CN108508750A - A kind of output feedback ontrol method of TORA systems - Google Patents
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Abstract
The present invention relates to a kind of output feedback ontrol methods of TORA systems, include the following steps：S1：Establish TORA system models；S2：Design TORA systems closed loop auxiliary system in the step S1；S3：Controller is set, stability contorting is carried out to the TORA systems.The present invention is based on integration controls and high-gain control method, and the indeterminate of system unknown state and system is estimated using the High-gain observer of extension, a kind of output feedback strategy is proposed for unknown single-input single-output non-minimum-phase nonlinear systems, practical value is high.
Description
Technical field
The present invention relates to control method more particularly to the output feedback ontrol methods of TORA systems.
Background technology
It is existing to be directed to non-minimum phase although the control method for non-minimum-phase nonlinear systems emerges one after another
The research of nonlinear system also has following insufficient：1) the existing research for unknown non-minimum-phase nonlinear systems is mainly examined
Consider Stabilization, also rarely has method that can solve the regulation problem of such system；2) the existing output for such system controls
Research be essentially all based on feedback of status, and for output feedback research it is more rare；And 3) existing method is i.e. enabled
Enough output feedback ontrols realized to unknown non-minimum-phase nonlinear systems, but export the system under feedback and respond compared with state
System performance when feedback is deteriorated.
Invention content
For the deficiency of the prior art, the present invention is based on integration controls and high-gain to control, and combines the high-gain of extension
Observer, it is proposed that a kind of control method based on output feedback, comprehensive solve problem above, and by this method Successful utilization
In the translation oscillator (TORA) with rotary actuator.
To achieve the above object, the following technical solution of the present invention：A kind of output feedback ontrol method of TORA systems, including
Following steps：
S1：Establish TORA system models；
S2：Design TORA systems closed loop auxiliary system in the step S1；
S3：Controller is set, stability contorting is carried out to the TORA systems.
As an improvement, the step S1 is as follows the step of establishing TORA system models：
S1a：Establish TORA systems：
The TORA systems include the rotary actuator for translating oscillator and being arranged on translation oscillator：
The translation oscillator includes platform and Hookean spring, and one end of the Hookean spring is fixed, the other end with it is described
Platform connects, and the platform is located on horizontal plane, and can only be in the horizontal plane motion for being parallel to axle of spring；
The rotary actuator is a mass block, and the mass block setting on the platform, and can turn with the platform
Dynamic connection；
S1b：The step S1a TORA systems established are modeled：
Power suffered by the mass block has Fx,Fy, u and ω carry out torque point using Newton's law to the barycenter of mass block
Analysis can obtain
Wherein, m indicates the quality of mass block；
FxIndicate power of the mass block suffered by x-axis direction；
FyIndicate power of the mass block suffered by y-axis direction；
L indicates the rotation center of mass block away from the distance of barycenter in TORA systems；
θ indicates the Angle Position of mass block；
ω indicates the sliding-frictional resistance that mass block rotation is generated with platform；
U indicates the torque being applied on mass block；
xcIndicate the translation position of platform；
J indicates rotary inertia；
Platform is in the opposite direction respectively by power Fx,Fy, while also by the restoring force of spring；
By FxAnd FyIt eliminates and can obtain in third expression formula and expression formula (1.2) from expression formula (1.1)：
Therefore,
Wherein,
Λ (θ)=(J+mL2)(m+M)-m2L2cos2θ≥M(J+mL2)+Jm>0 (1.6)；
S1c：Define x1=θ,x3=xcWithIt is inputted in order to control for TORA system modes and u, TORA systems
State equation can be expressed as：
S1d：Definition
The state equation (1.7) of TORA systems is transformed to：
Wherein,
E indicates to adjust error；
η1、η2Indicate the interior membrane stage of system shown in relational expression (1.9), ξ1, ξ2η2Indicate system shown in relational expression (1.9)
Outer membrane stage, a0(η1,η2,ξ1,ξ2) whole nonlinear terms for indicating system shown in relational expression (1.9)；The equation (1.10)
The as described TORA system models.
As an improvement, the process for designing closed loop auxiliary system in the step S2 is as follows：
S2a：The design in auxiliary system of the TORA system models is：
S2b：Selection matrix (L (), M (), N ()) enables pilot controller to ensure that the closed loop of augmentation assists system
System；
Wherein pilot controller is
Wherein, z is auxiliary system state；
The closed loop auxiliary system is：
Wherein,
WhereinIt is design parameter；
As an improvement, the controller designed in the step S3 includes state feedback controller and output feedback controller.
As an improvement, state feedback controller is as follows in the step S3：
Wherein, σ indicates that integration variable, κ indicate integral parameter, κ>0,
As an improvement, output feedback controller design process is as follows in the step S3：
1) in the case where output is fed back, the High-gain observer of extension will be used to observe ξ1,ξ2And ya, the expression formula of observer
For：
Wherein, γ1、γ2And γ3It is design parameter, and makes multinomial q3+γ1q2+…+γ2q+γ3Meet
Hurwitz conditions；
2) output feedback controller is designed as：
Wherein,K2>0 and K3>0 size is respectively by u under feedback of status and yaWidth in domain of attraction
Value determines.
The present invention at least has the advantages that：
The present invention is based on integration controls and high-gain control method, and unknown to system using the High-gain observer of extension
The indeterminate of state and system is estimated, is proposed for unknown single-input single-output non-minimum-phase nonlinear systems
A kind of output feedback strategy, has the following effects that：
A) system that the present invention considers is a kind of complicated unknown non-minimum-phase nonlinear systems, therefore to minimum phase
Linear system, non-minimum phase linear system are also effective；
B) indeterminate of system mode and system is estimated using the High-gain observer of extension, can realizes
To the output feedback ontrol of unknown non-minimum-phase nonlinear systems；
C) slow integration control, high-gain control and High-gain observer are used, can ensure the system under output feedback
Performance can be restored to level when feedback of status；
D) method proposed has certain practical value, is obtained in the translation oscillator (TORA) with rotary actuator
Successful application.
Description of the drawings
Fig. 1 is TORA systems, i.e. the translation oscillator with rotary actuator, and wherein Fig. 1 (a) indicates the structure of TORA systems
Schematic diagram, Fig. 1 (b) mass block force analysis figures.
Fig. 2 is the performance recovery of reduced order system.
Fig. 3 is the performance recovery of closed loop auxiliary system：Auxiliary system under solid line indicates noiseless responds；Dotted line indicates
Auxiliary system response under interference；Dotted line or chain-dotted line indicate high gain system response (no integrator)
Fig. 4 is the response of high gain feedback controller：Solid line indicates no integral element；Dotted line, chain-dotted line or dotted line table
It is shown with integral element.
Fig. 5 is the performance recovery of State Feedback System：SFB indicates feedback of status；OFB indicates output feedback.
Specific implementation mode
In order to make the objectives, technical solutions and advantages of the present invention clearer, With reference to embodiment and join
According to attached drawing, the present invention is described in more detail.It should be understood that these descriptions are merely illustrative, and it is not intended to limit this hair
Bright range.In addition, in the following description, descriptions of well-known structures and technologies are omitted, to avoid this is unnecessarily obscured
The concept of invention.
A kind of output feedback ontrol method of TORA systems, includes the following steps：
S1：Establish TORA system models；
S2：Design TORA systems closed loop auxiliary system in the step S1；
S3：Controller is set, stability contorting is carried out to the TORA systems.
Specifically, the step of step S1 establishes TORA system models is as follows：
S1a：Establish TORA systems：
The TORA systems include the rotary actuator for translating oscillator and being arranged on translation oscillator：
The translation oscillator includes platform and Hookean spring, and one end of the Hookean spring is fixed, for example can be fixed
On test-bed, wall is first-class, it is therefore an objective to prevent Hookean spring fixing end movement, the other end from being connect with the platform, institute
It states platform to be located on horizontal plane, and can only be in the horizontal plane motion for being parallel to axle of spring；
The rotary actuator is a mass block, and the mass block setting on the platform, and can turn with the platform
Dynamic connection；
S1b：The step S1a TORA systems established are modeled：
Power suffered by the mass block has Fx,Fy, u and ω carry out torque point using Newton's law to the barycenter of mass block
Analysis can obtain
Wherein, m indicates the quality of mass block；
FxIndicate power of the mass block suffered by x-axis direction；
FyIndicate power of the mass block suffered by y-axis direction；
L indicates the rotation center of mass block away from the distance of barycenter in TORA systems；
θ indicates the Angle Position of mass block, counterclockwise measures；
ω indicates the sliding-frictional resistance that mass block rotation is generated with platform；
U indicates the torque being applied on mass block；
xcIndicate the translation position of platform；
J indicates rotary inertia；
The above parameter is determined by system structure；
Platform is in the opposite direction respectively by power Fx,Fy, while also by the restoring force of spring；
By FxAnd FyIt eliminates and can obtain in third expression formula and expression formula (1.2) from expression formula (1.1)：
Therefore,
Wherein,
Λ (θ)=(J+mL2)(m+M)-m2L2cos2θ≥M(J+mL2)+Jm>0 (1.6)；
S1c：Define x1=θ,x3=xcWithIt is inputted in order to control for TORA system modes and u, TORA systems
State equation can be expressed as：
Our control targe is to use uniquely survey signal x1One output feedback controller of design makes system (1.7)
Stablize in origin x1=0；
S1d：Definition
The state equation (1.7) of TORA systems is transformed to：
Wherein,
E indicates to adjust error；
η1、η2Indicate the interior membrane stage of system shown in relational expression (1.9), ξ1, ξ2η2Indicate system shown in relational expression (1.9)
Outer membrane stage, a0(η1,η2,ξ1,ξ2) whole nonlinear terms for indicating system shown in relational expression (1.9)；
The equation (1.10) is the TORA system models.
As an improvement, the process for designing closed loop auxiliary system in the step S2 is as follows：
S2a：The design in auxiliary system of the TORA system models is：
S2b：Selection matrix (L (), M (), N ()) enables pilot controller to ensure that the closed loop of augmentation assists system
System；
Wherein pilot controller is
Wherein, z is auxiliary system state；
The closed loop auxiliary system is：
For arbitrary χ (ω), there is unique Exponential Stability equalization pointParticularly, if χ (ω)=
0, system (5.14) at the origin is exponentially stable；
Wherein,
WhereinIt is design parameter, wherein εaFor the normal number of very little
Here z is vector, z=[z1,z2]TSpecifically, for arbitrary χ (ω), there is unique Exponential Stability equalization pointParticularly, if χ (ω)=0, system (1.14) at the origin is exponentially stable.In the case, I
Can solve the problems, such as the design in auxiliary system of TORA according to following flow thinking：
1) the case where considering system (1.9) interference-free (i.e. χ (ω)=0), present matrix (L (), M (), N ())
Make system (1.14) at the origin Exponential Stability；
2) condition will be met | χ (ω) |≤χ0External disturbance χ (ω) " added " in system (1.14), then the system
Equalization point will from shift of origin to
This flow sets up linear system naturally, and for the nonlinear system of such as TORA, as long as χ (ω) is maintained at
Can also be establishment in one reasonable range.Therefore, by assuming χ (ω)=0, we can be walked by following four
It is rapid to obtain matrix (L (), M (), N ())：
Step 1：The output for redefining system (1.10) is：
Wherein
Step 2：It is by the In-put design of auxiliary system
Wherein | wa|≤1, then the auxiliary system of open loop be represented by
Work as εaWhen sufficiently small, formula (1.17) can be counted as a singular perturbation system.Set εa=0, then wa=sin
ξ1, the reduced-order model of system (1.17) can be expressed as：
Now we the problem of can be attributed to give linear system (1.18) design a compensator.
Step 3：According to LQR theories, we can be by waIt is designed as：
wa=-θ1η1-θ2η2(1.19)；
Carrying out saturated process to it at ± 1 can obtain
wa=-sat { θ1η1+θ2η2} (1.20)；
Wherein θ1>0 and θ2>0, design a following full order observer for system (1.18)
Wherein, wz=-sat { θ1z1+θ2z2,WithFor normal number；
Step 4：Contrast (1.21) and formula (1.13) can obtain
Bring formula (1.20) into formula (1.14), we can obtain from ξ1Stable state to χ is mapped as：
Wherein,
So as long asThen λ ≠ 0.In the case, stable state mapsBe strictly increasing or
It is strictly decreasing.In addition,
As an optimization, the controller designed in the step S3 includes state feedback controller and output feedback controller.
Specifically, the state feedback controller is as follows：
Wherein, σ indicates that integration variable, κ indicate integral parameter, κ>0,Specific value is by relational expression (1.14) institute
Show system from χ (ω) to ξ1Stable state mapping determine；The output feedback controller design process is as follows：
1) in the case where output is fed back, the High-gain observer of extension will be used to observe ξ1,ξ2And ya, the expression formula of observer
For：
2) wherein, γ1、γ2And γ3It is design parameter, and makes multinomial q3+γ1q2+…+γ2q+γ3Meet
Hurwitz conditions；Output feedback controller is designed as：
Wherein,K2>0 and K3>0 size is respectively by u under feedback of status and yaWidth in domain of attraction
Value determines.
Simulation result
In order to realize the emulation to TORA system models in Matlab, our selecting system parameters, specially：J=
0.0002175, L=0.0592, m=0.096, M=1.3608, k=186.3.Interference χ is limited to section [- 0.02,0.02]
It is interior.For arbitrary | χ |≤0.02, we can have unique Exponential Stability by simulating, verifying closed loop auxiliary system (1.14)
Equalization point.Control parameter and be that initial value is chosen to be：θ1=1, θ2=8,μ∈{0.01,0.001},K2=
5000,K3=45, γ1=γ2=γ3=10, κ ∈ { 0.1,0.01,0.002 }, σ (0)=0, εa∈{0.1,0.01}ε∈
{ 0.05,0.01 }, η1(0)=η2(0)=ξ2(0)=0,ξ1(0)=- 0.05, whereinIt is determined by formula (1.24).We verify the validity of system by adjusting control parameter step by step, emulation
As a result as shown in Figures 1 to 5.
Response of the entire adjustment process to match reduced order system (given by formula (1.18) and formula (1.21)), to adjust
High-gain observer parameter terminates to restore the performance of State Feedback System, includes four steps in total, specially：
The first step：The recovery process of reduced order system performance has (reference signal η shown in Fig. 21), wherein red line indicates depression of order
The response of system, green line represent response of the auxiliary system (1.14) in χ=0.By εaIt is reduced to 0.01 from 0.1, it is seen that
The response of auxiliary system is more nearly the response of reduced order system, and the Simultaneous Stabilization time is also with greatly shortening.We select εa
=0.01, it carries out in next step；
Second step：Selected χ=0.02, we (will have formula (1.9) and formula (1.25) given, and not include with high gain system
Integral elementThat is σ=0) performance go matching auxiliary system (1.14) performance.Corresponding simulation result such as Fig. 3
Shown, wherein reference signal is changed to ξ by us1.It can be seen that when interference signal χ becomes 0.02 from 0, ξ1Equalization point will be from
0 is transferred to a non-zero points.In the case, when reducing parameter μ, the response of high gain system will be more nearly auxiliary system
Response.We select μ=0.001, are walked into third；
Third walks：Integrator is added in High-Gain Controller, verification has been added the controller of integrator can be with by we
Allow ξ10 is converged to, simultaneously, by reducing integral parameter κ, which can be with recovery system in high gain system (nothing
Integrator) in the performance of ascent stage.Corresponding simulation result is provided by Fig. 4, therefrom it can be seen that integration control can actually
Make ξ10 is converged to, and as κ reduces, high gain system (no integrator) can obtain preferably in the performance of ascent stage
Restore, but stabilization time can be elongated therewith.We select κ=0.01, into final step；
4th step：Finally we will restore State Feedback System (by formula by adjusting the parameter ε of High-gain observer
(1.9) given with formula (1.25)) performance.ε is reduced to 0.0001 from 0.01, it is observed that output feedback system from Fig. 5
The response of system covers substantially the response of State Feedback System.Therefore we select the last one design parameter be ε=
0.0001。
The above description is merely a specific embodiment, but simultaneously difference is limited to this to protection scope of the present invention, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Lid is within protection scope of the present invention.Therefore, protection scope of the present invention should be subject to the protection scope in claims.
Claims (6)
1. a kind of output feedback ontrol method of TORA systems, it is characterised in that：Include the following steps：
S1：Establish TORA system models；
S2：Design TORA systems closed loop auxiliary system in the step S1；
S3：Controller is set, stability contorting is carried out to the TORA systems.
2. the output feedback ontrol method of TORA systems as described in claim 1, it is characterised in that：The step S1 is established
The step of TORA system models, is as follows：
S1a：Establish TORA system models：
The TORA systems include the rotary actuator for translating oscillator and being arranged on translation oscillator：
The translation oscillator includes platform and Hookean spring, and one end of the Hookean spring is fixed, the other end and the platform
Connection, the platform are located on horizontal plane, and can only be in the horizontal plane motion for being parallel to axle of spring；
The rotary actuator is a mass block, and the mass block setting on the platform, and rotatably connects with the platform
It connects；
S1b：The step S1a TORA systems established are modeled：
Power suffered by the mass block has Fx,Fy, u and ω, carrying out torque analysis to the barycenter of mass block using Newton's law can
Wherein, m indicates the quality of mass block；
FxIndicate power of the mass block suffered by x-axis direction；
FyIndicate power of the mass block suffered by y-axis direction；
L indicates the rotation center of mass block away from the distance of barycenter in TORA systems；
θ indicates the Angle Position of mass block；
ω indicates the sliding-frictional resistance that mass block rotation is generated with platform；
U indicates the torque being applied on mass block；
xcIndicate the translation position of platform；
J indicates rotary inertia；
Platform is in the opposite direction respectively by power Fx,Fy, while also by the restoring force of spring；
By FxAnd FyIt eliminates and can obtain in third expression formula and expression formula (1.2) from expression formula (1.1)：
Therefore,
Wherein,
Λ (θ)=(J+mL2)(m+M)-m2L2cos2θ≥M(J+mL2)+Jm>0 (1.6)；
S1c：Definitionx3=xcWithIt is inputted in order to control for TORA system modes and u, the shape of TORA systems
State equation can be expressed as：
S1d：Definition
The state equation (1.7) of TORA systems is transformed to：
Wherein,
E indicates to adjust error；
η1、η2Indicate the interior membrane stage of system shown in relational expression (1.9), ξ1, ξ2η2Indicate the outer membrane of system shown in relational expression (1.9)
State, a0(η1,η2,ξ1,ξ2) whole nonlinear terms for indicating system shown in relational expression (1.9)；The equation (1.10) is as
The TORA system models.
3. the output feedback ontrol method of TORA systems as claimed in claim 2, it is characterised in that：It is designed in the step S2
The process of closed loop auxiliary system is as follows：
S2a：The design in auxiliary system of the TORA system models is：
S2b：Selection matrix (L (), M (), N ()) enables pilot controller to ensure the closed loop auxiliary system of augmentation；
Wherein pilot controller is
Wherein, z is auxiliary system state；
The closed loop auxiliary system is：
Wherein,
WhereinεaIt is design parameter.
4. the output feedback ontrol method of TORA systems as described in claim 1, it is characterised in that：It is designed in the step S3
Controller include state feedback controller and output feedback controller.
5. the output feedback ontrol method of TORA systems as claimed in claim 4, it is characterised in that：State in the step S3
Feedback controller is as follows：
Wherein, σ indicates that integration variable, κ indicate integral parameter, κ>0,
6. the output feedback ontrol method of TORA systems as claimed in claim 4, it is characterised in that：It is exported in the step S3
Design of Feedback Controller process is as follows：
1) in the case where output is fed back, the High-gain observer of extension will be used to observe ξ1,ξ2And ya, the expression formula of observer is：
Wherein, γ1、γ2And γ3It is design parameter, and makes multinomial q3+γ1q2+…+γ2q+γ3Meet Hurwitz items
Part；
2) output feedback controller is designed as：
Wherein,K2>0 and K3>0 size is respectively by u under feedback of status and yaAmplitude in domain of attraction is determined
It is fixed.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113252802A (en) * | 2020-08-21 | 2021-08-13 | 国网河南省电力公司濮阳供电公司 | Full-automatic degasification of chromatogram vibrates appearance fixing device |
| CN117850246A (en) * | 2024-03-07 | 2024-04-09 | 泰山学院 | Tracking control method for single-wheel mobile robot |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7853338B1 (en) * | 2002-12-09 | 2010-12-14 | Georgia Tech Research Corporation | Adaptive output feedback apparatuses and methods capable of controlling a non-minimum phase system |
| CN104199291A (en) * | 2014-08-11 | 2014-12-10 | 浙江工业大学 | Dissipative structure theory based TORA (Translation oscillators with a rotating actuator) system self-adaption control method |
| CN104950682A (en) * | 2015-06-25 | 2015-09-30 | 浙江工业大学 | Constraining control method for under-actuated system |
| CN107024865A (en) * | 2017-05-02 | 2017-08-08 | 南开大学 | Drive lacking jib crane positions the pendulum nonlinear control method that disappears |
| CN107065553A (en) * | 2017-04-20 | 2017-08-18 | 南开大学 | Many rotation excitations translate oscilator system Non-linear coupling self-adaptation control method |
-
2018
- 2018-05-08 CN CN201810432938.9A patent/CN108508750B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7853338B1 (en) * | 2002-12-09 | 2010-12-14 | Georgia Tech Research Corporation | Adaptive output feedback apparatuses and methods capable of controlling a non-minimum phase system |
| CN104199291A (en) * | 2014-08-11 | 2014-12-10 | 浙江工业大学 | Dissipative structure theory based TORA (Translation oscillators with a rotating actuator) system self-adaption control method |
| CN104950682A (en) * | 2015-06-25 | 2015-09-30 | 浙江工业大学 | Constraining control method for under-actuated system |
| CN107065553A (en) * | 2017-04-20 | 2017-08-18 | 南开大学 | Many rotation excitations translate oscilator system Non-linear coupling self-adaptation control method |
| CN107024865A (en) * | 2017-05-02 | 2017-08-08 | 南开大学 | Drive lacking jib crane positions the pendulum nonlinear control method that disappears |
Non-Patent Citations (3)
| Title |
|---|
| YONGDUAN SONG: "Robust Adaptive Fault-Tolerant PID Control of MIMO Nonlinear Systems With Unknown Control Direction", 《IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS》 * |
| 刘翔等: "不稳定对象及非最小相位对象的自抗扰控制仿真研究", 《控制与决策》 * |
| 段敏等: "智能群体环绕运动控制", 《物理学报》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113252802A (en) * | 2020-08-21 | 2021-08-13 | 国网河南省电力公司濮阳供电公司 | Full-automatic degasification of chromatogram vibrates appearance fixing device |
| CN117850246A (en) * | 2024-03-07 | 2024-04-09 | 泰山学院 | Tracking control method for single-wheel mobile robot |
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