CN113110023B - Structure correction control method based on Hamiltonian model of diesel engine - Google Patents
Structure correction control method based on Hamiltonian model of diesel engine Download PDFInfo
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Abstract
The invention discloses a structural correction control method based on a Hamiltonian model of a diesel engine, which belongs to the technical field of control, wherein the output control of the diesel engine is a key problem in the operation of the diesel engine.
Description
Technical Field
The invention belongs to the technical field of diesel engine control, and particularly relates to a structural correction control method based on a Hamiltonian model of a diesel engine.
Background
The diesel engine belongs to mechanical equipment for providing power moment, and the control research on the output characteristics of the diesel engine is an important point in the research of the diesel engine. At present, control constructed based on a diesel engine model can be roughly divided into two types, namely, PID parameter optimization based on traditional PID control and combined with a new control theory, and new controller replacement PID control is constructed, and the design ideas of the two types of control are different, but the aim is to realize the inhibition of overshoot in the transient process and the reduction of transient oscillation time. The generalized Hamiltonian system has outstanding characteristics in solving the control problem of a nonlinear system, and the structure and the damping matrix of the generalized Hamiltonian system can display the dynamic information related between the internal parameters of the model, so that the research on the control characteristics of the diesel engine based on the Hamiltonian model is a new thought.
Disclosure of Invention
The invention adopts the hamilton structure correction method to design the additional control of the diesel engine, designs the control on the basis of the hamilton model of the diesel engine through the hamilton structure correction method,the diesel engine control law is obtained through structural matrix factor design under the condition of ensuring the stability of a diesel engine system, feedback stabilization control is realized, and the diesel engine is taken as a research object by the control method through simulation verification, so that the purpose of finding a corrected control variable is achieved; firstly, directly giving a Hamiltonian model of a diesel engine, and selecting a modified Hamiltonian function Hd and a modification matrix J on the basis of the Hamiltonian model α And R is α Calculating a vector function K (x), and deducing a control variable u according to the Hamiltonian correction theory α And M Lα 。
The invention is based on the Hamiltonian of the diesel engine:
wherein: h (x) is Hamiltonian, m 1 (kg) is the mass of the moving part of the diesel engine actuator, x 1 (m/s) is the displacement of the actuator output; x is x 2 (m) is the actuator movement speed; k (k) 1 Is the elastic coefficient of the spring in the actuator; t (T) j Is an inertial time constant; omega 1 Is the electrical angular velocity increment (per-sign value) of the rotation axis of the diesel engine; omega B =314 (rad/s) is a reference value of the electrical angular velocity;
a non-linear system port controlled hamiltonian system representation can be written as:
x is the state variable matrix, i.e. x= [ x ] 1 x 2 ω 1 ] T W (x) is a control variable, J (x) is an antisymmetric matrix, i.e., J (x) = -J T (x) R (x) is a damping symmetry matrix, i.e. R (x) =r T (x) More than or equal to 0, g (x) is an input matrix, and y is an output matrix;
wherein:
wherein: k (k) x1 、k u 、a 1 、d 1 、c 1 、k ω Is a diesel engine actuator parameter; d (D) d The equivalent damping coefficient of the diesel engine; w (x) is a control variable; m is M L Controlling the moment for the load; t (T) j Is an inertial time constant(s); u is the control amount of the diesel engine.
The design of the invention is based on the following:
theorem: given a balance point x 0 And desired structural modification J a (x) Damping correction R a (x) It is assumed that a control α (x) and a vector function K (x) can be found that satisfy:
and causing:
(i)J d (x)＝J(x)+J α (x)＝-[J(x)+J α (x)] T ；R d (x)＝R(x)+R α (x)＝[R(x)+R α (x)] T ；
(ii)
(iii) At the equilibrium point x 0 The method comprises the following steps:
(iv) At the equilibrium point x 0 The method comprises the following steps:
(iv)
the closed loop system at u (x) =α (x) can be:
wherein H is d (x)＝H(x)+H α (x)，x 0 Is the (local) stable equilibrium point of the closed loop system, H a (x) Is an energy correction function; h d (x) Is a quasi-Lyapunov function of the equilibrium point.
Based on the conditions, the invention provides a structure correction control method based on a Hamiltonian model of a diesel engine, wherein the diesel engine comprises an electromagnetic actuator and a body; on the basis of the Hamiltonian model of the diesel engine, a structural matrix J which is expected to be corrected is given α Finding the control α (x) and the vector function K (x) allows the system to obtain the additional control variable u under stable conditions α And M Lα The method comprises the following specific steps:
the first step: selecting Hamiltonian and correction matrix of corrected system
Selecting Hamiltonian H of the corrected system d The following are provided:
wherein x is 0 ＝[x 10 x 20 ω 1(0) ] T Is the initial value of the state variable;
and a second step of: design structure correction matrix J α (x)
Since there are three variables in the Hamiltonian model, the structural matrix J is sought α (x) For a 3×3 matrix, only the correction of the principal element is considered in the correction design, due to the actuator displacement x 1 And actuator speed x 2 Rotational speed omega of shaft 1 Is the influence of two main factors, so in the antisymmetric matrix J a (x) Setting correction element J at corresponding position of (2) 13 、J 23 Wherein J 13 Representing the effect of displacement on output shaft speed, J 23 The other positions are set to zero, representing the effect of actuator speed on shaft speed. Due to not matching R α The matrix is modified and may be given as a constant in design. J (J) α And R is α The following are provided:
and a third step of: calculating vector matrix function K (x)
Vector function K (x):
according to the relation that K should satisfy in theorem (iii), the following is calculated:
let the feedback control α be:
substituting (1) (2-1) (2-2) (4) (5) (6) (7) into (3), two expressions can be obtained as follows:
from (8) and (9) the control variable u can be derived α And a load moment M 2 The expression of (2) is as follows:
wherein:representing control before correction;
representing additional control resulting from the structural modification;
representing the load control torque before correction;
representing additional load control torque generated by the structural modification;
u α and M Lα Is a modified control variable, and after such design, formulas (10) and (11) contain J 13 And J 23 That is, the structure correction factor J is realized 13 And J 23 Is involved in the control of the diesel engine.
The beneficial effects of the invention are as follows:
the invention discloses a control method for structural modification on the basis of a Hamiltonian model of a diesel engine, which does not need to change the physical structure of the diesel engine, and achieves the purpose of modifying output by modifying structural parameters of a model of the diesel engine. The method is realized by means of software.
Drawings
FIG. 1 is J 23 Influence on diesel engine output;
FIG. 2 is J 13 Impact on diesel engine output.
Detailed Description
The invention will be further illustrated with reference to specific examples.
Example 1
The diesel engine hamilton function according to this embodiment:
wherein: h (x) is Hamiltonian, m 1 (kg) is the mass of the moving part of the diesel engine actuator, x 1 (m) is the displacement of the actuator output; x is x 2 (m/s) is the actuator movement speed; k (k) 1 Is the elastic coefficient of the spring in the actuator; t (T) j Is an inertial time constant; omega 1 Is the electrical angular velocity increment (per-sign value) of the rotation axis of the diesel engine; omega B =314 (rad/s) is a reference value of the electrical angular velocity;
a non-linear system port controlled hamiltonian system representation can be written as:
x is the state variable matrix, i.e. x= [ x ] 1 x 2 ω 1 ] T W (x) is a control variable, J (x) is an antisymmetric matrix, i.e., J (x) = -J T (x) R (x) is a damping symmetry matrix, i.e. R (x) =r T (x) More than or equal to 0, g (x) is an input matrix, and y is an output matrix;
wherein:
wherein: k (k) x1 、k u 、a 1 、d 1 、c 1 、k ω Is a diesel engine actuator parameter; d (D) d The equivalent damping coefficient of the diesel engine; w (x) is a control variable; m is M L Controlling the moment for the load; t (T) j Is an inertial time constant(s); u is the control amount of the diesel engine.
In the above prior art, the design of this embodiment is based on the following:
design theorem: given a balance point x 0 And desired structural modification J a (x) Damping correction R a (x) Assuming that a control α (x) and a vector function K (x) can be found, the following needs to be satisfied:
and causing:
(i)J d (x)＝J(x)+J α (x)＝-[J(x)+J α (x)] T ；R d (x)＝R(x)+R α (x)＝[R(x)+R α (x)] T ；
(ii)
(iii) At the equilibrium point x 0 The method comprises the following steps:
(iv) At the equilibrium point x 0 The method comprises the following steps:
(iv)
the closed loop system at u (x) =α (x) can be:
wherein H is d (x)＝H(x)+H α (x)，
x 0 Is the (local) stable equilibrium point of the closed loop system, H a (x) Is an energy correction function; h d (x) Is a quasi-Lyapunov function of the equilibrium point.
Based on the above conditions, the embodiment provides a structure correction control method based on a Hamiltonian model of a diesel engine, wherein the diesel engine comprises an electromagnetic actuator and a body; on the basis of the Hamiltonian model of the diesel engine, a structural matrix J alpha which is expected to be corrected is given, and the control alpha (x) and the vector function K (x) are searched, so that the system obtains an additional control variable u under the stable condition α And M Lα The method comprises the following specific steps:
the first step: selecting Hamiltonian and correction matrix of closed-loop system
Selecting Hamiltonian H of the corrected system d The following are provided:
wherein x is 0 ＝[x 10 x 20 ω 1(0) ] T Is the initial value of the state variable;
and a second step of: design structure correction matrix J α (x)
Since there are three variables in the Hamiltonian model, the structural matrix J is sought α (x) For a 3×3 matrix, only the correction of the principal element is considered in the correction design, due to the actuator displacement x 1 And actuator speed x 2 Rotational speed omega of shaft 1 Is the influence of two main factors, so in the antisymmetric matrix J a (x) Setting correction element J at corresponding position of (2) 13 、J 23 Wherein J 13 Representing the effect of displacement on output shaft speed, J 23 Representing the effect of actuator speed on shaft speed, other positions are set to zero, since R is not α The matrix is corrected, and can be given as a constant in design, J α And R is α The following are provided:
and a third step of: calculating vector matrix function K (x)
Vector function K (x):
according to the relation that K should satisfy in theorem (iii), the following is calculated:
let the feedback control α be:
substituting (1) (2-1) (2-2) (4) (5) (6) (7) into (3), two expressions can be obtained as follows:
from (8) and (9) the control variable u can be derived α And a load moment M Lα The expression of (2) is as follows:
wherein:representing control before correction;
representing additional control resulting from the structural modification;
representing the load control torque before correction;
representing additional load control torque generated by the structural modification; u (u) α And M Lα Is a modified control variable, and after such design, formulas (10) and (11) contain J 13 And J 23 That is, the structure correction factor J is realized 13 And J 23 Is involved in the control of the diesel engine.
Example 2
In this embodiment, the conclusion of embodiment 1 is simulated by using the data of a certain diesel engine, and the specific process is as follows:
the load carried by the diesel engine is selected as a generator under the simulation working condition, and the diesel generator is startedThe initial operating conditions are as follows: the active power output by the generator is p e =0.8 (normalized value), the generator power factor is 0.8, a step disturbance of 0.1 (normalized value) occurs at 0.1s generator load, and 0.2s disturbance disappears.
Simulation parameters: the rated power of the diesel engine is 1250kW omega B Rated rotation speed n=1500r/min, mass m 1 =0.8 kg, mechanical damping coefficient a 1 ＝-1245，c 1 ＝10.0N·s/mm，d 1 ＝15042，k c ＝0.2，k d ＝5.54，k ω ＝20，k x1 ＝200，k u =40, spring rate k 1 =3610; output shaft maximum stroke 10mm, moment of inertia j=71.822 kg.m 2 The method comprises the steps of carrying out a first treatment on the surface of the The number of pole pairs of the generator p=2; equivalent damping coefficient D of diesel engine d ＝2.1753。
The Hamiltonian models of the diesel engine in example 1, namely (2), (2-1), (2-2), (2-3), (2-4) and the deduced control expressions (10) and (11), are combined to obtain a diesel engine simulation model with correction control, and the correction factor J 13 And J 23 The results are shown in fig. 1 and 2 for the diesel engine.
As can be seen from the simulation results, in FIG. 1, change J 23 Different oscillation curves can be obtained, which shows that J23 plays different roles in inhibiting oscillation; in FIG. 2, change J 13 The oscillation of the load mutation can be effectively restrained, and the restraining effect on the active oscillation can be obtained by selecting proper structural factors.
Claims (1)
1. The structure correction control method based on the Hamiltonian model of the diesel engine is characterized in that the diesel engine comprises an electromagnetic actuator and a body; on the basis of the Hamiltonian model of the diesel engine, a structural matrix J which is expected to be corrected is given α Finding the control α (x) and the vector function K (x) allows the system to obtain the additional control variable u under stable conditions α And M Lα ；
The method comprises the following specific steps:
the first step: selecting Hamiltonian H of closed loop system d
Selecting and correctingHamiltonian function H of (1) d The following are provided:
wherein: x is a state variable; x is x 1 The displacement of the diesel engine actuator is m; x is x 2 For the movement speed of the actuator, m/s; omega 1 The value of the angular velocity increment of the main shaft of the diesel engine is shown as a per-mark value; x= [ x ] 1 x 2 ω 1 ] T ；x 0 Is the initial value of the state variable; x is x 0 ＝[x 10 x 20 ω 1(0) ] T k 1 N/m is the elastic coefficient of the actuator spring; m is m 1 Kg, the mass of the moving part of the actuator; t (T) j Is an inertial time constant, s; omega B =314 rad/s, which is a reference value of angular velocity;
and a second step of: design structure correction matrix J α (x)
Since the number of variables in the diesel engine model is three, the structural matrix J is sought α (x) For a 3 x 3 matrix, only the correction of the principal element is considered in the correction design, due to the actuator displacement x 1 And actuator speed x 2 Rotational speed omega of shaft 1 Is the influence of two main factors, so in the antisymmetric matrix J a (x) Setting correction element J at corresponding position of (2) 13 、J 23 Wherein J 13 Representing the effect of displacement on output shaft speed, J 23 Representing the effect of actuator speed on shaft speed, other positions are set to zero for R α The matrix can be given as constant, J, since it is not modified α And R is α The form is as follows:
and a third step of: calculating vector matrix function K (x)
According to H d And H (x) calculation:wherein H is a (x) Is an energy correction function, H α ＝H d -H (x); h (x) is a Hamiltonian of the diesel engine and is obtained from a Hamiltonian model of the diesel engine;
the invention is based on the Hamiltonian of the diesel engine:
wherein: h (x) is the diesel hamiltonian;
the hamilton model is:
w (x) is a control variable, J (x) is an antisymmetric matrix, i.e., J (x) = -J T (x) R (x) is a damping symmetry matrix, i.e. R (x) =r T (x) More than or equal to 0, g (x) is an input matrix, and y is an output matrix;
wherein:
wherein: k (k) x1 、k u 、a 1 、d 1 、c 1 、k ω Is a diesel engine actuator parameter; d (D) d The equivalent damping coefficient of the diesel engine; w (x) is a control variable; u is the control quantity of the diesel engine; m is M L Controlling the moment for the load;
let the feedback control be alpha-let,hamiltonian H (x), J (x), R (x) and H in Hamiltonian model of diesel engine d 、K(x)、J α 、R α Alpha is substituted into the following formula:
obtaining the control variable u a And a load moment M Lα The expression of (2) is as follows:
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