CN111736472A - Motor self-adaptive preset performance asymptotic control method based on RISE - Google Patents

Motor self-adaptive preset performance asymptotic control method based on RISE Download PDF

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CN111736472A
CN111736472A CN202010712826.6A CN202010712826A CN111736472A CN 111736472 A CN111736472 A CN 111736472A CN 202010712826 A CN202010712826 A CN 202010712826A CN 111736472 A CN111736472 A CN 111736472A
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CN111736472B (en
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徐张宝
刘庆运
郭永存
涂德浴
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Anhui University of Technology AHUT
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive 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
    • G05B13/042—Adaptive 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
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P29/00—Arrangements for regulating or controlling electric motors, appropriate for both AC and DC motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P7/00—Arrangements for regulating or controlling the speed or torque of electric DC motors
    • H02P7/06—Arrangements for regulating or controlling the speed or torque of electric DC motors for regulating or controlling an individual dc dynamo-electric motor by varying field or armature current
    • H02P7/18—Arrangements for regulating or controlling the speed or torque of electric DC motors for regulating or controlling an individual dc dynamo-electric motor by varying field or armature current by master control with auxiliary power

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Abstract

The invention discloses a RISE-based motor adaptive preset performance asymptotic control method in the technical field of electromechanical servo control, which comprises the following steps: establishing a motor position servo system model; designing a motor self-adaptive preset performance asymptotic controller based on RISE; adjusting the parameters in the steps to enable the system to meet the control performance index, suppressing the non-modeling interference and estimating unknown parameters of the system through a robust error symbol integral function and a parameter self-adaptation law, effectively solving the problem of uncertain nonlinearity of a motor servo system, and constraining the transient performance of the system based on a preset performance function; the designed adaptive asymptotic controller with preset performance has a good robust effect on uncertainty in a system, can realize the planning of transient and steady-state performance of the system, theoretically realizes asymptotic tracking of the system, and ensures the high-precision tracking performance of a motor servo system; the design of the controller is simplified, the use cost of the actual system is reduced, and the method is more beneficial to application in engineering practice.

Description

Motor self-adaptive preset performance asymptotic control method based on RISE
Technical Field
The invention relates to the technical field of electromechanical servo control, in particular to a motor adaptive preset performance asymptotic control method based on RISE.
Background
Because of the wide application in industry, high performance control of motor-driven motion systems has received much attention. However, the uncertainty of the model is widely existed in the motor system, and is especially the unmodeled nonlinearity such as the non-structural uncertainty. These uncertainty factors can severely degrade the achievable control performance, resulting in low control accuracy, limit cycle oscillations, and even instability, and thus require control methods to be designed to solve.
The traditional control mode is difficult to meet the requirement of uncertain nonlinear tracking precision, so that a control method which is simple and practical and meets the requirement of system performance needs to be researched. In recent years, various advanced control strategies are applied to a motor servo system, such as robust adaptive control, adaptive robustness and the like, and the control obtains good steady-state control accuracy; however, the above control strategies cannot analyze the transient performance of the system.
Aiming at the characteristics of uncertain nonlinearity and parameter uncertainty in motor servo, a control method meeting the requirement needs to be designed urgently, and based on the control method, the invention designs a motor self-adaptive preset performance asymptotic control method based on RISE to solve the problems.
Disclosure of Invention
The invention aims to provide a RISE-based motor adaptive preset performance asymptotic control method to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme: a motor adaptive preset performance asymptotic control method based on RISE comprises the following steps:
s1: establishing a motor position servo system model;
s2: designing a motor self-adaptive preset performance asymptotic controller based on RISE;
s3: and adjusting the parameters in the steps to enable the system to meet the control performance index.
Further, the step S1 is specifically: according to Newton's second law, a dynamic model equation of the inertial load of the motor is established as follows:
Figure BDA0002597133400000021
in the formula: y is angular displacement, m is inertial load, kfIs the torque constant, u is the system control input, b is the viscous friction coefficient,
Figure BDA0002597133400000022
for other unmodeled disturbances, including non-linear friction, external disturbances, and unmodeled dynamics;
establishing state variables
Figure BDA0002597133400000023
The entire system can then be written in the form of a state space as follows:
Figure BDA0002597133400000024
in the formula: x ═ x1,x2]TFor the state vector of position and velocity, an unknown parameter set θ ═ θ is defined1,θ2,]TWherein theta1＝kf/m，θ2＝b/m，
Figure BDA0002597133400000025
Representing concentrated interference;
if the structural uncertainty θ satisfies:
Figure BDA0002597133400000026
in the formula: thetamin＝[θ1min,θ2min]T，θmax＝[θ1max,θ2max]TIn addition, θ is known1min＞0，θ2minIs greater than 0; if d (x, t) and its first derivative are bounded, i.e.
Figure BDA0002597133400000027
In the formula:d,mare known.
Further, the step S2 includes the following steps:
s2 a: constructing a projection self-adaptive law with rate limitation;
s2 b: designing a controller;
s2 c: and verifying the stability of the system.
Further, the step S2a is specifically: order to
Figure BDA0002597133400000028
The estimate of the value of theta is represented,
Figure BDA0002597133400000029
error in the estimate of theta, i.e.
Figure BDA0002597133400000031
A projection function is established as follows:
Figure BDA0002597133400000032
in the formula, zeta ∈ R2,(t)∈R2×2Is a positive definite symmetric matrix that varies with time,
Figure BDA0002597133400000033
and
Figure BDA0002597133400000034
each represents omegaθThe inner portion and the boundary of (a),
Figure BDA00025971334000000316
to represent
Figure BDA0002597133400000035
An outer unit normal vector of time;
for the projection function (5), in the control parameter estimation process, a preset self-adaptive limiting speed is used; thus, a saturation function is established as follows:
Figure BDA0002597133400000036
in the formula:
Figure BDA0002597133400000037
is a preset limiting rate; the rationale behind the use of the parameter estimation process is as follows: assume that the following projection-type adaptation law and preset adaptive rate limit are used
Figure BDA0002597133400000038
Updating an estimated parameter
Figure BDA0002597133400000039
Figure BDA00025971334000000310
In the formula: tau is an adaptive function, and (t) > 0 is a continuous micro-directly symmetrical adaptive rate matrix; from this adaptive law, the following ideal characteristics can be obtained:
p1) parameter estimate is always at a known bounded ΩθIn-set, i.e. for any t, there is always
Figure BDA00025971334000000311
Thus, from hypothesis 1
Figure BDA00025971334000000312
P2)
Figure BDA00025971334000000313
P3) the law of parameter variation is consistently bounded, i.e. it is determined that the parameter variation is uniformly bounded
Figure BDA00025971334000000314
Further, the step S2b is specifically: definition of motor outputOut control error e ═ x1-x1dIt is assumed that it needs to meet the following performance criteria:
Figure BDA00025971334000000315
in the formula:l,ufor the parameters to be designed, for the upper and lower limits of the auxiliary constraint control error, ρ (t) is a positive strictly increasing smoothing function, as shown in the following equation:
Figure BDA0002597133400000041
in the formula: rho0、ρ∞And k are both positive designable parameters;
formula (8) -lρ0Anduρ0respectively constraining the maximum downward impulse and the maximum overshoot of the output force control error e (t), and constraining the convergence rate, rho, of the error e (t) by the parameter k∞A steady state bound on the error is constrained; equation (8) thus gives a specific plan for the performance of the output force control error by selecting the appropriate parameter ρ0、ρ∞、k、lAnduthe transient and stable performance of the output force control error can be planned in advance, and the transient performance can be improved according to the actual requirement of the system;
the following increasing function is established:
Figure BDA0002597133400000042
in the formula: z is a radical of1(t) is a conversion error variable corresponding to the control error e (t), and it is easy to analyze that the equation (10) is equivalent to e (t) ═ ρ (t) S (z)1(t)), and z1(t) when the interface is bounded, the preset performance characteristic formula (8) is always satisfied;
an increasing function S (z) satisfying the characteristic formula (10)1) The following can be selected:
Figure BDA0002597133400000043
the inverse function of equation (11) is found:
Figure BDA0002597133400000044
for the conversion error z1Designing a controller;
a set of functions is established as follows:
Figure BDA0002597133400000045
in the formula: k is a radical of1，k2Is the feedback gain;
by differentiating the equation (13) and substituting the equation (2), it is possible to obtain:
Figure BDA0002597133400000051
based on the system model, the controller can be designed as follows:
Figure BDA0002597133400000052
in the formula: k is a radical of3Is the feedback gain;
the controller (15) may be substituted for the equation (14):
Figure BDA0002597133400000053
the design parameter adaptation law is as follows:
Figure BDA0002597133400000054
in the formula:
Figure BDA0002597133400000055
then, it is possible to obtain:
Figure BDA0002597133400000056
design robust controller us2The following were used:
Figure BDA0002597133400000061
in the formula β2Are parameters to be designed.
Further, the step S2c includes selecting the initial condition of system controllρ(0)<e(0)<uρ (0) -l<λ(0)<uSimultaneous parameter β2Satisfies the following inequality:
Figure BDA0002597133400000062
while designing a sufficiently large parameter k1And k2So that the following matrix Λ is a positive definite matrix:
Figure BDA0002597133400000063
ensuring that the control error of the output force is bounded all the time, realizing better instruction tracking of the output force and adjusting rho0、ρ∞、k、lAnduthe parameters are equal, so that the control error can meet the preset performance requirement designed by the formula (8);
the method specifically comprises the following steps: the following Lyapunov function is established:
Figure BDA0002597133400000064
further derivation of V and substitution of the formulae (13), (18) and (19) gives:
Figure BDA0002597133400000071
in the formula: z ═ Z1,z2]TThe matrix Λ is defined as(21) (ii) a If passing through reasonable design parameter k1And k2Making the matrix Λ positive definite makes the following satisfied:
Figure BDA0002597133400000072
in the formula: lambda [ alpha ]min(Λ) represents the minimum eigenvalue of the matrix Λ, and the analytic expression (24) shows that the Lyapunov function is bounded, and the W integral is bounded, and further shows that the conversion error amount z is bounded1And z2All are bounded, and in combination with equations (7), (13) and (15), all signals in the system are bounded, so that the derivative of W is bounded, and as the time approaches infinity, W approaches zero, i.e., the transformation error amount z, as can be seen by the existing Barbalt theorem1And approaches zero, so that the control error e (t) is always bounded in conjunction with equation (8), thereby proving that the controller is convergent and the system is stable.
Further, the third step is specifically to adjust a parameter k of the control law u1、k2、k3、ρ0、ρ∞、k、l、u、β2And the system meets the control performance index.
Compared with the prior art, the invention has the beneficial effects that: aiming at the characteristics of a motor position servo system, a motor position servo system model and a designed RISE-based motor preset performance adaptive asymptotic controller are established, a robust error symbol integral strategy is used for inhibiting unmodeled interference, meanwhile, the adaptive controller is used for estimating system position parameters, the problems of uncertain nonlinearity and uncertain parameters of the motor servo system can be effectively solved, the controller is designed by fusing a preset performance function, and finally the overall stability of the system is proved by a certificate; under the interference condition, the parameter convergence is good, and the system control precision meets the performance index; the invention simplifies the design of the controller, and the final simulation result shows the effectiveness of the controller.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of a motor actuator of the present invention;
FIG. 2 is a schematic diagram of the system control strategy of the present invention;
FIG. 3 is a parameter estimation curve according to an embodiment of the present invention.
FIG. 4 is a schematic diagram of tracking errors of the controller and the PID controller according to an embodiment of the invention
FIG. 5 is a schematic diagram of the control error preset capability of the present invention;
FIG. 6 shows the function S (z) according to the present invention1) Schematic representation.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-2, the present invention provides a technical solution: a motor adaptive preset performance asymptotic control method based on RISE comprises the following steps:
s1: establishing a motor position servo system model;
s2: designing a motor self-adaptive preset performance asymptotic controller based on RISE;
s3: and adjusting the parameters in the steps to enable the system to meet the control performance index.
Wherein, the step S1 specifically includes: according to Newton's second law, a dynamic model equation of the inertial load of the motor is established as follows:
Figure BDA0002597133400000091
in the formula: y is angular displacement, m is inertial load, kfIs the torque constant, u is the system control input, b is the viscous friction coefficient,
Figure BDA0002597133400000092
for other unmodeled disturbances, including non-linear friction, external disturbances, and unmodeled dynamics;
establishing state variables
Figure BDA0002597133400000093
The entire system can then be written in the form of a state space as follows:
Figure BDA0002597133400000094
in the formula: x ═ x1,x2]TFor the state vector of position and velocity, an unknown parameter set θ ═ θ is defined1,θ2,]TWherein theta1＝kf/m，θ2＝b/m，
Figure BDA0002597133400000095
Representing concentrated interference;
if the structural uncertainty θ satisfies:
Figure BDA0002597133400000096
in the formula: thetamin＝[θ1min,θ2min]T，θmax＝[θ1max,θ2max]TIn addition, θ is known1min＞0，θ2minIs greater than 0; if d (x, t) and its first derivative are bounded, i.e.
Figure BDA0002597133400000097
In the formula:d,mare known.
The step S2 includes the following steps:
s2 a: constructing a projection self-adaptive law with rate limitation;
s2 b: designing a controller;
s2 c: and verifying the stability of the system.
The step S2a specifically includes: order to
Figure BDA0002597133400000098
The estimate of the value of theta is represented,
Figure BDA0002597133400000099
error in the estimate of theta, i.e.
Figure BDA00025971334000000910
A projection function is established as follows:
Figure BDA0002597133400000101
in the formula, zeta ∈ R2,(t)∈R2×2Is a positive definite symmetric matrix that varies with time,
Figure BDA0002597133400000102
and
Figure BDA0002597133400000103
each represents omegaθThe inner portion and the boundary of (a),
Figure BDA0002597133400000104
to represent
Figure BDA0002597133400000105
An outer unit normal vector of time;
for the projection function (5), in the control parameter estimation process, a preset self-adaptive limiting speed is used; thus, a saturation function is established as follows:
Figure BDA0002597133400000106
in the formula:
Figure BDA0002597133400000107
is a preset limiting rate; the rationale behind the use of the parameter estimation process is as follows: assume that the following projection-type adaptation law and preset adaptive rate limit are used
Figure BDA0002597133400000108
Updating an estimated parameter
Figure BDA0002597133400000109
Figure BDA00025971334000001010
In the formula: tau is an adaptive function, and (t) > 0 is a continuous micro-directly symmetrical adaptive rate matrix; from this adaptive law, the following ideal characteristics can be obtained:
p1) parameter estimate is always at a known bounded ΩθIn-set, i.e. for any t, there is always
Figure BDA00025971334000001011
Thus, from hypothesis 1
Figure BDA00025971334000001012
P2)
Figure BDA00025971334000001013
P3) the law of parameter variation is consistently bounded, i.e. it is determined that the parameter variation is uniformly bounded
Figure BDA00025971334000001014
The step S2b specifically includes: defining the motor output control error e ═ x1-x1dIt is assumed that it needs to meet the following performance criteria:
Figure BDA00025971334000001015
in the formula:l,ufor the parameters to be designed, for the upper and lower limits of the auxiliary constraint control error, ρ (t) is a positive strictly increasing smoothing function, as shown in the following equation:
Figure BDA0002597133400000111
in the formula: rho0、ρ∞And k are both positive designable parameters, and the approximate curve of the performance index inequality (8) is shown in FIG. 5;
formula (8) -lρ0Anduρ0respectively constraining the maximum downward impulse and the maximum overshoot of the output force control error e (t), and constraining the convergence rate, rho, of the error e (t) by the parameter k∞A steady state bound on the error is constrained; equation (8) thus gives a specific plan for the performance of the output force control error by selecting the appropriate parameter ρ0、ρ∞、k、lAnduthe transient and stable performance of the output force control error can be planned in advance, and the transient performance can be improved according to the actual requirement of the system;
the following increasing function is established:
Figure BDA0002597133400000112
in the formula: z is a radical of1(t) is a conversion error variable corresponding to the control error e (t), and it is easy to analyze that the equation (10) is equivalent to e (t) ═ ρ (t) S (z)1(t)), and z1(t) when the interface is bounded, the preset performance characteristic formula (8) is always satisfied;
an increasing function S (z) satisfying the characteristic formula (10)1) The following can be selected:
Figure BDA0002597133400000113
increasing function S (z)1) The curve of (a) is shown in fig. 6;
the inverse function of equation (11) is found:
Figure BDA0002597133400000114
for the conversion error z1Designing a controller;
a set of functions is established as follows:
Figure BDA0002597133400000121
in the formula: k is a radical of1，k2Is the feedback gain;
by differentiating the equation (13) and substituting the equation (2), it is possible to obtain:
Figure BDA0002597133400000122
based on the system model, the controller can be designed as follows:
Figure BDA0002597133400000123
in the formula: k is a radical of3Is the feedback gain;
the controller (15) may be substituted for the equation (14):
Figure BDA0002597133400000124
the design parameter adaptation law is as follows:
Figure BDA0002597133400000125
in the formula:
Figure BDA0002597133400000126
then, it is possible to obtain:
Figure BDA0002597133400000127
design robust controllerus2The following were used:
Figure BDA0002597133400000128
in the formula β2Are parameters to be designed.
The step S2c includes selecting the initial condition of system controllρ(0)<e(0)<uρ (0) -l<λ(0)<uSimultaneous parameter β2Satisfies the following inequality:
Figure BDA0002597133400000131
while designing a sufficiently large parameter k1And k2So that the following matrix Λ is a positive definite matrix:
Figure BDA0002597133400000132
ensuring that the control error of the output force is bounded all the time, realizing better instruction tracking of the output force and adjusting rho0、ρ∞、k、lAnduthe parameters are equal, so that the control error can meet the preset performance requirement designed by the formula (8);
the method specifically comprises the following steps: the following Lyapunov function is established:
Figure BDA0002597133400000133
further derivation of V and substitution of the formulae (13), (18) and (19) gives:
Figure BDA0002597133400000141
in the formula: z ═ Z1,z2]TThe matrix Λ is defined as formula (21) if the reasonable design parameter k is passed1And k2Making the matrix Λ positive definite makes the following satisfied:
Figure BDA0002597133400000142
in the formula: lambda [ alpha ]min(Λ) represents the minimum eigenvalue of the matrix Λ, and the analytic expression (24) shows that the Lyapunov function is bounded, and the W integral is bounded, and further shows that the conversion error amount z is bounded1And z2All are bounded, and in combination with equations (7), (13) and (15), all signals in the system are bounded, so that the derivative of W is bounded, and as the time approaches infinity, W approaches zero, i.e., the transformation error amount z, as can be seen by the existing Barbalt theorem1And approaches zero, so that the control error e (t) is always bounded in conjunction with equation (8), thereby proving that the controller is convergent and the system is stable.
Step three is specifically to adjust the parameter k of the control law u1、k2、k3、ρ0、ρ∞、k、l、u、β2And the system meets the control performance index.
The first embodiment is as follows:
in the simulation, a system design controller takes the following parameters to model the system: m is 0.01kg m2，kf＝5、b＝1.25N·s/m、θ1n＝600、θ2n＝60、k1＝70、k2＝100、k3＝200、＝[100 46]T、β2＝200、ρ0＝0.1、ρ∞＝0.1、k＝0.001、l0.02 andu0.005; PID controller parameter is kp＝110、k i70 and kd0.3; position angle input signal yd(t)＝0.2sin(πt)[1-exp(-0.01t3)]rad, d (x, t) ═ 1.5sin (2 π t) N · m; the control law effects are shown in fig. 3 and 4 below; FIG. 3 is a representation of a system parameter estimation curve; fig. 4 represents the tracking error of the designed controller (APFRISE) and the PID controller.
As can be seen from the figure, the algorithm provided by the invention can accurately estimate the system parameters in a simulation environment, compared with the traditional PID control, the controller (APFRISE) designed by the invention can greatly improve the control precision of the system and better restrict the system control error, and research results show that the method provided by the invention can meet performance indexes under uncertain nonlinear influence and has good robustness.
In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims (7)

1. A motor adaptive preset performance asymptotic control method based on RISE is characterized by comprising the following steps:
s1: establishing a motor position servo system model;
s2: designing a motor self-adaptive preset performance asymptotic controller based on RISE;
s3: and adjusting the parameters in the steps to enable the system to meet the control performance index.
2. A RISE-based motor adaptive preset performance asymptotic control method according to claim 1, characterized in that: the step S1 specifically includes: according to Newton's second law, a dynamic model equation of the inertial load of the motor is established as follows:
Figure FDA0002597133390000011
in the formula: y is angular displacement, m is inertial load, kfIs the torque constant, u is the system control input, b is the viscous friction coefficient,
Figure FDA0002597133390000012
for other unmodeled disturbances, including non-linear friction, external disturbances, and unmodeled dynamics;
establishing state variables
Figure FDA0002597133390000013
The entire system can then be written in the form of a state space as follows:
Figure FDA0002597133390000014
in the formula: x ═ x1,x2]TFor the state vector of position and velocity, an unknown parameter set θ ═ θ is defined1,θ2,]TWherein theta1＝kf/m，θ2＝b/m，
Figure FDA0002597133390000017
Representing concentrated interference;
if the structural uncertainty θ satisfies:
Figure FDA0002597133390000015
in the formula: thetamin＝[θ1min,θ2min]T，θmax＝[θ1max,θ2max]TIn addition, θ is known1min＞0，θ2minIs greater than 0; if d (x, t) and its first derivative are bounded, i.e.
Figure FDA0002597133390000016
In the formula:d,mare known.
3. A RISE-based motor adaptive preset performance asymptotic control method according to claim 1, characterized in that: the step S2 includes the following steps:
s2 a: constructing a projection self-adaptive law with rate limitation;
s2 b: designing a controller;
s2 c: and verifying the stability of the system.
4. A RISE-based motor adaptive preset performance asymptotic control method according to claim 3, characterized in that: the step S2a specifically includes: order to
Figure FDA0002597133390000021
The estimate of the value of theta is represented,
Figure FDA0002597133390000022
error in the estimate of theta, i.e.
Figure FDA0002597133390000023
A projection function is established as follows:
Figure FDA0002597133390000024
in the formula, zeta ∈ R2,(t)∈R2×2Is a positive definite symmetric matrix that varies with time,
Figure FDA0002597133390000025
and
Figure FDA0002597133390000026
each represents omegaθThe inner portion and the boundary of (a),
Figure FDA0002597133390000027
to represent
Figure FDA0002597133390000028
An outer unit normal vector of time;
for the projection function (5), in the control parameter estimation process, a preset self-adaptive limiting speed is used; thus, a saturation function is established as follows:
Figure FDA0002597133390000029
in the formula:
Figure FDA00025971333900000210
is a preset limiting rate; the rationale behind the use of the parameter estimation process is as follows: assume that the following projection-type adaptation law and preset adaptive rate limit are used
Figure FDA00025971333900000211
Updating an estimated parameter
Figure FDA00025971333900000212
Figure FDA00025971333900000213
In the formula: tau is an adaptive function, and (t) > 0 is a continuous micro-directly symmetrical adaptive rate matrix; from this adaptive law, the following ideal characteristics can be obtained:
p1) parameter estimate is always at a known bounded ΩθIn-set, i.e. for any t, there is always
Figure FDA0002597133390000031
Thus, from hypothesis 1
Figure FDA0002597133390000032
P2)
Figure FDA0002597133390000033
P3) the law of parameter variation is consistently bounded, i.e. it is determined that the parameter variation is uniformly bounded
Figure FDA0002597133390000034
5. A RISE-based motor adaptive preset performance asymptotic control method according to claim 3, characterized in that: the step S2b specifically includes: defining the motor output control error e ═ x1-x1dIt is assumed that it needs to meet the following performance criteria:
Figure FDA0002597133390000035
in the formula:l,ufor the parameters to be designed, for the upper and lower limits of the auxiliary constraint control error, ρ (t) is a positive strictly increasing smoothing function, as shown in the following equation:
Figure FDA0002597133390000036
in the formula: rho0、ρ∞And k are both positive designable parameters;
formula (8) -lρ0Anduρ0respectively constraining the maximum downward impulse and the maximum overshoot of the output force control error e (t), and constraining the convergence rate, rho, of the error e (t) by the parameter k∞A steady state bound on the error is constrained; equation (8) thus gives a specific plan for the performance of the output force control error by selecting the appropriate parameter ρ0、ρ∞、k、lAnduthe transient and stable performance of the output force control error can be planned in advance, and the transient performance can be improved according to the actual requirement of the system;
the following increasing function is established:
Figure FDA0002597133390000037
in the formula: z is a radical of1(t) is a conversion error variable corresponding to the control error e (t), and it is easy to analyze that the equation (10) is equivalent to e (t) ═ ρ (t) S (z)1(t)), and z1(t) when the interface is bounded, the preset performance characteristic formula (8) is always satisfied;
an increasing function S (z) satisfying the characteristic formula (10)1) The following can be selected:
Figure FDA0002597133390000038
the inverse function of equation (11) is found:
Figure FDA0002597133390000041
for the conversion error z1Designing a controller;
a set of functions is established as follows:
Figure FDA0002597133390000042
in the formula: k is a radical of1，k2Is the feedback gain;
by differentiating the equation (13) and substituting the equation (2), it is possible to obtain:
Figure FDA0002597133390000043
based on the system model, the controller can be designed as follows:
Figure FDA0002597133390000044
in the formula: k is a radical of3Is the feedback gain;
the controller (15) may be substituted for the equation (14):
Figure FDA0002597133390000045
the design parameter adaptation law is as follows:
Figure FDA0002597133390000046
in the formula:
Figure FDA0002597133390000051
then, it is possible to obtain:
Figure FDA0002597133390000052
design robust controller us2The following were used:
Figure FDA0002597133390000053
in the formula β2Are parameters to be designed.
6. A RISE based motor adaptive preset capability asymptotic control method according to claim 5, characterized in that: the step S2c includes selecting the initial condition of system controllρ(0)<e(0)<uρ (0) -l<λ(0)<uSimultaneous parameter β2Satisfies the following inequality:
Figure FDA0002597133390000054
while designing a sufficiently large parameter k1And k2So that the following matrix Λ is a positive definite matrix:
Figure FDA0002597133390000055
ensuring that the control error of the output force is bounded all the time, realizing better instruction tracking of the output force and adjusting rho0、ρ∞、k、lAnduthe parameters are equal, so that the control error can meet the preset performance requirement designed by the formula (8);
the method specifically comprises the following steps: the following Lyapunov function is established:
Figure FDA0002597133390000056
further derivation of V and substitution of the formulae (13), (18) and (19) gives:
Figure FDA0002597133390000061
in the formula: z ═ Z1,z2]TThe matrix Λ is defined as formula (21) if the reasonable design parameter k is passed1And k2Making the matrix Λ positive definite makes the following satisfied:
Figure FDA0002597133390000062
in the formula: lambda [ alpha ]min(Λ) represents the minimum eigenvalue of the matrix Λ, and the analytic expression (24) shows that the Lyapunov function is bounded, and the W integral is bounded, and further shows that the conversion error amount z is bounded1And z2All are bounded, and in combination with equations (7), (13) and (15), all signals in the system are bounded, so that the derivative of W is bounded, and as the time approaches infinity, W approaches zero, i.e., the transformation error amount z, as can be seen by the existing Barbalt theorem1And approaches zero, so that the control error e (t) is always bounded in conjunction with equation (8), thereby proving that the controller is convergent and the system is stable.
7. A RISE based motor adaptive preset capability asymptotic control method according to claim 6, characterized in that: the third step is concreteFor adjusting the parameter k of the control law u1、k2、k3、ρ0、ρ∞、k、l、u、β2And the system meets the control performance index.
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