CN107045285B - A kind of servo system self-adaptive parameter identification and control method with input saturation - Google Patents
A kind of servo system self-adaptive parameter identification and control method with input saturation Download PDFInfo
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- CN107045285B CN107045285B CN201710279942.1A CN201710279942A CN107045285B CN 107045285 B CN107045285 B CN 107045285B CN 201710279942 A CN201710279942 A CN 201710279942A CN 107045285 B CN107045285 B CN 107045285B
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract
A kind of servo system self-adaptive parameter identification and control method with input saturation, comprising: establish the servo system models with input saturation, initialize system mode and control parameter；Extracting parameter control information, and online design auto-adaptive parameter identifier, on-line identification system unknown parameter；Modified exponentially approaching rule is designed, converts input correlation function for saturation, and identified parameters is combined to design Reaching Law sliding mode controller.On-line parameter identification designed by the present invention and control algolithm have good identification and tracing control effect to positional servosystem, can high-precision on-line identification system parameter, and improve the control performance of servo-system, weaken the buffeting of input controller.
Description
Technical field
The invention belongs to servo system control technical field, it is related to a kind of online adaptive parameter identification and modified index
Reaching Law sliding-mode control, especially for servo system self-adaptive parameter identification and control method containing input saturation.
Background technique
With the development of industrial automation, servo-system is in industrial control field using more and more extensive.It is high-precision for having
For the positional servosystem that degree control requires, since system is easy by nonlinear characteristics such as external disturbance, saturation, frictions
It influences, high performance control relative difficulty.Therefore, for how to improve the parameter identification precision of system, and so as to improve system
Tracing control performance is current one of research hotspot.
Currently, the algorithm majority for being used to complete servo parameter identification belongs to offline identification method, but off-line identification
Method can not reaction system parameter in time variation, and can further influence the control performance of system.Therefore, for proposing one
Kind can online adaptive identification system parameter, and exterior nonlinear characteristic and the timely reaction system parameter of mechanical property is followed to become
The method of change is necessary.
Input saturation is the inevitable nonlinear characteristic of each servo-system, can reduce the control performance of system.
In order to improve the tracking accuracy and response speed of servo-system, many control methods are all suggested.It is sliding in numerous control methods
Mould control is widely studied due to its good robustness and performance of noiseproof.But the buffeting problem of sliding formwork control limits
Its application in practice.Reaching Law sliding-mode control is to reduce one of the scheme that sliding mode controller is buffeted, and how to improve
Nearly rule further weakens so that sliding formwork buffets problem, gets a good eye meaning.
Summary of the invention
In order to solve so that system is completed high-precision with the positional servosystem parameter identification and control problem of input saturation
Parameter identification and tracing control, the present invention provides a kind of online adaptive Identification of parameter and modified exponentially approaching rule control
Method processed, this method can design Adaptive Identification rule with the control information and tracking error of extracting parameter itself with this, by subtracting
Small parameter error is come so that parameter converges to itself virtual value, meanwhile, consider system input saturation, designs exponentially approaching rule, cut
Weak sliding formwork buffets problem, guarantees the high precision tracking control of system containing input saturation.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows:
A kind of servo system self-adaptive parameter identification and control method with input saturation, comprising the following steps:
Step 1, the positional servosystem model for establishing the saturation containing input, initializes system mode and control parameter, process
It is as follows:
1.1, positional servosystem model is expressed as follows:
Wherein, ktIt is the torque coefficient of system；J is rotary inertia；B is viscous friction coefficient；θ indicates motor Angle Position,
It is system output；ω is motor speed；I indicates torque current, is system input；
1.2, consider system saturation, motor saturation input is rewritten into i=sat (u), and u is actually entering for system, sat (u)
Form write as:
Wherein, umaxIt is the maximum input of system；
1.3, define x1=θ,Formula (2) is rewritten into:
Wherein,
Step 2, the extraction of parameter error information, process are as follows:
2.1, formula (3) is written as follow form:
Wherein,
2.2, definitionBy Φ andIt is filtered following operation:
Wherein, Φf、Be respectively Φ andFiltered value；Φf(0)、It is Φ respectivelyf、Initial value；R is to adjust
Save parameter；
It is obtained by formula (4) and formula (5):
2.3, it is as follows to define two dynamical equations P and Q:
Wherein, l is adjustment parameter；P (0), Q (0) are the initial value of P and Q respectively；
It is obtained by formula (7):
2.4, it is obtained by (6) and (8) as follows about the information of parameter error:
Q=P Θ (9)
Step 3, the design of control law based on modified exponentially approaching rule, process are as follows:
3.1, define sliding formwork Reaching Law are as follows:
Wherein, s is sliding variable；D (s)=δ0+(1-δ0)e-β|s|, δ0It is positive regulator parameter with β, and δ0≤1；K is gain
Parameter；
3.2, definition tracking error is e=x1-xd, thenWherein xdIt is the reference position signal of system, design
Sliding variable are as follows:
Then s derivation obtains:
3.3, definition input correlation function φ (u)=sat (u)-u, then φ (u) is bounded, and meets following condition:
|φ(u)|≤c1+c2|e|+c3e2 (14)
Wherein, c1、c2、c3It is the variable on unknown boundary；
3.4, the control law of designing system are as follows:
Wherein,It is c respectively1、c2、c3Estimated value；
3.5,Estimation rule design it is as follows:
Wherein, p1、p2、p3It is adjustment parameter；
3.6, definitionWherein γ1、γ2It is normal number, then hasDesign is restrained in the identification of system unknown parameter are as follows:
3.7, it is as follows to define liapunov function:
Wherein, Respectively indicate a1、b1、c1、c2、c3The evaluated error of each variable,Respectively indicate a1、b1、
c1、c2、c3The estimated value of each variable；
Formula (20) derivation is obtained:
3.5, formula (13)-(20) substitution formula (21) is known,System Asymptotic Stability.
The present invention is based on parameter identification theories and Reaching Law sliding formwork sliding formwork control technology, devise a kind of with input saturation
Servo-system on-line parameter identification and modified exponentially approaching rule control algolithm, realize the on-line identification of system unknown parameter
With the high-precision control of servo-system, problem is buffeted in the input for weakening sliding formwork control.
Technical concept of the invention are as follows: for the positional servosystem with input saturation, the present invention passes through extraction system
Parameter error information and tracking error, online design identification rule carrys out the unknown parameter of identification system, meanwhile, system is inputted full
It is converted into an input correlation function with problem, designs its border coefficient adaptive law, and combine follow-on exponentially approaching rule
Carry out designing system control law, completes the high precision tracking control and accurate parameters on-line identification of system.The present invention provides one kind
It is capable of the method for online adaptive identification system unknown parameter, enables system parameter effectively to converge to true value, and devise
Inhibiting the Reaching Law sliding mode control algorithm of saturation, it is ensured that servo-system can reach preferable control effect, meanwhile, reduce tradition
The buffeting problem of sliding formwork control.
The invention has the benefit that realizing that parameter effectively recognizes online, reduces sliding formwork input and buffet, realize servo-system
High-performance tracing control.
Detailed description of the invention
Fig. 1 is control flow chart of the invention；
Fig. 2 is that reference signal is xd1When pursuit path effect picture；
Fig. 3 is that reference signal is xd1When tracking error effect picture；
Fig. 4 is that reference signal is xd1When control input u effect picture；
Fig. 5 is that reference signal is xd1When system parameter a1Identification effect figure；
Fig. 6 is that reference signal is xd1When system parameter b1Identification effect figure；
Fig. 7 is that reference signal is xd1When Boundary Variables c1、c2、c3Estimation effect figure；
Fig. 8 is that reference signal is xd2When pursuit path effect picture；
Fig. 9 is that reference signal is xd2When tracking error effect picture；
Figure 10 is that reference signal is xd2When control input u effect picture；
Figure 11 is that reference signal is xd2When system parameter a1Identification effect figure；
Figure 12 is that reference signal is xd2When system parameter b1Identification effect figure；
Figure 13 is that reference signal is xd2When Boundary Variables c1、c2、c3Estimation effect figure.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
- Figure 13 referring to Fig.1, it is a kind of based on the calm electromechanical servo system friciton compensation with finite time parameter identification of error
Control method, comprising the following steps:
Step 1, the positional servosystem model for establishing the saturation containing input, initializes system mode and control parameter, process
It is as follows:
1.1, positional servosystem model is expressed as follows:
Wherein, ktIt is the torque coefficient of system；J is rotary inertia；B is viscous friction coefficient；θ indicates motor Angle Position,
It is system output；ω is motor speed；I indicates torque current, is system input；
1.2, consider system saturation, motor saturation input is rewritten into i=sat (u), and u is actually entering for system, sat (u)
Form write as:
Wherein, umaxIt is the maximum input of system；
1.3, define x1=θ,Formula (2) is rewritten into:
Wherein,
Step 2, the extraction of parameter error information, process are as follows:
2.1, formula (3) is written as follow form:
Wherein,
2.2, definitionBy Φ andIt is filtered following operation:
Wherein, Φf、Be respectively Φ andFiltered value；Φf(0)、It is Φ respectivelyf、Initial value；R is to adjust
Save parameter；
It is obtained by formula (4) and formula (5):
2.3, it is as follows to define two dynamical equations P and Q:
Wherein, l is adjustment parameter；P (0), Q (0) are the initial value of P and Q respectively；
It is obtained by formula (7):
2.4, it is obtained by (6) and (8) as follows about the information of parameter error:
Q=P Θ (9)
Step 3, the design of control law based on modified exponentially approaching rule, process are as follows:
3.1, define sliding formwork Reaching Law are as follows:
Wherein, s is sliding variable；D (s)=δ0+(1-δ0)e-β|s|, δ0It is positive regulator parameter with β, and δ0≤1；K is gain
Parameter；
3.2, definition tracking error is e=x1-xd, thenWherein xdIt is the reference position signal of system, design
Sliding variable are as follows:
Then s derivation obtains:
3.3, definition input correlation function φ (u)=sat (u)-u, then φ (u) is bounded, and meets following condition:
|φ(u)|≤c1+c2|e|+c3e2 (14)
Wherein, c1、c2、c3It is the variable on unknown boundary；
3.4, the control law of designing system are as follows:
Wherein,It is c respectively1、c2、c3Estimated value；
3.5,Estimation rule design it is as follows:
Wherein, p1、p2、p3It is adjustment parameter；
3.6, definitionWherein γ1、γ2It is normal number, then hasDesign is restrained in the identification of system unknown parameter are as follows:
3.7, it is as follows to define liapunov function:
Wherein, Respectively indicate a1、b1、c1、c2、c3The evaluated error of each variable,Respectively indicate a1、b1、c1、
c2、c3The estimated value of each variable；
Formula (20) derivation is obtained:
3.5, formula (13)-(20) substitution formula (21) is known,System Asymptotic Stability.
In order to verify the on-line identification performance and control effect of proposed method, the present invention has carried out emulation experiment to it.If
Set the various parameters primary condition in experiment are as follows: system parameter J=0.8, B=0.5, kt=2, then a1=0.25, b1=0.4；It distinguishes
Know and control parameter k=10, δ0=0.6, β=2, γ1=0.02, γ2=0.004, r=0.01, l=[0.001 0；0
0.001], λ=5, p1=0.001, p2=0.2, p3=0.2；Primary conditionΦf(0)=0, P (0)=0, Q (0)
=0, a1(0)=b0(0)=0, c1(0)=c2(0)=c3(0)=0；The input saturation limiting of system is set as umax=100.It is real
Test middle reference signal xdX is taken respectivelyd1=10sin (2t) and xd2=5sin (0.1 π t)+4sin (0.5 π t)+5sin (π t).
Fig. 2-Figure 13 is positional servosystem online adaptive parameter identification and control emulation experiment with input saturation
Effect picture.It is x that Fig. 2 and Fig. 3, which respectively indicates reference signal,d1When pursuit path and tracking error, bright the mentioned side of this two width chart
Preferable tracking performance may be implemented in method, and tracking error e can achieve a very small range [- 4 × 10-3,4×10-3]。
Fig. 4 is that reference signal is xd1When system input, it can be seen that system is only first 0.075 second when by being saturated
Influence, later, input correlation function φ (u)=0, and even if by saturation influence when, the tracking performance of system still compared with
It is good.Meanwhile by improved exponentially approaching rule, the buffeting of system input is relatively small.Fig. 5 and Fig. 6 is that reference signal is xd1When
System parameter on-line identification result figure, it can be seen from the figure that a1True value can be effectively converged to, and finally above and below true value
Slight jitter, and Identification Errors are further decreasing, b1True value can also be converged in a very short period of time, finally had one minimum
Identification static difference 0.00025.Fig. 7 indicates that reference signal is xd1When input correlation function φ (u) Boundary Variables c1、c2、c3Estimate
Meter is as a result, the figure shows inputs to be saturated the influence to system, and parameter quickly tends towards stability after saturation influences to disappear.Fig. 8 and
Fig. 9 is that reference signal is xd2When pursuit path and tracking error effect picture, the chart it is bright when reference signal change when system still
There is preferable tracking effect, and maximum tracking error amplitude is 5 × 10-3.Figure 10 is that reference signal is xd2When system it is defeated
Enter, the bright saturation of the chart influences only there was only first 0.1 second, and inputs to buffet and also reduce within the acceptable range.Figure 11 and figure
12 be reference signal be xd2When parameter identification result, the results showed that converge to true value in the time that system parameter can be extremely short,
And identification precision is higher.Figure 13 is that reference signal is xd2When Boundary Variables c1、c2、c3Estimated result effect picture, the chart is bright
Parameter will restrain in 0.5 second, and the input saturation of system will not influence too much system under the influence of mentioned method.
From the point of view of the result of emulation experiment, online adaptive Identification of parameter proposed by the invention and modified exponentially approaching rule control
Method processed, can high-precision on-line identification system unknown parameter, and realize system high-performance tracing control.
Described above is validity of the emulation experiment of the invention provided to show method designed by the present invention, but aobvious
The right present invention is not limited only to examples detailed above, without departing from essence spirit of the present invention and without departing from involved by substantive content of the present invention
And various deformations can be made under the premise of range to it and be implemented.On-line parameter identification designed by the present invention and control method pair
Positional servosystem with input saturation has preferable identification and tracing control effect, can be realized servo-system high-precision
Parameter identification and tracing control.
Claims (1)
1. a kind of servo system self-adaptive parameter identification and control method with input saturation, it is characterised in that: including following
Step:
Step 1, the positional servosystem model for establishing the saturation containing input initializes system mode and control parameter, process is as follows:
1.1, positional servosystem model is expressed as follows:
Wherein, ktIt is the torque coefficient of system；J is rotary inertia；B is viscous friction coefficient；θ indicates motor Angle Position, is system
Output；ω is motor speed；I indicates torque current, is system input；
1.2, consider system saturation, motor saturation input is rewritten into i=sat (u), and u is actually entering for system, the shape of sat (u)
Formula is write as:
Wherein, umaxIt is the maximum input of system；
1.3, define x1=θ,Formula (2) is rewritten into:
Wherein,
Step 2, the extraction of parameter error information, process are as follows:
2.1, formula (3) is written as follow form:
Wherein,
2.2, definitionBy Φ andIt is filtered following operation:
Wherein, Φf、Be respectively Φ andFiltered value；Φf(0)、It is Φ respectivelyf、Initial value；R is to adjust ginseng
Number；
It is obtained by formula (4) and formula (5):
2.3, it is as follows to define two dynamical equations P and Q:
Wherein, l is adjustment parameter；P (0), Q (0) are the initial value of P and Q respectively；
It is obtained by formula (7):
2.4, it is obtained by (6) and (8) as follows about the information of parameter error:
Q=P Θ (9)
Step 3, the design of control law based on modified exponentially approaching rule, process are as follows:
3.1, define sliding formwork Reaching Law are as follows:
Wherein, s is sliding variable；D (s)=δ0+(1-δ0)e-β|s|, δ0It is positive regulator parameter with β, and δ0≤1；K is gain ginseng
Number；
3.2, definition tracking error is e=x1-xd, thenWherein xdIt is the reference position signal of system, designs sliding formwork
Variable are as follows:
Then s derivation obtains:
3.3, definition input correlation function φ (u)=sat (u)-u, then φ (u) is bounded, and meets following condition:
|φ(u)|≤c1+c2|e|+c3e2 (14)
Wherein, c1、c2、c3It is the variable on unknown boundary；
3.4, the control law of designing system are as follows:
Wherein,It is c respectively1、c2、c3Estimated value；
3.5,Estimation rule design it is as follows:
Wherein, p1、p2、p3It is adjustment parameter；
3.6, definitionWherein γ1、γ2It is normal number, then hasDesign is restrained in the identification of system unknown parameter are as follows:
3.7, it is as follows to define liapunov function:
Wherein, Respectively indicate a1、b1、c1、c2、c3The evaluated error of each variable,Respectively indicate a1、b1、c1、
c2、c3The estimated value of each variable；
Formula (20) derivation is obtained:
3.8, formula (13)-(20) substitution formula (21) is known,System Asymptotic Stability.
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