CN106292279B - Motor position servo system output feedback ontrol method based on nonlinear observer - Google Patents

Motor position servo system output feedback ontrol method based on nonlinear observer Download PDF

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CN106292279B
CN106292279B CN201610698040.7A CN201610698040A CN106292279B CN 106292279 B CN106292279 B CN 106292279B CN 201610698040 A CN201610698040 A CN 201610698040A CN 106292279 B CN106292279 B CN 106292279B
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formula
motor
servo
state
follows
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CN201610698040.7A
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CN106292279A (en
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李旭东
姚建勇
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南京理工大学
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention discloses a kind of output feedback ontrol methods of motor position servo system based on nonlinear observer, belong to motor servo control field, method includes the following steps: establishing the mathematical model of motor position servo system;Nonlinear Observer is designed, the output feedback controller based on nonlinear observer of motor position servo system is designed.The present invention in only location status it is known that and Velocity-acceleration it is unknown in the case where, a kind of output feedback ontrol method of motor position servo system based on nonlinear observer is provided, hardware cost is reduced, is conducive to apply in practical projects;Controller designed by the present invention, has fully considered the non-linear friction characteristic and outer interference etc. of system, and guarantees that system mode tends to balance state in finite time, improves the tracking performance of system.

Description

Motor position servo system output feedback ontrol method based on nonlinear observer

Technical field

The present invention relates to motor position servo system field, especially a kind of motor position based on nonlinear observer is watched Dress system output feedback ontrol method.

Background technique

Motor servo system has outstanding advantages of response is fast, easy to maintain, transmission efficiency is high and energy acquisition facilitates, It is widely used in each key areas, such as robot, lathe, aerospace.With the fast development in these fields, to motor The requirement of servo-system tracking performance is also higher and higher, and the performance of system and the design of controller are closely related.Motor servo system System is a typical nonlinear system, can be faced during designing controller many modelings it is uncertain include structure not Certainty and unstructured uncertainty, these factors may the desired control performance of severe exacerbation, lead to undesirable control Precision processed, generating limit cycles oscillations even keeps designed controller unstable, so that the design of controller be made to become difficult.

At present for the control of motor servo system, the method based on classical three close-loop control is still industry and national defence Main method, based on linear control theory, layer-by-layer design current ring from inside to outside, speed ring and position ring, each ring Control strategy mostly uses pid correction and its modification.But it is constantly progressive with industrial and national defence technical level, tradition Three close-loop control method based on linear theory has not been able to satisfy the high performance demands of system gradually, becomes limiting motor servo-system One of bottleneck factor of development.In order to improve the tracking performance of electric system, many advanced gamma controllers are ground Study carefully, such as Robust Adaptive Control, adaptive robust control, sliding formwork control etc..However, full shape used in all above methods State feedback, that is to say, that in motion control, in addition to requiring position signals, it is also necessary to velocity and acceleration signal. But in many applications, due to reducing the needs of cost, only location information is known.In addition, serious measurement noise would generally Surveyed velocity and acceleration signal is polluted, and then deteriorates the full state feedback controller for realizing performance.Therefore, there is an urgent need to set Count more practical nonlinear output feedback control strategy.

Summary of the invention

The purpose of the present invention is to provide a kind of output of motor position servo system based on nonlinear observer feedbacks Control method.

Realize the technical solution of the object of the invention are as follows: a kind of motor position servo system based on nonlinear observer it is defeated Feedback out, comprising the following steps:

Step 1, the mathematical model of motor position servo system is established;

Step 2, Nonlinear Observer is designed;

Step 3, the output feedback controller based on nonlinear observer of motor position servo system is designed.

Compared with prior art, remarkable advantage of the invention are as follows:

(1) present invention in only location status it is known that and Velocity-acceleration it is unknown in the case where, provide a kind of based on non-thread Property observer motor position servo system output feedback ontrol method, reduce hardware cost, be more conducive in practical work It is applied in journey.

(2) controller designed by the present invention has fully considered the non-linear friction characteristic and interference etc. outside of system, and And guarantee that system mode tends to balance state in finite time, improve the tracking performance of system.

Detailed description of the invention

Fig. 1 is that the present invention is based on the output feedback ontrol method flows of the motor position servo system of nonlinear observer Figure.

Fig. 2 is motor servo system schematic diagram of the present invention.

Fig. 3 is that two kinds of controller track followings instruct schematic diagram.

Fig. 4 is system mode x under controller action designed by the present invention2Estimated value time history plot.

Fig. 5 is two kinds of controller tracking error time history plots.

Fig. 6 is its control input time history plot of controller designed by the present invention.

Specific embodiment

In conjunction with Fig. 1, Fig. 2, a kind of output of motor position servo system based on nonlinear observer of the invention is fed back Control method, comprising the following steps:

Step 1: establishing motor position servo system mathematical model

Electric dynamic according to Newton's second law and simplified motor is proportional component, the movement of motor position servo system Equation are as follows:

M is inertia load parameter in formula (1), and y is inertia load displacement, kfFor torque error constant, u is the control of system System input, B is viscosity friction coefficient,For the non-linear friction model that can be modeled,For speed command, ydFor position Instruction, Δ are the uncertain item such as outer interference and unmodeled friction.

Choose continuous static friction model are as follows:

L in formula (2)1、l2、l3、l4、l5It is known constant;The feature of this continuous static friction model is as follows: 1. this rubs Wiping model is can be micro- about Time Continuous and about origin symmetry;2. Coulomb friction characteristic available expression Characterization;3. static friction coefficient can use l1+l3Value carry out approximate representation;4. expression formulaIt can characterize Stribeck effect.

Choose state variable are as follows: x=[x1,x2]T, then the kinematical equation of motor position servo system can be converted into shape State equation form:

X in formula (3)1Indicate the displacement of inertia load, x2Indicate another unknowable motion state.

Step 2: design Nonlinear Observer

To unknown state x2Estimated, be firstly introduced into coordinate converting system, introduces new state ξ:

ξ=x2-k1x1 (4)

K in formula (4)1For design parameter.Then to formula (4) the right and left while differential, and combinatorial formula (3) can obtain The dynamic of ξ are as follows:

According to equation (5), state observer is designed are as follows:

In formula (6)It is the estimated value of state ξ.

DefinitionFor the evaluated error of state observer, the dynamic side of evaluated error can be obtained by formula (5), (6) Journey are as follows:

It can be obtained according to formula (7):

δ in formula (8)dFor a unknown constant.By adjusting design parameter k1Evaluated error can be made to become in finite time In the value of very little, therefore state observer has good stable state observation performance.

Step 3: the output feedback controller based on nonlinear observer of design motor position servo system, specific Steps are as follows:

The target of controller design is that the position of motor position servo system is made to export x1Tracking expectation as precisely as possible The position command x of tracking1d

The output feedback controller based on nonlinear observer for designing motor position servo system is as follows:

Defined variable is as follows:

Wherein α1For virtual controlling amount, design as follows:

K in formula (10)s1For design parameter,For speed command, α1s2Meet following condition:

Wherein ε1> 0 is a design parameter, provides the α of satisfaction (11) herein1s2A form

Wherein δξIt isThe upper bound

Output feedback controller design based on nonlinear observer is as follows:

Wherein ks2For design parameter,For α1It can calculating section in time-derivative.us2Meet following condition

Wherein ε2> 0 is a design parameter.The u of satisfaction (14) is provided hereins2A form

Analyze the stability of motor position servo system:

According to the stability analysis of system in control theory, Lyapunov Equation is chosen are as follows:

With lyapunov stability theory carry out stability prove, to (16) formula derivation, and by formula (10), (12), (13), (15) are brought into obtain:

Wherein λ is a positive real number, so as to so that system reaches asymptotically stability.

The present invention is further explained in the light of specific embodiments.

Embodiment

The parameter value of motor servo system is as follows:

M=0.02kgm2,kf=5NmV-1, B=10Nmrad-1s-1,l1=0.1Nm, l2= 700s·rad-1,l3=0.06Nm, l4=15srad-1,l5=1.5srad-1

Controller parameter k of the invention1=800, ks1=2000, ks2=500.

PID controller parameter is kp=1000, ki=50, kd=0.1.

Position angle input signal x1d=0.8sin (t) (1-e-0.01t3)

Fig. 3 is two kinds of controller track following instruction schematic diagrames.

Fig. 4 is system mode x under controller action designed by the present invention2The curve that changes over time of estimated value, from figure In it can be seen that its estimated value gradually close to nominal value, and fluctuates near the nominal value in a certain range, so as to accurate Ground comes out the state estimation of system.

Fig. 5 is the curve that two kinds of controller tracking errors change over time, it can be seen that controller designed by the present invention is bright It is aobvious to be better than PID controller.

Fig. 6 is its curve for changing over time of control input of controller designed by the present invention, it can be seen from the figure that this It is continuous to invent obtained control input signal, is applied in practice conducive in engineering.

Claims (1)

1. a kind of output feedback ontrol method of the motor position servo system based on nonlinear observer, which is characterized in that packet Include following steps:
Step 1, the mathematical model of motor position servo system is established, specifically:
Electric dynamic according to Newton's second law and simplified motor is proportional component, the equation of motion of motor position servo system Are as follows:
M is inertia load parameter in formula (1), and y is inertia load displacement, kfFor torque error constant, u is that the control of system is defeated Entering, B is viscosity friction coefficient,For the non-linear friction model that can be modeled,For speed command, ydFor position command, Δ is outer interference and unmodeled friction;
Non-linear friction modelChoose continuous static friction model:
L in formula (2)1、l2、l3、l4、l5It is known constant, the feature of this continuous static friction model is as follows: 1. this friction mould Type is can be micro- about Time Continuous and about origin symmetry;2. Coulomb friction characteristic passes through expression formulaCharacterization; 3. static friction coefficient passes through l1+l3Value approximate representation;4. expression formulaStribeck can be characterized Effect;
Choose state variable are as follows: x=[x1,x2]T, then the kinematical equation of motor position servo system can be converted into state side Journey form:
X in formula (3)1Indicate the displacement y, x of inertia load2Indicate another unknowable motion state;
Step 2, Nonlinear Observer is designed, specifically:
Nonlinear Observer is designed to unknown state x2Estimated, be firstly introduced into coordinate converting system, introduces new state ξ:
ξ=x2-k1x1 (4)
K in formula (4)1For design parameter, then to formula (4) the right and left while differential, and combinatorial formula (3) can obtain the dynamic of ξ State are as follows:
According to equation (5), state observer is designed are as follows:
In formula (6)It is the estimated value of state ξ;
DefinitionFor the evaluated error of state observer, the dynamical equation of evaluated error can be obtained by formula (5), (6) are as follows:
It can be obtained according to formula (7):
δ in formula (8)dFor a unknown constant;By adjusting design parameter k1Evaluated error can be made to tend to very in finite time Small value, therefore state observer has good stable state observation performance;
Step 3, the output feedback controller based on nonlinear observer of motor position servo system is designed, specifically:
Defined variable is as follows:
Wherein, x1dFor the position command of expectation tracking, α1For virtual controlling amount, design as follows:
K in formula (10)s1For design parameter,For speed command, α1s2Meet following condition:
Wherein ε1> 0 is a design parameter, provides the α of satisfaction (11) herein1s2A form
Wherein δξIt isThe upper bound;
Output feedback controller design based on nonlinear observer is as follows:
Wherein ks2For design parameter,For α1It can calculating section in time-derivative;us2Meet following condition
Wherein ε2> 0 is a design parameter;The u of satisfaction (14) is provided hereins2A form
CN201610698040.7A 2016-08-20 2016-08-20 Motor position servo system output feedback ontrol method based on nonlinear observer CN106292279B (en)

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CN104065322A (en) * 2014-06-13 2014-09-24 南京理工大学 Method for controlling output feedback of motor position servo system
CN104111607A (en) * 2014-06-13 2014-10-22 南京理工大学 Motor position servo system control method taking input time lag into consideration
CN104238572A (en) * 2014-07-23 2014-12-24 南京理工大学 Motor servo system jitter-free sliding mode position control method based on disturbance compensation
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CN104065322A (en) * 2014-06-13 2014-09-24 南京理工大学 Method for controlling output feedback of motor position servo system
CN104111607A (en) * 2014-06-13 2014-10-22 南京理工大学 Motor position servo system control method taking input time lag into consideration
CN104238572A (en) * 2014-07-23 2014-12-24 南京理工大学 Motor servo system jitter-free sliding mode position control method based on disturbance compensation
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