METHOD FOR CONSTRUCTING LINEAR LUENBERGER OBSERVER FOR VEHICLE CONTROL

Abstract

The present invention discloses a method for constructing linear luenberger observer for vehicle control. The method for constructing linear luenberger observer for vehicle control comprises the following steps: step 1: building a state-space equation of a driving system of a vehicle to judge observability of the driving system; step 2: dividing the state of the driving system into blocks, and reconstructing state components of the driving system to obtain an rewritten state observation equation of the driving system; step 3: introducing transformation into the rewritten state equation of the driving system to obtain an expression equation and an error equation of the Luenberger observer. The linear luenberger observer constructed by the present invention has low implementation difficulty. High-frequency noise in an output signal of a rotational speed sensor is reduced.

Claims

1. A method for constructing linear Luenberger observer for vehicle control, specifically comprising the following steps: step 1: building a state-space equation of a driving system of a vehicle to judge observability of the driving system; wherein a state equation of the driving system is built by utilizing {dot over ()}.sub.B, {dot over ()}.sub.v and T.sub.s as state variables, {dot over ()}.sub.B and {dot over ()}.sub.v as the output of the driving system, and T.sub.P and T.sub.v as the input of the driving system; the state-space equation of the driving system is shown in equation (1): $\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{x}=\mathrm{Ax}+\mathrm{Bu}\\ y=\mathrm{Cx}.Math.\end{array}& \left(1\right)\end{array}$ wherein x is the input of the state-space equation; y is the output of the state-space equation; $x=\left[\begin{array}{c}{\stackrel{.}{}}_B\\ {\stackrel{.}{}}_v\\ T_s\end{array}\right],A=\left[\begin{array}{ccc}-\frac{C_l}{J_P}& 0& -\frac{1}{J_P.Math.i_r}\\ 0& -\frac{C_v}{J_v}& \frac{1}{J_v}\\ \frac{k_s}{i_r}-\frac{C_s.Math.C_l}{J_P.Math.i_r}& \frac{C_s.Math.C_v}{J_v}-k_s& -\frac{C_s}{J_P.Math.i_r^2}-\frac{C_s}{J_v}\end{array}\right],.Math.B=\left[\begin{array}{cc}\frac{1}{J_P}& 0\\ 0& -\frac{1}{J_v}\\ \frac{C_s}{J_P.Math.i}& \frac{C_s}{J_v}\end{array}\right],C=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\end{array}\right],u=\left[\begin{array}{c}{T}_P\\ T_v\end{array}\right];$ {dot over ()}.sub.B is a rotation angle of an electric motor B; {dot over ()}.sub.v is a rotation angle of a vehicle wheel; .sub.B is a rotational speed of the electric motor; .sub.v is a rotational speed of the vehicle wheel; {dot over ()}.sub.B and {dot over ()}.sub.v are obtained by conducting integration on the rotational speeds .sub.B and .sub.v; T.sub.s is a torque of a drive shaft; C.sub.t is a damping of a speed reducer; J.sub.P is an inertia of a rotor of the electric motor B; i.sub.r is a main speed reducer transmission ratio; C.sub.v is a damping of the vehicle wheel; J.sub.v is the sum of an inertia of the vehicle wheel and an equivalent inertia equivalent from a vehicle body to the vehicle wheel; k.sub.s is a rigidity of the drive shaft; C.sub.s is a damping of the drive shaft; i is a transmission ratio of a main speed reducer; T.sub.P is a torque of an output shaft of the driving system; T.sub.v is a moment of resistance of a vehicle; an observability matrix of the driving system is $N=\left[\begin{array}{c}C\\ \mathrm{CA}\\ {\mathrm{CA}}^2\end{array}\right];$ when a rank of the observability matrix N is 3, the driving system is observable; step 2: dividing the state of the driving system into blocks, and reconstructing state components of the driving system to obtain a rewritten state observation equation of the driving system; step 3: introducing transformation into the rewritten state equation of the driving system to obtain an expression equation and an error equation of the Luenberger observer.

2. The method for constructing linear luenberger observer for vehicle control according to claim 1, wherein step 2 specifically comprises the following steps: the two measurable state variables are the output of the driving system: y=x.sub.1=[{dot over ()}.sub.B {dot over ()}.sub.v].sup.T; the state variable T.sub.s needs to be observed and is recorded as x.sub.2=[T.sub.s]; because the rank of a matrix C is 2, the state-space equation of the driving system is rewritten to be: $\{\begin{array}{c}\left[\begin{array}{c}{\stackrel{.}{x}}_1\\ {\stackrel{.}{x}}_2\end{array}\right]=\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}{B}_1\\ B_2\end{array}\right].Math.u\\ y=\left[I.Math..Math.0\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]=x_1.Math.\end{array}.Math..Math.A_{11}=\left[\begin{array}{cc}-\frac{C_l}{J_p}& 0\\ 0& -\frac{C_v}{J_v}\end{array}\right],A_{12}=\left[\begin{array}{c}-\frac{1}{J_P.Math.i}\\ \frac{1}{J_v}\end{array}\right],.Math.\mathrm{wherein}.Math..Math.A_{21}=\left[\frac{k_s}{i}-\frac{C_s.Math.C_t}{J_P.Math.i}.Math..Math.\frac{C_s.Math.C_v}{J_v}-k_s\right],A_{22}=\left[-\frac{C_s}{J_P.Math.i^2}-\frac{C_s}{J_v}\right],.Math.B_1=\left[\begin{array}{cc}\frac{1}{J_P}& 0\\ 0& -\frac{1}{J_v}\end{array}\right],B_2=\left[\frac{C_s}{J_P.Math.i}.Math..Math.\frac{C_s}{J_v}\right];$ I is a unit matrix; the driving system is divided into two subsystems .sub.1 and .sub.2; the two subsystems .sub.1 and .sub.2 are mutually coupled; a state equation of the subsystem .sub.1 is: $\{\begin{array}{c}{\stackrel{.}{x}}_1=A_{11}.Math.x_1+A_{12}.Math.x_2+B_1.Math.u\\ y=x_1.Math.\end{array}$ a state equation of the subsystem .sub.2 is:
X.sub.2=A.sub.21x.sub.1+A.sub.22x.sub.2+B.sub.2u the system state x.sub.2=[T.sub.s] of the subsystem .sub.2 is reconstructed; the input and the output of the system state x.sub.2 respectively are: $\{\begin{array}{c}{u}_{\mathrm{oblu}}=A_{21}.Math.x_1+B_2.Math.u.Math.\\ y_{\mathrm{oblu}}={\stackrel{.}{x}}_1-A_{11}.Math.x_1-B_1.Math.u\end{array}.Math.;$ an output error feedback item G(y) is introduced into the state equation of the subsystem .sub.2 to obtain an observer equation of the driving system as follows: $\begin{array}{c}{\stackrel{.}{\hat{x}}}_2=A_{21}.Math.x_1+A_{22}.Math.x_2+B_2.Math.u+G\left(y-\hat{y}\right)\\ =\left(A_{22}-{\mathrm{GA}}_{12}\right).Math.{\hat{x}}_2+u_{\mathrm{oblu}}+{\mathrm{Gy}}_{\mathrm{oblu}}\end{array}$ wherein G is a feedback gain matrix; G=[g.sub.1g.sub.2]; g.sub.1 is a feedback gain of the two measurable state variables; g.sub.2 is a feedback gain of the state variable T.sub.s.

3. The method for constructing linear luenberger observer for vehicle control according to claim 1, wherein in step 3, transformation ={circumflex over (x)}.sub.1Gy is introduced into the rewritten observer equation of the driving system to obtain an expression equation and an error equation of the Luenberger observer as follows: $\{\begin{array}{c}\stackrel{.}{\hat{w}}=\left(\frac{k_s}{i}-\frac{C_s.Math.C_l}{J_P.Math.i}-\frac{C_l.Math.g_1}{J_P}\right).Math.x_1+\left(\frac{C_s.Math.C_v}{J_v}-k_s+\frac{C_v.Math.g_2}{J_v}\right).Math.x_2+.Math.\\ \left(-\frac{C_d}{J_P.Math.i^2}-\frac{C_s}{J_v}+\frac{g_1}{J_P.Math.i}-\frac{g_2}{J_v}\right).Math.{\hat{x}}_3+\left(\frac{C_s}{J_P.Math.i}-\frac{g_1}{J_P}\right).Math.T_s+\left(\frac{C_s}{J_v}+\frac{g_2}{J_v}\right).Math.T_v\\ {\hat{x}}_3=\hat{w}+g_1.Math.x_1+g_2.Math.x_2.Math.\end{array}.Math..Math.{\stackrel{.}{\stackrel{~}{x}}}_3=\left(-\frac{C_s}{J_P.Math.i^2}-\frac{C_s}{J_v}+\frac{g_1}{J_P.Math.i}-\frac{g_2}{J_v}\right).Math.{\tilde{x}}_3.$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] To describe the technical solutions in the embodiments of the present invention or the prior art more clearly, the following briefly introduces the accompanying drawings required for describing the embodiments or the prior art. Apparently, the accompanying drawings in the following description show merely some embodiments in the present invention, and a person of ordinary skill in the art may still derive other drawings from these accompanying drawings without creative efforts.

[0021] FIG. 1 is a block diagram of a linear Luenberger observer.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] The following clearly and completely describes the technical solutions in the embodiments of the present invention with reference to accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are merely a part rather than all of the embodiments of the present invention. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0023] A hybrid vehicle has three power sources, namely an engine, an electric motor A and an electric motor B. The engine and the electric motor A are coupled to drive front wheels of a vehicle. The electric motor B is used for driving rear wheels of the vehicle. Power batteries are electrically connected with the electric motor A and the electric motor B. An external force acted on the vehicle during straight running mainly comprises a traction force, a rolling resistance, an air resistance, a grade resistance, an acceleration resistance and the like. If such external force is transformed into a moment of force acted on the vehicle, a kinetic equation of the driving system is shown as follows:

[00009]$.Math.\{\begin{array}{c}{J}_P.Math.{\stackrel{\mathrm{.Math.}}{}}_B=T_P-C_i.Math.{\stackrel{.}{}}_B-\frac{1}{\text{?}}.Math.T_s\\ J_v.Math.{\stackrel{\mathrm{.Math.}}{}}_v=T_s-C_v.Math.{\stackrel{.}{}}_v-T_v\\ T_s=C_s\left(\frac{{\stackrel{.}{}}_B}{\text{?}}-{\stackrel{.}{}}_v\right)+k_s\left(\frac{{}_B}{i_r}-{}_v\right)\end{array}.Math..Math.\text{?}.Math.\text{indicates text missing or illegible when filed}$

[0024] wherein {dot over ()}.sub.B is a rotation angle of the electric motor B; {dot over ()}.sub.v is a rotation angle of a vehicle wheel; .sub.B is a rotational speed of the electric motor; .sub.v is a rotational speed of the vehicle wheel; {dot over ()}.sub.B and {dot over ()}.sub.v are obtained by conducting integration on the rotational speeds .sub.B and .sub.v; J.sub.P is an inertia of a rotor of the electric motor B; T.sub.P is a torque of an output shaft of a driving system; C.sub.t is a damping of a speed reducer; i.sub.r is a transmission ratio of a main speed reducer; J.sub.v is the sum of an inertia of the vehicle wheel and an equivalent inertia equivalent from a vehicle body to the vehicle wheel; C.sub.v is a damping of the vehicle wheel; C.sub.s is a damping of the drive shaft; k.sub.s is a rigidity of the drive shaft; T.sub.v is a moment of resistance of the vehicle; based on this, a state observer is built for the torque T.sub.s of the driving shaft to observe, wherein {umlaut over ()}.sub.B is a rotation angle acceleration of the electric motor B, and {umlaut over ()}.sub.v is a rotation angle acceleration of the vehicle wheel.

[0025] A method for constructing linear luenberger observer for vehicle control comprises the following steps:

[0026] step 1: building a state-space equation of a driving system of a vehicle to judge observability of the driving system;

[0027] wherein a state equation of the driving system is built by utilizing {dot over ()}.sub.B, {dot over ()}.sub.v and T.sub.s as state variables, {dot over ()}.sub.B and {dot over ()}.sub.v as the output of the driving system, and T.sub.P and T.sub.v as the input of the driving system; the state-space equation of the driving system is shown in equation (1):

[00010]$\begin{array}{cc}.Math.\{\begin{array}{c}\hat{x}=\mathrm{Ax}+\mathrm{Bu}\\ y=\mathrm{Cx}\end{array}.Math..Math..Math.\mathrm{wherein}.Math..Math.x=\left[\begin{array}{c}\text{?}\\ \text{?}\\ \text{?}\end{array}\right],.Math..Math.A=\left[\begin{array}{ccc}-\frac{\text{?}}{J_P}& 0& -\frac{1}{J_p.Math.i_v}\\ 0& -\frac{C_v}{J_v}& \frac{1}{J_v}\\ \frac{\text{?}}{\text{?}}-\frac{\text{?}}{\text{?}}& \frac{C_s.Math.C_v}{J_v}-\text{?}& -\frac{\text{?}}{J_p.Math.i_r^2}-\frac{\text{?}}{J_v}\end{array}\right],.Math..Math.B=\left[\begin{array}{cc}\frac{1}{J_p}& 0\\ 0& -\frac{1}{J_v}\\ \frac{\text{?}}{J_p.Math.i}& \frac{\text{?}}{J_v}\end{array}\right],C=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\end{array}\right],u=\left[\begin{array}{c}\text{?}\\ T_v\end{array}\right];.Math..Math.\text{?}.Math.\text{indicates text missing or illegible when filed}& \left(1\right)\end{array}$

i is a transmission ratio of the main speed reducer, x is the input of the state-space equation, and y is the output of the state-space equation; therefore, an observability matrix of the driving system is

[00011]$N=\left[\begin{array}{c}C\\ \mathrm{CA}\\ {\mathrm{CA}}^2\end{array}\right];$

[0028] equation (1) is substituted into the observability matrix to obtain:

[00012]$.Math.N=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ -\frac{C_i}{J_p}& 0& -\frac{1}{J_p.Math.i}\\ 0& -\frac{C_v}{J_v}& \frac{1}{J_v}\\ \begin{array}{c}\frac{\text{?}}{J_p^2}-\\ \frac{1}{J_p.Math.i}.Math.\left(\frac{\text{?}}{i}-\frac{C_s.Math.C_i}{J_p.Math.i}\right)\end{array}& -\frac{1}{J_p.Math.i}.Math.\left(\frac{C_s.Math.C_v}{J_v}-\text{?}\right)& \begin{array}{c}\frac{C_i}{J_p^2.Math.i}+\\ \frac{1}{J_p.Math.i}.Math.\left(\frac{\text{?}}{J_p.Math.i^2}+\frac{C_s}{J_v}\right)\end{array}\\ \frac{1}{J_v}.Math.\left(\frac{k_s}{i}-\frac{C_s.Math.C_i}{J_p.Math.i}\right)& \frac{C_v^2}{J_v^2}+\frac{1}{J_v}.Math.\left(\frac{C_s.Math.C_v}{J_v}-k_s\right)& \begin{array}{c}-\frac{C_v}{J_v^2}-\\ \frac{1}{J_v}.Math.\left(\frac{C_s}{J_p.Math.i^2}+\frac{\text{?}}{J_v}\right)\end{array}\end{array}\right]$$\text{?}.Math.\text{indicates text missing or illegible when filed}$

[0029] a rank (N) of the observability matrix of the driving system is 3, so the driving system is observable;

[0030] step 2: dividing the state of the driving system into blocks according to the state-space equation of the driving system, and reconstructing state components of the driving system to obtain a rewritten observer equation of the driving system;

[0031] the state variables {dot over ()}.sub.B and {dot over ()}.sub.v can be directly obtained through measurement, so, only a one-dimension dimension-reduction observer needs to be built to reconstruct T.sub.s to build a system with excellent dynamic property, strong robustness and operation stability, thereby improving the observability of the system;

[0032] the two measurable state variables are the output of the driving system: y=x.sub.1=[{dot over ()}.sub.B {dot over ()}.sub.v].sup.T; the state variable T.sub.s needs to be observed and is recorded as x.sub.2=[T.sub.s]; because the rank (C) is 2, the state of the torque of the drive shaft of the driving system is divided into the blocks, so the driving system can be rewritten to be:

[00013]$\{\begin{array}{c}A=\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right]\\ B=\left[\begin{array}{c}{B}_1\\ B_2\end{array}\right].Math.\\ C=\left[I.Math..Math.0\right].Math.\end{array}.Math..Math.A_{11}=\left[\begin{array}{cc}-\frac{C_l}{J_p}& 0\\ 0& -\frac{C_v}{J_v}\end{array}\right],A_{12}=\left[\begin{array}{c}-\frac{1}{J_P.Math.i}\\ \frac{1}{J_v}\end{array}\right],.Math.\mathrm{wherein}.Math..Math.A_{21}=\left[\frac{k_s}{i}-\frac{C_s.Math.C_t}{J_P.Math.i}.Math..Math.\frac{C_s.Math.C_v}{J_v}-k_s\right],.Math.A_{22}=\left[-\frac{C_s}{J_P.Math.i^2}-\frac{C_s}{J_v}\right],B_1=\left[\begin{array}{cc}\frac{1}{J_P}& 0\\ 0& -\frac{1}{J_v}\end{array}\right],.Math.B_2=\left[\frac{C_s}{J_P.Math.i^2}.Math..Math.\frac{C_s}{J_v}\right];$

I is a unit matrix;

[0033] the rewritten state-space equation of the driving system is:

[00014]$\{\begin{array}{c}\left[\begin{array}{c}{\stackrel{.}{x}}_1\\ {\stackrel{.}{x}}_2\end{array}\right]=\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}{B}_1\\ B_2\end{array}\right].Math.u\\ y=\left[I.Math..Math.0\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]=x_1.Math.\end{array}$

[0034] according to the state-space equation of the driving system, the driving system is divided into two subsystems .sub.1 and .sub.2; the two subsystems .sub.1 and .sub.2 are mutually coupled; a state equation of the subsystem .sub.1 is:

[00015]$\{\begin{array}{c}{\stackrel{.}{x}}_1=A_{11}.Math.x_1+A_{12}.Math.x_2+B_1.Math.u\\ y=x_1.Math.\end{array}$

[0035] a state equation of the subsystem .sub.2 is:

X.sub.2=A.sub.21x.sub.1+A.sub.22x.sub.2+B.sub.2u

[0036] the system state x.sub.2=[T.sub.s] of the subsystem .sub.2 is reconstructed; the input and the output of the system state x.sub.2 respectively are:

[00016]$\{\begin{array}{c}{u}_{\mathrm{oblu}}=A_{21}.Math.x_1+B_2.Math.u.Math.\\ y_{\mathrm{oblu}}={\stackrel{.}{x}}_1-A_{11}.Math.x_1-B_1.Math.u\end{array}$

[0037] an output error feedback item G(y) is introduced into the state equation of the subsystem .sub.2, wherein G is a feedback gain matrix; G=[g.sub.1g.sub.2], g.sub.1 is a feedback gain of two measurable state variables; g.sub.2 is a feedback gain of the state variable T.sub.s; so the observer equation of the driving system is obtained:

[00017]$\begin{array}{c}{\stackrel{.}{\hat{x}}}_2=A_{21}.Math.x_1+A_{22}.Math.x_2+B_2.Math.u+G\left(y-\hat{y}\right)\\ =\left(A_{22}-{\mathrm{GA}}_{12}\right).Math.{\hat{x}}_2+u_{\mathrm{oblu}}+{\mathrm{Gy}}_{\mathrm{oblu}}\end{array}$

[0038] step 3: introducing transformation into the rewritten state equation of the driving system to correct the state equation of the driving system, thereby obtaining an equation and a structure of the linear Luenberger observer;

[0039] because the rewritten observer equation of the driving system has a differential of an output quantity y of the driving system, the implementation difficulty of state variable observation is increased. Additionally, high-frequency noise in an output signal of a rotational speed sensor is also amplified such that an observation error is increased. To eliminate influence of the differential on the observation result, transformation is introduced into the rewritten observer equation of the driving system ={circumflex over (x)}.sub.1Gy;

[0040] the rewritten observer equation of the driving system is transformed to be:

[00018]$\{\begin{array}{c}\stackrel{.}{\hat{w}}=\left(A_{22}-{\mathrm{GA}}_{12}\right).Math.{\hat{x}}_2+\left(A_{21}-{\mathrm{GA}}_{11}\right).Math.y+\left(B_2-{\mathrm{GB}}_1\right).Math.u\\ {\hat{x}}_2=\hat{w}+\mathrm{Gy}.Math.\end{array}$

[0041] observation of the torque T.sub.s of the drive shaft is achieved by the observer equation of the driving system in step 3;

[0042] a state estimation error equation of the driving system is:

{dot over ({tilde over (x)})}.sub.2=x.sub.2{dot over ({circumflex over (x)})}.sub.2=(A.sub.22GA.sub.12){tilde over (x)}.sub.2

[0043] a pole of (A.sub.22GA.sub.12) is configured by utilizing a pole configuration method such that the estimation error {tilde over (x)}.sub.2 is quickly attenuated to be zero, thereby helping the estimation error {tilde over (x)}.sub.2 to quickly attenuate to be zero; the state-space equation of the driving system is substituted into the above equation to obtain an equation and a state observation error expression of the linear Luenberger observer to be:

[00019]$\{\begin{array}{c}\stackrel{.}{\hat{w}}=\left(\frac{k_s}{i}-\frac{C_s.Math.C_l}{J_P.Math.i}-\frac{C_l.Math.g_1}{J_P}\right).Math.x_1+\left(\frac{C_s.Math.C_v}{J_v}-k_s+\frac{C_v.Math.g_2}{J_v}\right).Math.x_2+.Math.\\ \left(-\frac{C_d}{J_P.Math.i^2}-\frac{C_s}{J_v}+\frac{g_1}{J_P.Math.i}-\frac{g_2}{J_v}\right).Math.{\hat{x}}_3+\left(\frac{C_s}{J_P.Math.i}-\frac{g_1}{J_P}\right).Math.T_s+\left(\frac{C_s}{J_v}+\frac{g_2}{J_v}\right).Math.T_v\\ {\hat{x}}_3=\hat{w}+g_1.Math.x_1+g_2.Math.x_2.Math.\end{array}.Math..Math.{\stackrel{.}{\stackrel{~}{x}}}_3=\left(-\frac{C_s}{J_P.Math.i^2}-\frac{C_s}{J_v}+\frac{g_1}{J_P.Math.i}-\frac{g_2}{J_v}\right).Math.{\tilde{x}}_3.Math..Math.\mathrm{wherein}.Math..Math.x=\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}{\stackrel{.}{}}_B\\ {\stackrel{.}{}}_v\\ T_s\end{array}\right];$

the design of the linear Luenberger observer is completed. The structure of the linear Luenberger observer is shown in FIG. 1.

[0044] Each embodiment of the present specification is described in a correlative manner, the same and similar parts between the embodiments may refer to each other, and each embodiment focuses on the difference from other embodiments. For a system disclosed in the embodiments, since it is basically similar to the method disclosed in the embodiments, the description is relatively simple, and reference can be made to the method description.

[0045] The above merely describes preferred embodiments of the present invention, but are not used to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, and the like within the spirit and principles of the invention are intended to be included within the protection scope of the present invention.