseAs a transfer function G of the outpuths(s); ground resisting moment T for vehicle by ground actionloadFor inputting, torque sensor signals TseAs a transfer function G of the outputls(s)；
And step 3: establishing a torque sensor signal TseFor input, target moment TcmdFor the control strategy of the output torque control loop, the motor assisting torque TmUsing torque control loop and torque sensor signal TseThe transfer function H which has obvious influence on the steering feeling of a driver is obtained through a mathematical model of the power-assisted steering system and a torque control loophs(s)；
And 4, step 4: will torque sensor signal TseAs the main disturbance of the EPS system, the torque control loop utilizes a second order feedforward controller Qff(s) performing disturbance compensation;
and 5: considering the change of the EPS system transfer characteristic caused by the main disturbance as the uncertainty of the system, a nominal system transfer function G containing an estimation is establishedeq(j ω) and transfer function G of nominal measurable disturbance to process outputd_eq(j ω) an internal model control structure; establishing a design target of the robust feedforward controller by using a robust control theory, and solving an optimal algorithm to obtain a robust second-order feedforward controller;
step 6: by adding a high frequency gain compensator Hhfg(s) adjusting the control effect of the controller in the high frequency band.
According to the EPS system dynamics modeling diagram, as shown in FIG. 2. The differential equation of the system is listed by Newton's second law, and the input of the system is hand force moment ThMotor torque TmAnd ground moment of resistance TloadThe output of the system is a torque signal T acquired by a torque sensor on a torsion bar at the joint of the upper pipe column and the middle shaft of the pipe columnse. Considering the motor part as an external input T to the systemmOnly the inertia and the damping of the motor are considered, and the electrical characteristics and the control strategy are ignored. The differential equation describing the dynamic behavior of the system is as follows:
Tse＝Kse(θh-θc) (2)
in the formula ThFor steering wheel steering torque, TmIs the assistance torque of the motor, TloadMoment of resistance to the vehicle for ground application, JhRepresenting the moment of inertia of the steering wheel and upper column, JcRepresenting the moment of inertia of the intermediate shaft, JmRepresenting the moment of inertia of the motor, MrIndicating the mass of the rack, JfwRepresenting the moment of inertia of the wheel and steering mechanism, BhRepresents the damping coefficient of the steering wheel and the upper column, BcExpressing the damping coefficient of the intermediate shaft, BmRepresenting the damping coefficient of the motor, BrExpressing the damping coefficient of the rack and pinion, BfwDamping coefficient, K, representing wheel and steering dampingseRepresenting torsional stiffness of the torsion bar of the pipe string, KcIs composed ofTorsional rigidity of the intermediate shaft, KrRepresenting the stiffness of the rack and pinion, KzRepresenting the steering stiffness, theta, of the wheelshIndicating the angle of rotation, theta, of the steering wheelcRepresenting the angle of rotation, theta, of the intermediate shaftmIndicating the angle of rotation, X, of the motorrIndicating the displacement of the rack, thetafwThe turning angle of the front wheel is shown, G is the reduction ratio of the worm gear reducer, and A is the transmission ratio of the steering mechanism.
In modeling, the rigidity of the motor is not considered, so that the rotation angle of the motor and the rotation angle of the intermediate shaft have a proportional relation, namely:
θm＝G·θc(7)
the mathematical model of the EPS system established in the embodiment is a multi-input single-output model, and the motor-assisted torque T is obtained through Laplace transform arrangement of a differential equationmFor input, the torque sensor signal TseAs a transfer function G of the outputms(s); by hand force moment ThFor input, the torque sensor signal TseAs a transfer function G of the outpuths(s); moment of resistance T applied to vehicle by groundloadFor input, the torque sensor signal TseAs a transfer function G of the outputls(s)。
The moment control loop comprises a power-assisted curve and a controller, can be simplified as shown in figure 3 at a certain vehicle speed, and can be controlled according to a moment sensor signal T in the power-assisted curveseWith target torque TcmdThe target torque T is obtained by calculating the mapping relationcmd。
Then in the whole EPS system, according to the mathematical model of the system, the transfer characteristic of the system can be expressed in the form of the following transfer function:
Tse(s)＝Ghs(s)·Th(s)+Gms(s)·Tm(s)+Gls(s)·Tload(s) (8)
according to fig. 3, at a certain vehicle speed:
Tm(s)＝a(Tse)·Tse(s) (9)
the motor power-assisted torque T is used in modelingmAs an external input to the system, this meansMotor assisting torque TmWithout affecting the transfer characteristics of the system. However, in the actual working process of EPS, the motor assisting torque TmIs an intermediate quantity that can be determined from the control strategy and the real-time sensor torque signal according to equation 9. Substituting equation 9 for equation 8, a system transfer function incorporating the control strategy can be obtained:
Tse(s)＝Ghs(s)·Th(s)+Gms(s)·a(Tse)·Tse(s)+Gls(s)·Tload(s) (10)
the EPS system will be simplified to dual input (T)h，Tload) Single output (T)se) The system, equation 10, can be converted to:
t can be obtained from formula 11hFor input, TseAs an equivalent transfer function H of the outpuths(s) that significantly affects the steering feeling of the driver, and the controller will be designed around the frequency response characteristic of the transfer function as follows.
Considering the change of the transfer characteristic of the EPS system as the uncertainty of the system, the uncertainty of the system can be represented by equation 13, and the uncertainty of the transfer function of the measurable disturbance acting on the process output can be represented by equation 14:
the torque control strategy of the EPS is converted into the internal model control structure shown in fig. 1, and the expression of the process output obtained by the structure shown in fig. 1 is:
assuming without loss of generality that the target input r(s) is set to zero, the process output can be written as:
when considering the uncertainties described by equations 13 and 14, the effect of the disturbance on the process output can be adjusted by the action of the controller, thus increasing the robustness of the control system, and the structure and parameters of the controller need to be adjusted to minimize equation 17:
for the robust performance analysis of the feedforward controller based on the internal model, in order to reduce the influence of disturbance in an uncertain system on process output, the design target of the robust feedforward controller of the EPS system is as follows:
w is a frequency weighting function, a frequency range with expected control performance attenuation as little as possible is set, and the main operating frequency range of the EPS system is a low frequency band, so that W(s) ((0.3 s + 1)/s) is selected for frequency weighting, so that the controller keeps a good control effect in the main operating frequency range of the EPS system.
Using the torque control loop equivalent, equation 18 can be obtained:
the second order controller is shown in equation 20. And the design target of the robust feedforward controller provided by the formula 18 is utilized to optimize the second-order controller, so as to obtain the optimal robust feedforward controller:
the second-order controller comprises 4 optimization parameters, namely two poles P1And P2Damping ratio ξ and undamped oscillation frequency omegan. With the optimization algorithm, 4 optimization parameters can be obtained.
A high-frequency gain compensator shown in figure 4 is added in the torque control loop to make up for the lack of control effect of the high-frequency part of the secondary controller.
In order to solve the problem that the control effect of the second-order feedforward controller in a high-frequency range is not ideal enough, a high-frequency gain compensator is added in a feedforward control channel to compensate the second-order controller in a high-frequency part. The high-frequency gain compensator has a structure as shown in fig. 5, wherein an input signal passes through a low-pass filter to separate a low-frequency signal and a high-frequency signal, and the low-frequency signal and the high-frequency signal are summarized and output after the low-frequency signal and the high-frequency signal respectively pass through the action of a low-frequency gain and a high-frequency gain.
Wherein the transfer function H of the low-pass filterlp(s) is:
ωlpthe cut-off frequency of the low-pass filter is determined by the resonant peak frequency of the EPS system.
Equivalent transfer function H of high-frequency gain compensatorhfg(s) is:
Hhfg(s)＝LG·Hlp(s)+HG·(1-Hlp(s)) (22)
where LG is the low frequency gain HG is the high frequency gain. And adjusting the control effect of the secondary controller in the high frequency band by adjusting the high frequency gain parameter.
As shown in fig. 6, which is a graph illustrating the improvement effect of the high frequency gain compensator on the transfer function of the second-order controller, it can be seen that the high frequency gain compensator only changes the transfer characteristic of the second-order controller in the high frequency band, but does not change the transfer characteristic of the second-order controller in the low frequency band. Compared with adjusting the parameters of the second-order control, the method is simpler and more effective.
The controller 1 was designed using the classical feedforward controller design method, while the controller 2 was designed using the robust feedforward controller design method of the present invention. The transfer function H under the action of the controllerhsThe performance index(s) is shown in table 1, and it can be seen from the table that under the action of the controller 2, the amplitude margin and the phase margin of the system are both larger than those under the action of the controller 1, and the resonance peak value of the system is both smaller than those under the action of the controller 1, that is, the system under the action of the controller 2 has higher relative stability and better robustness. Due to the uncontrolled transfer function H under the boosting gain of 0.8hs(s) worst performance, so the system performance at a boost gain of 0.8 is of interest here, from the transfer function H shown in FIG. 7 with control and without controller at boost gainhs(s) bode plot, it can be seen that the controller 2 can maintain the amplitude of the system at 0dB over a wide frequency range; the influence on the response of the system in the medium-high frequency range is lower than that of the controller 1 while the resonance peak value is reduced, and the control effect of the controller 2 is better than that of the controller 1.
TABLE 1 transfer function H under the action of the controllerhs(s) performance index
Fig. 8 is a unit step response diagram of the EPS system, in the unit step response simulation process, the performance of the controller 2 is better than that of the controller 1, and on the basis of similar response speed, the overshoot of the controller 2 is smaller.
And the effect of the controller is verified by utilizing the motor corner to drive the input rack. The experimental input working condition is as shown in fig. 9, and the condition that a normal person rotates the steering wheel in different directions is simulated. The experimental load was about 30Nm of torque provided by a magnetic particle clutch. And a torque sensor in the EPS system is used for acquiring a torque signal, and the torque fluctuation conditions of the EPS system under the control of different controllers are analyzed.
Fig. 10 shows a time domain result of a motor corner drive input torque response experiment, where a standard deviation and an overshoot of a calculated torque response are used as quantization indexes of a torque fluctuation control effect, and the quantization indexes are shown in table 2. Under the condition that the quality of the control effect is difficult to judge through the time domain result, the quantitative index can assist people in judging, wherein the standard deviation of the moment response can reflect the moment fluctuation of the EPS system to a certain extent, and the smaller the standard deviation of the moment response, the smaller the moment fluctuation. As can be seen from table 4, controller 2 has a significantly lower standard deviation and overshoot of the torque response than under the control of controller 1, while controller 2 has a further lower standard deviation and overshoot of the torque response after the addition of the high frequency gain compensator. Therefore, the robust feedforward controller has a better control effect than a classical feedforward controller, and the robust feedforward controller and the high-frequency gain compensator can effectively reduce the moment fluctuation of the system and have a better control effect.
Table 2 control effect quantization indices:
the present invention has been illustrated by the foregoing examples, but it should be understood that the foregoing examples are for purposes of illustration and description only and are not intended to limit the invention to the scope of the examples described. Furthermore, it will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that many variations and modifications may be made in accordance with the teachings of the present invention, all of which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (6)
1. A robust feedforward controller and high-frequency gain compensator optimization method is characterized by comprising the following steps:
step 1: build up torque T by hand forcehMotor assisting torque TmAnd ground moment of resistance TloadFor inputting, a torque sensor signal T is acquired by a torque sensor on a torsion bar at the joint of a pipe column on the pipe column and the intermediate shaftseAn output mathematical model of the electric power steering system;
step 2: tong (Chinese character of 'tong')The laplace transform of the over-differential equation is collated to yield: with motor assisting torque TmFor input, the torque sensor signal TseAs a transfer function G of the outputms(s); by hand force moment ThFor inputting, torque sensor signals TseAs a transfer function G of the outpuths(s); ground resisting moment T for vehicle by ground actionloadFor inputting, torque sensor signals TseAs a transfer function G of the outputls(s)；
And step 3: establishing a torque sensor signal TseFor input, target moment TcmdFor the control strategy of the output torque control loop, the motor assisting torque TmUsing torque control loop and torque sensor signal TseThe transfer function H which has obvious influence on the steering feeling of a driver is obtained through a mathematical model of the power-assisted steering system and a torque control loophs(s)；
And 4, step 4: will torque sensor signal TseAs the main disturbance of the EPS system, the torque control loop utilizes a second order feedforward controller Qff(s) performing disturbance compensation;
and 5: considering the change of the EPS system transfer characteristic caused by the main disturbance as the uncertainty of the system, a nominal system transfer function G containing an estimation is establishedeq(j ω) and transfer function G of nominal measurable disturbance to process outputd_eq(j ω) an internal model control structure; establishing a design target of the robust feedforward controller by using a robust control theory, and solving an optimal algorithm to obtain a robust second-order feedforward controller;
step 6: by adding a high frequency gain compensator Hhfg(s) adjusting the control effect of the controller in the high frequency band.
2. The method as claimed in claim 1, wherein in step 3, the torque control loop comprises a boost curve and a feedforward controller, the boost curve determining a motor boost torque T at a certain vehicle speedmAnd torque sensor signal TseThe function mapping relation of the motor is that the power-assisted torque is equal to the power-assisted gain a (T)se) Multiplying by the torque sensor signal Tse：
Tm(s)＝a(Tse)·Tse(s)。
3. A robust feedforward controller and high-frequency gain compensator optimization method according to claim 2, wherein in step 3, the transfer function Hhs(s) the expression is:
4. the method as claimed in claim 1, wherein the robust feedforward controller and the high-frequency gain compensator are designed to have the following design objectives in step 5:
where w(s) is a frequency weighting function that sets a frequency range where the expected control performance is attenuated as little as possible.
5. A robust feedforward controller and high-frequency gain compensator optimization method as in claim 4, wherein the frequency weighting function W(s) is frequency weighted according to the following equation:
W(s)＝(0.3s+1)/s。
6. the method as claimed in claim 1, wherein the step 6 is performed by using a robust feedforward controller and a high-frequency gain compensator to optimize the equivalent transfer function H of the high-frequency gain compensatorhfg(s) is:
Hhfg(s)＝LG·Hlp(s)+HG·(1-Hlp(s))
where LG is the low frequency gain, HG is the high frequency gain, the transfer function H of the low pass filterlp(s) Comprises the following steps:
cut-off frequency omega of low-pass filterlpIs the EPS system resonance peak frequency.
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| CN113848939A (en) * | 2021-10-14 | 2021-12-28 | 河南嘉晨智能控制股份有限公司 | Method for improving acceleration and deceleration dynamic performance of industrial vehicle |
| CN114802425A (en) * | 2022-05-09 | 2022-07-29 | 中国第一汽车股份有限公司 | Motor output torque determination method, device, equipment and storage medium |
| CN115214764A (en) * | 2021-12-20 | 2022-10-21 | 广州汽车集团股份有限公司 | Steering control method, device and readable storage medium |
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