CN108828943A - A kind of Auto-disturbance-rejection Control with disturbance compensation and finite time convergence control - Google Patents
A kind of Auto-disturbance-rejection Control with disturbance compensation and finite time convergence control Download PDFInfo
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Abstract
Invention broadly provides a kind of Auto-disturbance-rejection Control with disturbance compensation and finite time convergence control, including disturbance compensation and finite time convergence control two parts, wherein：Disturbance compensation is exactly to be introduced into dead zone and anti-saturation link in control rate design, and error is disturbed and is compensated by observer, to inhibit load disturbance；Finite time convergence control is active disturbance rejection error feedback rate control of the design based on finite time convergence control.
Description
Technical field：
The present invention relates to marine diesel controls, more particularly to the Active Disturbance Rejection Control with disturbance compensation and finite time convergence control
Method.
Background technique：
Load disturbance caused by complicated sea situation frequently results in ship control system fluctuation frequently, not only increases control system and holds
The abrasion of row mechanism, and diesel engine speed is caused to vibrate, speed oscillation make distributive value big ups and downs again, and charger boost pressure
Power lags behind the variation of distributive value, eventually deteriorates diesel combustion characteristic, increases pollutant emission；If being in extreme load
When disturbance, or even there is the problems such as controlling input saturated phenomenon, this can cause overshoot to increase, control lag, regulating time is elongated,
Keep system unstable when serious.Currently, diesel speed control rule mainly uses PID control, but pid control parameter need to be with work
Condition changes and changes, and otherwise control effect is limited.Therefore, some scholars combine fuzzy control, neural network etc. with PID,
Improve its adaptive performance；Some scholars jump out PID control frame, are controlled using modern control theory, such as synovial membrane, model-free control
The design control methods such as system, improve control effect.Above-mentioned document does not all cause control system to act frequently, very load disturbance
It is studied to control input saturated phenomenon.The problem of acting frequently for control system, document introduce in control input quantity
Dead zone function, control effect is preferable, but is only applicable to discrete control；It is to the control input simplest treating method of saturated phenomenon
Control system gain is reduced, avoids the generation of saturated phenomenon, but the method is reduced and held because underusing control system capacity
The actual performance of row device eventually leads to the decline of control system performance.Therefore, study and design inhibit control system act frequently and
The method of control input saturated phenomenon has critically important theoretical and practical significance.
Summary of the invention：
To solve the above-mentioned problems, the Active Disturbance Rejection Control with disturbance compensation and finite time convergence control that the present invention provides a kind of
Dead zone and anti-saturation disturbance compensation module are introduced observer, the movement of propulsion control system when reducing load disturbance by method
Frequency improves control performance when control input saturation；The error feedback element of active disturbance rejection uses the sliding formwork of finite time convergence control
Feedback Control Laws, the convergence for reducing error feedback control link prove difficulty.
Technical solution：
A kind of Auto-disturbance-rejection Control with disturbance compensation and finite time convergence control, including disturbance compensation and finite time are received
Two parts are held back, wherein：
Disturbance compensation is exactly to be introduced into dead zone and anti-saturation link in control rate design, and error disturbance is passed through observer
It compensates, to inhibit load disturbance；
Finite time convergence control is active disturbance rejection error feedback rate control of the design based on finite time convergence control.
The disturbance compensation the specific steps are：
Step 1: establishing the mathematical model of control system under load disturbance：
And is inferred according to formula (1) and obtained：
Wherein, k1、k2It is the coefficient of fitting function, VdVolume, K are emptied for the every circulation of cylinderQIt is torque coefficient, NstIt is punching
Number of passes, ρ are densities of sea water, and D is airscrew diameter, ηiIt is indicated thermal efficiency,It is that the fuel oil that every circulation flows into cylinder is averaged matter
Amount, I are diesel engine, shafting and the total rotary inertia of each blade of propeller, HuIt is fuel low heating value, neIt (t) is diesel engine speed,
Set automatically controlled diesel engine system quantity of state peculiar to vessel as：x1(t)=∫ ne(t) dt, x2(t)=ne(t), then formula (1)
It can be write as：
Wherein, f (x1(t), x2(t))+g(x1(t), x2(t))u(t)-b0U (t) is to promote to disturb into system summation, and have
Boundary, u (t) are the input quantities of propulsion system, and y (t) is the output quantity of propulsion system, b0> 0 is estimated value；
Step 2: combining ship load disturbance using formula (2), the automatically controlled diesel propulsion peculiar to vessel of bringing onto load disturbance is obtained
Control system：
Wherein, l (t) is system load disturbance, is met | l (t) | < L, L are constant；
Enable x3=f (x1(t), x2(t))+g(x1(t), x2(t))u(t)-b0U (t)+l (t) is expansion state amount, and is rememberedThen formula (3), which is expanded, is：
Step 3: establish differentiator, use arc-function establish differentiator for：
Wherein：e1(t)=∫ e2(t) dt, e2(t)=v2(t)-r(t)；R (t) is system reference signal；Parameter R > 0, a1>
0, a20,0 < b < 1 of >, then, to any integrable bounded function r (t), pursuit gain v2(t) meet
Step 4：Dead zone and anti-saturation link introduce, and set the input quantity of anti-saturation control system as u, umaxFor actuator
Saturation value, then saturation function is represented by
Assuming that uaFor the saturation value of setting；It is exported for actuator,It obtains
Wherein τ=1.1；
By anti-saturation control principle it is found that when system in a saturated state, saturation disturbance quantity through observer as
A part of control system disturbance compensates,
According to the design of advanced anti-saturation, obtaining observer is：
In formula, β1> 0, β2> 0, β3> 0, K > 0, chooses appropriate β1、β2、β3, K, observer can with predictor formula (4)
All state variable x1(t)、x2(t) and x3(t), i.e. z1(t)→x1(t), z2(t)→x2(t), z3(t)→x3(t), anti-saturation is mended
Repaying COEFFICIENT K value is 0.4.
The finite time convergence control the specific steps are：
Set automatically controlled diesel propulsion control system quantity of state error peculiar to vessel as：e6(t)=∫ e7(t) dt, e7(t)=y
(t)-r=x2(t)-r, r are system reference signal, andζ is a smaller positive value, is dead zone valve
It is worth, ζ=0.05, then the corresponding error system of formula (3) is
By active disturbance rejection Feedback Control Laws it is found that u (t)=(u0(t)-z3(t))/b0, bring formula (10) into, can obtain
Because of expansion observer convergence, i.e.,：z1(t)→x1(t), z2(t)→x2(t), z3(t)→x3(t)=f (x1(t), x2
(t))+g(x1(t), x2(t))u(t)-b0U (t)+l (t), formula (11) can be written as
For formula (12), designing sliding-mode surface is
S=e7(t)+k1|e6(t)|γsgn(e6(t)) (13)；
In formula, 0 < γ < 1, k1> 0；
According to sliding mode control theory, to make system mode approach sliding-mode surface and moving along sliding-mode surface, choosing Reaching Law is：
In formula, R=| e7|, 0 < R < R0, R0=r；
From formula (13) and formula (14)
To meet sliding formwork reaching condition, i.e. system mode can reach sliding-mode surface；
Formula (13) derivation, then joint type (11), formula (14) can be obtained：
The Nonlinear control law is taken to be
Therefore, can obtain system control amount is：
In the case where considering dead zone and saturation, (18) formula can be written as
The beneficial effects of the present invention are：
Dead zone and anti-saturation disturbance compensation module are introduced observer, Solid rocket engine system when reducing load disturbance by the present invention
The operating frequency of system improves control performance when control input saturation；The error feedback element of active disturbance rejection is received using finite time
The sliding formwork Feedback Control Laws held back, the convergence for reducing error feedback control link prove difficulty.
Detailed description of the invention：
Fig. 1 is the propulsion control system of the invention containing load disturbance；
Fig. 2 is anti-saturation control system schematic diagram of the present invention；
Fig. 3 is the automatically controlled diesel engine speed response curve comparison diagram peculiar to vessel in dead zone of the present invention and anti-saturation；
Fig. 4 is the automatically controlled diesel engine speed error curve comparison diagram peculiar to vessel in dead zone of the present invention and anti-saturation；
Fig. 5 is the present invention using compensation and the rotating speed response curve comparison figure for not using compensation；
Fig. 6 is the present invention using compensation and the speed error curve comparison figure for not using compensation；
Fig. 7 is the present invention using compensation and the control of compensation is not used to input comparison diagram；
Fig. 8 is the present invention using compensation and the output torque comparison diagram for not using compensation.
Specific embodiment：
To keep goal of the invention of the invention, technical solution and advantage clearer, below in conjunction with attached drawing to of the invention
Embodiment is described in further detail.
A kind of disclosed Auto-disturbance-rejection Control with disturbance compensation and finite time convergence control, including disturbance are mended
Repay with finite time convergence control two parts, wherein：
Disturbance compensation is exactly to be introduced into dead zone and anti-saturation link in control rate design, and error disturbance is passed through observer
It compensates, to inhibit load disturbance, the specific steps are：
Establish the mathematical model of control system under load disturbance：
And is inferred according to formula (1) and obtained：
Wherein, k1、k2It is the coefficient of fitting function, VdVolume, K are emptied for the every circulation of cylinderQIt is torque coefficient, NstIt is punching
Number of passes, ρ are densities of sea water, and D is airscrew diameter, ηiIt is indicated thermal efficiency,It is that the fuel oil that every circulation flows into cylinder is averaged matter
Amount, I are diesel engine, shafting and the total rotary inertia of each blade of propeller, HuIt is fuel low heating value, neIt (t) is diesel engine speed,
Set automatically controlled diesel engine system quantity of state peculiar to vessel as：x1(t)=∫ ne(t) dt, x2(t)=ne(t), then formula (1)
It can be write as：
Wherein, f (x1(t), x2(t))+g(x1(t), x2(t))u(t)-b0U (t) is to promote to disturb into system summation, and have
Boundary, u (t) are the input quantities of propulsion system, and y (t) is the output quantity of propulsion system, b0> 0 is estimated value.
Electronic controlled diesel propulsion control system load disturbance refers in ship's navigation, because the unknown load such as complicated sea situation causes
Disturbance, with load disturbance characteristic Active Disturbance Rejection Control system structure it is as shown in Figure 1.
The ship load disturbance shown in Fig. 1 is combined using formula (2), obtains the electronic controlled diesel peculiar to vessel of bringing onto load disturbance
Propulsion control system：
Wherein, l (t) is system load disturbance, is met | l (t) | < L, L are constant；
Enable x3=f (x1(t), x2(t))+g(x1(t), x2(t))u(t)-b0U (t)+l (t) is expansion state amount, and is rememberedThen formula (3), which is expanded, is：
Establish differentiator, use arc-function establish differentiator for：
Wherein：e1(t)=∫ e2(t) dt, e2(t)=v2(t)-r(t)；R (t) is system reference signal；Parameter R > 0, a1>
0, a20,0 < b < 1 of >, then, to any integrable bounded function r (t), pursuit gain v2(t) meet
Anti-saturation control working principle based on observer (ESO) error compensation is as shown in Figure 2.Differentiator, observation in figure
Device uses counter-hyperbolic sine function, and error feedback control uses finite time convergence control nonlinear feedback.
The input quantity of anti-saturation control system is set as u, umaxFor actuator saturation value, then saturation function is represented by
Assuming that uaFor the saturation value of setting；K is anti-saturation penalty coefficient, and value is bigger, and compensating action is more obvious, but excessive,
It is easy to cause system unstable.It is exported for actuator,It obtains
Wherein τ=1.1；
By anti-saturation control principle it is found that when system in a saturated state, saturation disturbance quantity through observer as
A part of control system disturbance compensates,
According to the design of advanced anti-saturation, obtaining observer is：
In formula, β1> 0, β2> 0, β3> 0, K > 0, chooses appropriate β1、β2、β3, K, observer can be with predictor formula (4)
All state variable x1(t)、x2(t) and x3(t), i.e. z1(t)→x1(t), z2(t)→x2(t), z3(t)→x3(t), anti-saturation is mended
Repaying COEFFICIENT K value is 0.4.
The finite time convergence control the specific steps are：
Set automatically controlled diesel propulsion control system quantity of state error peculiar to vessel as：e6(t)=∫ e7(t) dt, e7(t)=y
(t)-r=x2(t)-r, r are system reference signal, andζ is a smaller positive value, is dead zone valve
It is worth, ζ=0.05, then the corresponding error system of formula (3) is
By active disturbance rejection Feedback Control Laws it is found that u (t)=(u0(t)-z3(t))/b0, bring formula (10) into, can obtain
Because of expansion observer convergence, i.e.,：z1(t)→x1(t), z2(t)→x2(t), z3(t)→x3(t)=f (x1(t), x2
(t))+g(x1(t), x2(t))u(t)-b0U (t)+l (t), formula (11) can be written as
For formula (12), designing sliding-mode surface is
S=e7(t)+k1|e6(t)|γsgn(e6(t)) (13)；
In formula, 0 < γ < 1, k1> 0；
According to sliding mode control theory, to make system mode approach sliding-mode surface and moving along sliding-mode surface, choosing Reaching Law is：
In formula, R=| e7|, 0 < R < R0, R0=r；
From formula (13) and formula (14)
To meet sliding formwork reaching condition, i.e. system mode can reach sliding-mode surface；
Formula (13) derivation, then joint type (11), formula (14) can be obtained：
The Nonlinear control law is taken to be
Therefore, can obtain system control amount is：
In the case where considering dead zone and saturation, (18) formula can be written as
Before carrying out theory analysis, finite time convergence control related notion is first introduced.
For following system
In formula, f：D→RnIt is domainTo RnOn locally Lipschitz function mapping, x=[x1, x2... xn]TFor
State variable.
Lemma 1：Consider nonlinear system (20), it is assumed that there are one is defined on the field of originOn C1
Smooth function V (x), there are real number c > 0 and 0 < a < 1, so that V (x) existsUpper positive definite, and?
Upper negative semidefinite, then the origin of system (20) is finite time stability.Stablize Time Dependent in initial value x (0)=x0, the upper bound
It is
In formula, x0It is any point in a certain open-neck collar domain of origin.IfAnd V (x) is
Radially unbounded (work as | | x | | →+∞) when, V (x) →+∞), then the origin of formula (20) is global finite time stability.
Below with stability in finite time theory, convergence is carried out to sliding formwork error feedback control link.
For the system (3) by load disturbance, just like drawing a conclusion：
Theorem 1：Consideration system (3), if design form such as (16) formula system control amount
The then state error e of control system6(t)、e7It (t) will be in finite time convergence control to zero, and when the finite convergence of system
Between meet：
It proves：Control system motion state can be divided into two steps：
Sliding-mode surface reaches the stage：It is close to sliding-mode surface by Reaching Law, until reaching sliding-mode surface；
Along sliding-mode surface motion stage：It is moved along the sliding-mode surface of selection, until reaching equalization point.
Stage progress theory analysis is reached to sliding-mode surface first.Herein for the approach sliding formwork stage, choose as follows
Lyapunov function
V=S2 (23)
Above formula derivation can be obtained
(14) formula is brought into, can be obtained
Through Lyapunov Theory of Stability it is found that control system is asymptotically stability.I.e. as t → ∞, S → 0.
It can be obtained by formula (23) and formula (25)
For control system operation in, R=| e7(t) |, 0 < R < R0, R0=r.
It can thus be concluded that
It can be obtained by lemma 1, control system will be in Finite-time convergence to sliding-mode surface, and finite convergence time satisfaction is as follows
Situation
By formula (28) it is found that control system will be in T1Sliding-mode surface is converged in time, i.e. control system is reached in sliding formwork
Stage is finite time convergence control.
Along sliding-mode surface motion stage theory analysis, i.e. system has been converged on sliding-mode surface and has been moved along sliding-mode surface, at this time
Control system state meets
S=e7(t)+k1|e6(t)|γsgn(e6(t))=0 (29)
Cause
It can be obtained by (29), (30)
It enables
e6=S ' (32)
Equation (31) can be changed to
For above formula, the Lyapunov function is taken to be
V '=S′2 (34)
Above formula derivation can be obtained
It can be obtained by (32), (33)
According to Lyapunov Theory of Stability it is found that system (33) is asymptotically stability, i.e., as t → ∞, S ' → 0.I.e.
As t → ∞, e6→0.By formula (29) it is found that working as e6When → 0, e7→0.Because of e7=y-r illustrates that control system output y finally will
Converge to setting value r.
According to (34) Shi Ke get
It can be obtained by lemma 1, system (33) is finite time convergence control, and the finite convergence time meets following situation
In conjunction with two motion stages of control system it is found that control system is finite time convergence control, i.e. finite time convergence control
To diesel engine setting speed.Two stages total convergence time THIt is represented by：
Card is finished.
For the validity for verifying the finite time convergence control Active Disturbance Rejection Control algorithm based on dead zone and anti-saturation, the present invention is used
Matlab/Simulink software to dead zone and saturation disturbance compensation active disturbance rejection algorithm (dead zone and anti-saturation FT-SADRC) and
It is studied in the application of automatically controlled diesel engine control system peculiar to vessel, and carries out emulation experiment pair with active disturbance rejection algorithm (ADRC)
Than.
In simulating, verifying, Active Disturbance Rejection Control algorithm observer parameter is β1、β2、β3, error feedback parameter is β01And β02,
Differentiator simulation step length is T0, velocity factor r0, filtering factor h, b0It is estimated value.Active Disturbance Rejection Control parameter is set as, T0
=0.01, r0=10, h=0.2, b0=1000, β1=15, β2=200, β3=80, β01=120, β02=21.Satisfy with anti-in dead zone
It is with FT-SADRC parameter designing：R=10, a1=1, a2=1, b=0.3, b0=1000, ts=3, K=0.4, k1=0.6, γ
=0.8, α=0.4, η=0.5.Load disturbance is l (t)=25 × 103Sin (t20 π) and unknown in control process, specifically
Policy correlation data is referring to shown in attached drawing 3~8.
Above-described embodiment is presently preferred embodiments of the present invention, is not a limitation on the technical scheme of the present invention, as long as
Without the technical solution that creative work can be realized on the basis of the above embodiments, it is regarded as falling into the invention patent
Rights protection scope in.
Claims (3)
1. a kind of Auto-disturbance-rejection Control with disturbance compensation and finite time convergence control, it is characterised in that including disturbance compensation and have
Time Convergence two parts are limited, wherein：
Disturbance compensation is exactly to be introduced into dead zone and anti-saturation link in control rate design, and error disturbance is carried out by observer
Compensation, to inhibit load disturbance；
Finite time convergence control is active disturbance rejection error feedback rate control of the design based on finite time convergence control.
2. the Auto-disturbance-rejection Control according to claim 1 with disturbance compensation and finite time convergence control, it is characterised in that：
Disturbance compensation the specific steps are：
Step 1: establishing the mathematical model of control system under load disturbance：
And is inferred according to formula (1) and obtained：
Wherein, k1、k2It is the coefficient of fitting function, VdVolume, K are emptied for the every circulation of cylinderQIt is torque coefficient, NstIt is number of stroke,
ρ is density of sea water, and D is airscrew diameter, ηiIt is indicated thermal efficiency,It is the fuel oil average quality that every circulation flows into cylinder, I is
Diesel engine, shafting and the total rotary inertia of each blade of propeller, HuIt is fuel low heating value, neIt (t) is diesel engine speed,
Set automatically controlled diesel engine system quantity of state peculiar to vessel as：x1(t)=∫ ne(t) dt, x2(t)=ne(t), then formula (1) can be write
At：
Wherein, f (x1(t), x2(t))+g(x1(t), x2(t))u(t)-b0U (t) is to promote into the disturbance of system summation, and bounded, u
(t) be propulsion system input quantity, y (t) is the output quantity of propulsion system, b0> 0 is estimated value；
Step 2: combining ship load disturbance using formula (2), the automatically controlled diesel propulsion control peculiar to vessel of bringing onto load disturbance is obtained
System：
Wherein, l (t) is system load disturbance, is met | l (t) | < L, L are constant；
Enable x3=f (x1(t), x2(t))+g(x1(t), x2(t))u(t)-b0U (t)+l (t) is expansion state amount, and is remembered
Then formula (3), which is expanded, is：
Step 3: establish differentiator, use arc-function establish differentiator for：
Wherein：e1(t)=∫ e2(t) dt, e2(t)=v2(t)-r(t)；R (t) is system reference signal；Parameter R > 0, a1> 0, a2
0,0 < b < 1 of >, then, to any integrable bounded function r (t), pursuit gain v2(t) meet
T > 0；
Step 4：Dead zone and anti-saturation link introduce, and set the input quantity of anti-saturation control system as u, umaxFor actuator saturation
Value, then saturation function is represented by
Assuming that uaFor the saturation value of setting；It is exported for actuator,It obtainsWherein
τ=1.1；
By anti-saturation control principle it is found that when system in a saturated state, disturbance quantity is saturated through observer as control
A part of system disturbance compensates,
According to the design of advanced anti-saturation, obtaining observer is：
In formula, β1> 0, β2> 0, β3> 0, K > 0, chooses appropriate β1、β2、β3, K, observer can be with all of predictor formula (4)
State variable x1(t)、x2(t) and x3(t), i.e. z1(t)→x1(t), z2(t)→x2(t), z3(t)→x3(t), anti-saturation compensation system
Number K value is 0.4.
3. the Auto-disturbance-rejection Control according to claim 2 with disturbance compensation and finite time convergence control, it is characterised in that：
Finite time convergence control the specific steps are：
Set automatically controlled diesel propulsion control system quantity of state error peculiar to vessel as：e6(t)=∫ e7(t) dt, e7(t)=y (t)-r=
x2(t)-r, r are system reference signal, andζ is a smaller positive value, be dead zone threshold values, ζ=
0.05, then the corresponding error system of formula (3) be
By active disturbance rejection Feedback Control Laws it is found that u (t)=(u0(t)-z3(t))/b0, bring formula (10) into, can obtain
Because of expansion observer convergence, i.e.,：z1(t)→x1(t), z2(t)→x2(t),
z3(t) → x3 (t)=f (x1(t), x2(t))+g(x1(t), x2(t))u(t)-b0U (t)+l (t), formula (11) can be written as
For formula (12), designing sliding-mode surface is
S=e7(t)+k1|e6(t)|γsgn(e6(t)) (13)；
In formula, 0 < γ < 1, k1> 0；
According to sliding mode control theory, to make system mode approach sliding-mode surface and moving along sliding-mode surface, choosing Reaching Law is：
In formula, R=| e7|, 0 < R < R0, R0=r；
From formula (13) and formula (14)
To meet sliding formwork reaching condition, i.e. system mode can reach sliding-mode surface；
Formula (13) derivation, then joint type (11), formula (14) can be obtained：
The Nonlinear control law is taken to be
Therefore, can obtain system control amount is：
In the case where considering dead zone and saturation, (18) formula can be written as
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| CN113406888A (en) * | 2021-08-18 | 2021-09-17 | 河南工学院 | LADRC-based steam turbine generator control system and static compensation coefficient determination method thereof |
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