Method for constructing linear luenberger observer for vehicle control

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 (θ)}B, {dot over (θ)}v and Ts as state variables, {dot over (θ)}B and {dot over (θ)}v as the output of the driving system, and TP and Tv as the input of the driving system;
• the state-space equation of the driving system is shown in equation (1):
• {
• x
• .
• =
• Ax
• +
• Bu
• y
• =
• Cx
• 
• (
• 1
• )
• wherein x is the input of the state-space equation;
• y is the output of the state-space equation;
• x
• =
• [
• θ
• .
• B
• θ
• .
• v
• T
• s
• ]
• ,
• A
• =
• [
• -
• C
• l
• J
• P
• 0
• -
• 1
• J
• P
• 
• i
• r
• 0
• -
• C
• v
• J
• v
• 1
• J
• v
• k
• s
• i
• r
• -
• C
• s
• 
• C
• l
• J
• P
• 
• i
• r
• C
• s
• 
• C
• v
• J
• v
• -
• k
• s
• -
• C
• s
• J
• P
• 
• i
• r
• 2
• -
• C
• s
• J
• v
• ]
• ,
• 
• B
• =
• [
• 1
• J
• P
• 0
• 0
• -
• 1
• J
• v
• C
• s
• J
• P
• 
• i
• C
• s
• J
• v
• ]
• ,
• C
• =
• [
• 1
• 0
• 0
• 0
• 1
• 0
• ]
• ,
• u
• =
• [
• T
• P
• T
• v
• ]
• ;
• {dot over (θ)}B is a rotation angle of an electric motor B;
• {dot over (θ)}v is a rotation angle of a vehicle wheel;
• θB is a rotational speed of the electric motor;
• θv is a rotational speed of the vehicle wheel;
• {dot over (θ)}B and {dot over (θ)}v are obtained by conducting integration on the rotational speeds θB and θv;
• Ts is a torque of a drive shaft;
• Ct is a damping of a speed reducer;
• JP is an inertia of a rotor of the electric motor B;
• ir is a main speed reducer transmission ratio;
• Cv is a damping of the vehicle wheel;
• Jv is the sum of an inertia of the vehicle wheel and an equivalent inertia equivalent from a vehicle body to the vehicle wheel;
• ks is a rigidity of the drive shaft;
• Cs is a damping of the drive shaft;
• i is a transmission ratio of a main speed reducer;
• TP is a torque of an output shaft of the driving system;
• Tv is a moment of resistance of a vehicle;
• an observability matrix of the driving system is
• N
• =
• [
• C
• CA
• CA
• 2
• ]
• ;
• 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.