CN114321319B - Harmonic reducer output moment strong disturbance rejection control method based on phase optimization - Google Patents
Harmonic reducer output moment strong disturbance rejection control method based on phase optimization Download PDFInfo
- Publication number
- CN114321319B CN114321319B CN202111620691.1A CN202111620691A CN114321319B CN 114321319 B CN114321319 B CN 114321319B CN 202111620691 A CN202111620691 A CN 202111620691A CN 114321319 B CN114321319 B CN 114321319B
- Authority
- CN
- China
- Prior art keywords
- observer
- friction
- disturbance
- output
- harmonic
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 239000003638 chemical reducing agent Substances 0.000 title claims abstract description 57
- 238000000034 method Methods 0.000 title claims abstract description 29
- 238000005457 optimization Methods 0.000 title claims abstract description 29
- 230000005540 biological transmission Effects 0.000 claims abstract description 33
- 238000005259 measurement Methods 0.000 claims description 16
- 230000003068 static effect Effects 0.000 claims description 15
- 238000013016 damping Methods 0.000 claims description 9
- 230000001419 dependent effect Effects 0.000 claims description 6
- 230000007246 mechanism Effects 0.000 claims description 5
- 230000008859 change Effects 0.000 claims description 4
- 230000008878 coupling Effects 0.000 claims description 4
- 238000010168 coupling process Methods 0.000 claims description 4
- 238000005859 coupling reaction Methods 0.000 claims description 4
- 238000006073 displacement reaction Methods 0.000 claims description 4
- 230000033001 locomotion Effects 0.000 claims description 4
- 230000008569 process Effects 0.000 claims 1
- 238000013461 design Methods 0.000 description 4
- 230000004044 response Effects 0.000 description 4
- 101710163391 ADP-ribosyl cyclase/cyclic ADP-ribose hydrolase Proteins 0.000 description 3
- 238000012512 characterization method Methods 0.000 description 3
- 230000036039 immunity Effects 0.000 description 3
- 230000000694 effects Effects 0.000 description 2
- 238000005312 nonlinear dynamic Methods 0.000 description 2
- 230000001629 suppression Effects 0.000 description 2
- 230000003044 adaptive effect Effects 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 230000000052 comparative effect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000004069 differentiation Effects 0.000 description 1
- 238000001914 filtration Methods 0.000 description 1
- 238000005755 formation reaction Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 230000002401 inhibitory effect Effects 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
Abstract
The invention relates to a phase optimization-based harmonic speed reducer output moment strong disturbance rejection control method, which comprises the steps of firstly, establishing a harmonic speed reducer transmission model containing friction, transmission errors, rigidity nonlinearity and other multisource disturbances, and designing a disturbance observer by utilizing model information to estimate unknown hysteresis moment caused by friction and flexible members; secondly, regarding the uncompensated parts of the uncompensated dynamic and external disturbance and disturbance observer of the system as lumped disturbance, and designing an extended state observer to estimate and compensate through a feedback control law; and finally, aiming at phase lag caused by estimation errors, designing a phase optimization law of the extended state observer to eliminate so as to enhance the estimation capability of the extended state observer on the total disturbance. The strong disturbance rejection control method based on phase optimization effectively combines the disturbance observer and the phase optimization extended state observer, can better estimate multi-source disturbance, and enhances the tracking control precision of the output moment of the harmonic reducer.
Description
Technical Field
The invention relates to a phase optimization-based harmonic reducer output torque strong disturbance rejection control method, which can realize nonlinear multisource disturbance estimation and compensation of friction, transmission error and rigidity of a harmonic reducer and can be used for precise electromechanical deceleration control.
Background
The harmonic reducer has the advantages of near zero backlash, compactness, light weight, high torque, high gear ratio, and coaxial assembly, which make harmonic drives suitable for precise motion mechanisms such as lightweight robots/operators, force feedback haptic devices, and steer-by-wire systems. For example, james weber space telescopes require steering accuracy of 0.004 angular seconds. The high precision steering requirement places extremely high demands on the speed/torque control capability of the harmonic drive, however, there is a complex dynamic relationship between the harmonic drive input and output speed/torque due to inherent factors such as friction, drive errors and stiffness nonlinearities. First, the effect of friction dissipation is such that the transmitted power loss exceeds 10% and the output torque is lower than expected. It has been found that speed dependent damping in harmonic drives may decrease in structural damping at higher speeds with an increase in magnitude less than at low speeds, even at very high speeds. Such irregular friction and damping variations present a significant challenge for high precision rotational speed/torque control of harmonic drives. And secondly, the transmission error between the output end and the input end of the harmonic reducer directly influences the accuracy of a transmission system and is coupled with various interferences, so that accurate modeling is difficult. Again, the flexible members in harmonic reducers deform under high radial forces and result in relatively low torsional stiffness, and non-linearities in stiffness can lead to displacement and hysteresis losses. Hysteresis losses, however, are more difficult objects to model than stiffness nonlinearities, and are typically ignored. Hysteresis is not only related to the current state of the system, but also related to the historical value of the state, and the control accuracy is often reduced by the control of the rotating speed/moment by neglecting hysteresis, and even the system is unstable when the state of the system is changed rapidly. Finally, the harmonic transmission rotation speed/torque sensor inevitably has measurement noise, and noise is introduced when the measurement signal is used for constructing an output rotation angle or the rotation speed change rate to inhibit the natural vibration frequency of the system, so that the improvement of the rotation speed/torque control system is further restricted, and the performance of the closed-loop system is influenced.
Aiming at the difficult problem of high-precision rotating speed/moment control of the harmonic speed reducer in the presence of multi-source interference, the existing research is less, and modeling work for optimizing the structural performance and exploring dynamics of the harmonic speed reducer is more than control work. The control methods applied to harmonic drive include PID control, sliding mode control, self-adaptive control and the like. The PID control is mainly used in industrial control because of simple structure and independence of the model characteristics of the controlled object. However, PID control has limitations in that it is completely abandoned using system model information, differentiation is difficult to achieve, and noise and integration can be amplified to bring about control saturation. The sliding mode control can improve response speed and robustness, but buffeting is inevitably introduced. Adaptive control is only effective for system parameter perturbation and has limited processing power for structural changes and external disturbances.
In order to improve the anti-interference capability of the traditional method and break through the limitation of only inhibiting single homogeneous interference, the control based on an interference observer is greatly developed. There are two types of interference observers currently in mainstream: an interference observer using system or interference information and an extended state observer not using such information. However, control methods based on both observer formations have their limitations: firstly, when modeling interference based on interference observer control (DOBC) estimation, neglecting nonlinear dynamics mainly comprising model errors; then, when estimating the disturbance based on the extended state observer control (ADRC), the feature information known to the disturbance is underutilized, and the conservation is large. Aiming at the problem of high-precision rotating speed/moment control of a harmonic speed reducer, which is caused by multi-source interference such as friction, transmission error and rigidity nonlinearity, various interference and state mutual coupling, nonlinear dynamics and interference estimation error mutual influence and limitation of measurement noise on the bandwidth of an observer are difficult to multi-source interference compensation and suppression of a rotating speed/moment control system, therefore, modeling and characterization of the multi-source interference existing in the harmonic speed reducer are needed, the advantages of DOBC and ADRC are combined, the hysteresis moment of which the estimated dynamics is known by the interference observer is designed, in the design of a phase optimization expansion state observer, real-time online estimation and closed-loop compensation of the interference such as friction and transmission error of the harmonic speed reducer and the like and measurement noise filtering suppression are realized, and the high-precision rotating speed/moment control of a harmonic transmission system is completed, so that theoretical basis and technical support are provided for precision electromechanical deceleration control.
Disclosure of Invention
The technical solution of the invention is as follows: aiming at the problems that the existing observer is difficult to accurately estimate due to nonlinear multi-source interference including friction, transmission error and rigidity of the harmonic reducer, the method for controlling the harmonic reduction output moment to be strong and disturbance-free based on phase optimization is provided, and the disturbance observer is utilized to estimate the known dynamic hysteresis moment; the extended state observer estimates lumped disturbances other than hysteresis and designs a phase optimization law to reduce the estimation error. The extended state observer uses the estimated output of the interference observer, can effectively reduce the estimated load of a single observer, has the advantages of strong interference estimating capability, high following precision of a controller and the like, and can be used for precision electromechanical high-precision rotating speed control of a speed reducer containing harmonic waves.
The technical scheme of the invention is as follows: a harmonic speed reducer output moment strong disturbance rejection control method based on phase optimization aims at a harmonic speed reducer rotating speed control system containing friction, transmission error and rigidity nonlinear multisource disturbance, firstly, a multisource disturbance model of the system is built by taking the angular position of an input end and an output end as generalized coordinates according to Lagrange equation; secondly, designing an interference observer to estimate hysteresis moment on the basis of mathematical modeling and interference characterization; thirdly, designing an extended state observer to estimate the total disturbance of the system except for hysteresis according to the output of the disturbance observer; finally, using the outputs of the two observers, designing a strong immunity control law, and configuring the observer and controller bandwidths by using a bandwidth parameterization method. The specific implementation steps are as follows:
firstly, establishing a harmonic reducer dynamics model comprising friction, transmission error, rigidity nonlinearity and other multi-source interference:
Aiming at inherent stress contact friction loss and hysteresis nonlinearity generated by insufficient torsional rigidity of a flexible member in a harmonic gear transmission mechanism, and simultaneously considering a coupling relation between transmission errors and rigidity nonlinearity, a dynamic model of the harmonic speed reducer comprising friction, transmission errors and rigidity nonlinearity is established as follows:
Wherein J i and J o respectively represent the rotational inertia of the input end and the output end of the harmonic reducer; b h represents the damping coefficient inside the harmonic reducer; θ i and θ o represent the input end and output end rotation angles, respectively; f (·) represents the non-linearity of stiffness between the input and output of the harmonic reducer, b 2 represents the transmission error doubling factor, N represents the harmonic reducer transmission ratio, τ f represents the friction loss, τ m represents the harmonic reducer input torque, q represents the hysteresis, α and a are hysteresis model parameters, and d represents the external random disturbance.
Wherein the stiffness nonlinearity is modeled as an odd function symmetric to the origin:
f(θ)＝a1θ+a2θ3+a3θ5
a 1,a2,a3 is the coefficient of stiffness nonlinearity.
The nonlinear friction tau f existing in the harmonic gear transmission is divided into a static part and a dynamic part.
τf＝F+τp
Where F represents a static average friction term and τ p represents a position-dependent dynamic friction term. Wherein the static average tribodynamic characteristics are described by the Lund-Grenobel (LuGre) model:
where z represents the average displacement of the bristles during the relative movement of the contact surfaces, σ 0 represents the stiffness of the friction characteristics, σ 1 and σ 2 represent respectively AndThe corresponding damping coefficients (the former dominates in the low speed region and the latter dominates in the high speed region), F s denotes static friction, F c denotes coulomb friction, v s denotes Stribeck velocity, g (·) is the friction internal function. Due to angular velocity of input endIt is known that static average friction model parameters can be obtained through a priori knowledge.
Dynamic friction is position dependent and can be described as:
Where a and b are friction model parameters, N f(θi) represents a nonlinear function related to input position, which can be approximated by a finite number of fourier functions, a fi,i＝0,…n;bfi, i=1, … N being fourier coefficients.
Secondly, according to a dynamics model of the harmonic reducer, designing an interference observer to estimate the hysteresis moment:
taking the system state of a harmonic reducer The dynamics model of the harmonic reducer is rewritten as:
Where u=τ m denotes a control input, y=θ o +v denotes a measurement output, and v denotes measurement noise.
For hysteresis due to insufficient torsional stiffness of the flexible member due to friction caused by stress contact, the following disturbance observer is constructed:
In the middle of Wherein the method comprises the steps ofAnd the estimation of the hysteresis interference moment is shown, w is the internal virtual state of the interference observer, and K is the gain of the interference observer.
Thirdly, estimating the model error parameter uncertainty, unmodeled dynamic and external interference design phase optimization expansion state observer of the harmonic reducer:
Sigma 4 is equivalently replaced by f 0 to obtain Where f is the lumped disturbance distinct from the double integrator series, defined as the system's expanded state, split into two parts based on the estimated output of the disturbance observerB 0 is the control gain. Taking outThe extended state observer taking into account the interference observer output is designed to:
Where z E＝[z1,z2,z3]T denotes the output vector of the extended state observer, y=θ o +v denotes the measurement output, z 1 denotes the estimate of the system output, z 2 denotes the estimate of the rate of change of the system output, z 3 denotes the estimate of the divide-by-lag portion F 0 in the extended state, For the extended state observer gain vector, wherein ω o is the observer bandwidth, the observer bandwidth ω o should satisfy a range of 10 to 500 in consideration of the observation performance and the measurement noise.
Designing a phase optimization law for the expansion state estimation value z 3:
Taking z EPO＝[z1,z2,z3PO]T as the output vector of the phase optimized extended state observer.
Fourthly, constructing a strong disturbance rejection controller based on phase optimization according to the output of the disturbance observer and the phase optimization extended state observer, and realizing expected control performance through the pole allocation of the controller bandwidth and the observer bandwidth:
designing a strong disturbance rejection control law:
where K u is the controller gain, The first and second set-up leads are indicated respectively.
The controller gain is configured according to a bandwidth parameterization method to obtain:
Wherein omega c is the expected controller bandwidth, and the value range of omega c is 2-100.
Compared with the prior art, the invention has the advantages that:
(1) The strong disturbance rejection control method based on phase optimization effectively combines the disturbance observer and the phase optimization extended state observer, can better estimate multi-source disturbance, and enhances the tracking control precision of the output moment of the harmonic reducer.
(2) The invention comprehensively considers multi-source interference such as friction, transmission error and rigidity nonlinearity in harmonic transmission, performs digital modeling and interference characterization, combines the advantages of DOBC and phase optimization ADRC, overcomes the limitation of a single method, and can be used for high-precision rotating speed/torque control of the harmonic reducer under the multi-source interference.
Drawings
FIG. 1 is a flow chart diagram of a harmonic reducer output moment strong disturbance rejection control method based on phase optimization of the invention;
FIG. 2 is a graph comparing the effect of harmonic reducer output angular position control;
FIG. 3 is an enlarged view of a portion of FIG. 2 when an external torque disturbance occurs;
FIG. 4 is a graph comparing the control amounts of input torque of the harmonic reducer when disturbance occurs.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
As shown in fig. 1, the specific implementation steps of the present invention are as follows:
first, establishing a harmonic reducer dynamics equation comprising friction, transmission error and rigidity nonlinearity:
Aiming at inherent stress contact friction loss and hysteresis nonlinearity generated by insufficient torsional rigidity of a flexible member in a harmonic gear transmission mechanism, and simultaneously considering a coupling relation between transmission errors and rigidity nonlinearity, a dynamic model of the harmonic speed reducer comprising friction, transmission errors and rigidity nonlinearity is established as follows:
Wherein J i and J o respectively represent the rotational inertia of the input end and the output end of the harmonic reducer; b h represents the damping coefficient inside the harmonic reducer; θ i and θ o represent the input end and output end rotation angles, respectively; f (·) represents the non-linearity of stiffness between the input and output of the harmonic reducer, b 2 represents the transmission error doubling factor, N represents the harmonic reducer transmission ratio, τ f represents the friction loss, τ m represents the harmonic reducer input torque, q represents the hysteresis, α and a are hysteresis model parameters, and d represents the external random disturbance.
Wherein the stiffness nonlinearity is modeled as an odd function symmetric to the origin:
f(θ)＝a1θ+a2θ3+a3θ5
a 1,a2,a3 is the coefficient of stiffness nonlinearity.
The nonlinear friction tau f existing in the harmonic gear transmission is divided into a static part and a dynamic part.
τf＝F+τp
Where F represents a static average friction term and τ p represents a position-dependent dynamic friction term. Wherein the static average tribodynamic characteristics are described by the Lund-Grenobel (LuGre) model:
where z represents the average displacement of the bristles during the relative movement of the contact surfaces, σ 0 represents the stiffness of the friction characteristics, σ 1 and σ 2 represent respectively AndThe corresponding damping coefficients (the former dominates in the low speed region and the latter dominates in the high speed region), F s denotes static friction, F c denotes coulomb friction, v s denotes Stribeck velocity, g (·) is the friction internal function. Due to angular velocity of input endIt is known that static average friction model parameters can be obtained through a priori knowledge.
Dynamic friction is position dependent and can be described as:
Where a and b are friction model parameters, N f(θi) represents a nonlinear function related to input position, which can be approximated by a finite number of fourier functions, a fi,i＝0,…n;bfi, i=1, … N being fourier coefficients.
Secondly, designing an interference observer for the hysteresis moment:
fetching system state Rewriting the harmonic reducer dynamics model as:
Where u=τ m denotes a control input, y=θ o +v denotes a measurement output, and v denotes measurement noise.
For hysteresis due to insufficient torsional stiffness of the flexible member due to friction caused by stress contact, the following disturbance observer is constructed:
In the middle of Wherein the method comprises the steps ofAnd the estimation of the hysteresis interference moment is shown, w is the internal virtual state of the interference observer, and K is the gain of the interference observer.
Thirdly, estimating the model error parameter uncertainty, unmodeled dynamic and external interference design phase optimization expansion state observer of the harmonic reducer:
Sigma 4 is equivalently replaced by f 0 to obtain Where f is the lumped disturbance distinct from the double integrator series, defined as the system's expanded state, split into two parts based on the estimated output of the disturbance observerB 0 is the control gain. Taking outThe extended state observer taking into account the interference observer output is designed to:
Where z E＝[z1,z2,z3]T denotes the output vector of the extended state observer, y=θ o +v denotes the measurement output, z 1 denotes the estimate of the system output, z 2 denotes the estimate of the rate of change of the system output, z 3 denotes the estimate of the divide-by-lag portion F 0 in the extended state, For the extended state observer gain vector, wherein ω o is the observer bandwidth, the observation performance and the measurement noise are considered in a compromise, and the range of the observer bandwidth ωo should satisfy 10-500.
Designing a phase optimization law for the expansion state estimation value z 3:
Taking z EPO＝[z1,z2,z3PO]T as the output vector of the phase optimized extended state observer.
Fourthly, designing a strong anti-interference controller according to the output of the interference observer and the output of the extended state observer, and determining the bandwidths of the observer and the controller through a bandwidth parameterization method:
designing a strong disturbance rejection control law:
where K u is the controller gain, The first and second set-up leads are indicated respectively.
The controller gain is configured according to a bandwidth parameterization method to obtain:
Wherein omega c is the expected controller bandwidth, and the value range of omega c is 2-100.
As shown in fig. 2, the output responses of the two different methods are compared at the step angle position setting. To achieve a fair comparison, the control parameters are adjusted so that the output responses have the same rise time. However, the comparative approach suffers from significant overshoot and steady state errors; the strong disturbance rejection based on phase optimization is free from overshoot and can accurately follow the set value.
As shown in fig. 3, the phase-optimized strong immunity output angular position is hardly affected when external torque disturbance occurs. However, the compared method has obvious jump and insufficient anti-interference capability.
As shown in fig. 4, when an external torque disturbance occurs, the control torque changes are compared. The strong disturbance rejection control moment based on phase optimization can be changed rapidly to counteract the influence of disturbance on angular position output by the estimation of disturbance by the disturbance observer and the extended state observer and the compensation of a control law. However, the compared method controls the lag of the force distance to the interference response, and the fast switching mode can only inhibit the interference to a certain extent, so that the interference cannot be effectively counteracted. In addition, the control quantity of the method is smooth, and the method is friendly to an executing mechanism.
From a combination of fig. 2-4, it can be seen that the phase optimization-based strong immunity control proposed by the present invention has good set following and disturbance compensation capabilities.
What is not described in detail in the present specification belongs to the prior art known to those skilled in the art.
Claims (1)
1. The harmonic reducer output moment strong disturbance rejection control method based on phase optimization is characterized by comprising the following steps of:
firstly, establishing a harmonic reducer dynamics model of multi-source interference including friction, transmission error and rigidity nonlinearity;
secondly, designing an interference observer to estimate hysteresis moment according to the dynamics model of the harmonic reducer in the first step;
Thirdly, the error parameter uncertainty, unmodeled dynamics and external interference of the dynamics model of the harmonic reducer in the first step are estimated by designing a phase optimization extended state observer;
Fourthly, constructing a strong disturbance rejection controller based on phase optimization according to the outputs of the disturbance observer in the second step and the phase optimization extended state observer in the third step, and realizing expected control performance through pole allocation of the controller bandwidth and the observer bandwidth;
The first step is specifically implemented as follows:
Aiming at inherent stress contact friction loss and hysteresis nonlinearity generated by insufficient torsional rigidity of a flexible member in a harmonic gear transmission mechanism, and simultaneously considering a coupling relation between transmission errors and rigidity nonlinearity, a dynamic model of the harmonic speed reducer comprising friction, transmission errors and rigidity nonlinearity is established as follows:
，
Wherein J i and J o respectively represent the rotational inertia of the input end and the output end of the harmonic reducer; b h represents the damping coefficient inside the harmonic reducer; θ i and θ o represent the input end and output end rotation angles, respectively; f (·) represents the non-linearity of the stiffness between the input and output of the harmonic reducer, b 2 represents the transmission error doubling factor, N represents the harmonic reducer transmission ratio, f Indicating the loss of friction and, m The input end torque of the harmonic reducer is represented, q represents hysteresis, alpha and A are hysteresis model parameters, and d represents external random interference;
Wherein the stiffness nonlinearity is modeled as an odd function symmetric to the origin:
，
,, Coefficients that are nonlinear functions f (·) of stiffness;
For non-linear friction present in harmonic gear drives f It is divided into static and dynamic two parts:
，
Wherein F represents a static average friction term, p The dynamic friction term is expressed in relation to the position, wherein the static average tribodynamic behaviour is described by the Lund-Grenobel (LuGre) model:
，
where z represents the average displacement of the bristles during the relative movement of the contact surfaces, σ 0 represents the stiffness of the friction characteristics, σ 1 and σ 2 represent respectively AndThe corresponding damping coefficient, F s, represents static friction, F c represents coulomb friction, v s represents Stribeck speed, g (·) is the friction internal function; due to angular velocity of input endThe static average friction model parameters are obtained through priori knowledge through sensor measurement;
Dynamic friction is position dependent, described as:
，
Where a and b are friction model parameters, N f (θi) represent a nonlinear function related to input position, approximated by a finite number of fourier functions, Is a fourier coefficient;
The second step is specifically implemented as follows:
taking the system state of a harmonic reducer The dynamics model of the harmonic reducer is rewritten as:
，
in the formula, u= m Representing control input, y=θ o +v representing measurement output, v representing measurement noise;
for hysteresis due to insufficient torsional stiffness of the flexible member due to friction caused by stress contact, the following disturbance observer is constructed:
，
In the middle of WhereinThe estimation of the hysteresis interference moment is shown, w is the internal virtual state of the interference observer, and K is the gain of the interference observer;
the third step is specifically implemented as follows:
Through f 0 for equivalent replacement, the method obtains Wherein f is a lumped disturbance different from the double integrator in series, which is defined as an expanded state of the harmonic reducer and split into two parts according to an estimated output of the disturbance observerB 0 is the control gain, takenThe extended state observer taking into account the interference observer output is designed to:
，
in the method, in the process of the invention, Representing the output vector of the extended state observer,Representing the measured output, z 1 representing an estimate of the system output, z 2 representing an estimate of the rate of change of the system output, z 3 representing an estimate of the divide-by-lag portion F 0 in the expanded state,For the gain vector of the extended state observer, wherein omega o is the bandwidth of the observer, the observation performance and the measurement noise are considered in a compromise, and the value range of the bandwidth omega o of the observer is 10-500;
Designing a phase optimization law for the expansion state estimation value z 3:
，
Taking out Optimizing an output vector of the extended state observer for the phase;
The fourth step is specifically implemented as follows:
using the output of the second-step disturbance observer And output of the third step extended state observerDesigning a strong disturbance rejection control law:
，
where K u is the controller gain, Respectively representing the setting, the first-order derivative and the second-order derivative of the setting;
the controller gain is configured according to a bandwidth parameterization method to obtain:
，
Wherein omega c is the expected controller bandwidth, and the value range should satisfy 2-100.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111620691.1A CN114321319B (en) | 2021-12-27 | Harmonic reducer output moment strong disturbance rejection control method based on phase optimization |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111620691.1A CN114321319B (en) | 2021-12-27 | Harmonic reducer output moment strong disturbance rejection control method based on phase optimization |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114321319A CN114321319A (en) | 2022-04-12 |
| CN114321319B true CN114321319B (en) | 2024-07-16 |
Family
ID=
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107168071A (en) * | 2017-07-17 | 2017-09-15 | 北京航空航天大学 | A kind of nonlinear system Auto-disturbance-rejection Control based on interference observer |
| CN107992110A (en) * | 2018-01-18 | 2018-05-04 | 北京航空航天大学 | A kind of magnetic levitation control moment gyroscope frame angular speed servo-drive system based on harmonic speed reducer |
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107168071A (en) * | 2017-07-17 | 2017-09-15 | 北京航空航天大学 | A kind of nonlinear system Auto-disturbance-rejection Control based on interference observer |
| CN107992110A (en) * | 2018-01-18 | 2018-05-04 | 北京航空航天大学 | A kind of magnetic levitation control moment gyroscope frame angular speed servo-drive system based on harmonic speed reducer |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109927032B (en) | Mechanical arm track tracking control method based on high-order sliding-mode observer | |
| CN111152225B (en) | Uncertain mechanical arm fixed time trajectory tracking control method with input saturation | |
| Yao et al. | Adaptive robust motion control of single-rod hydraulic actuators: theory and experiments | |
| CN112817231B (en) | High-precision tracking control method for mechanical arm with high robustness | |
| Ro et al. | Robust friction compensation for submicrometer positioning and tracking for a ball-screw-driven slide system | |
| CN110071676B (en) | Vibration suppression method and device for flexible robot joint servo system | |
| JPH05216504A (en) | Adaptive sliding mode control system for control object including spring system | |
| CN108536185B (en) | Double-framework magnetic suspension CMG framework system parameter optimization method based on reduced-order cascade extended state observer | |
| CN110649845B (en) | Photoelectric turntable position tracking control method based on robust generalized predictive control | |
| CN111258220B (en) | Flexible mechanical arm cascade control method and system based on disturbance observer | |
| CN114536334A (en) | High-order sliding mode anti-interference control method for flexible mechanical arm system | |
| CN113241973A (en) | Trajectory tracking control method for linear motor by iterative learning control of S-shaped filter | |
| CN112643670A (en) | Flexible joint control method based on sliding-mode observer | |
| Zhou et al. | Trajectory tracking control for electro-optical tracking system using ESO based fractional-order sliding mode control | |
| Wang et al. | Design of full-order state observer for two-mass joint servo system based on the fixed gain filter | |
| US5532565A (en) | Controller | |
| Lim et al. | Torsional displacement compensation in position control for machining centers | |
| CN114321319B (en) | Harmonic reducer output moment strong disturbance rejection control method based on phase optimization | |
| CN114321319A (en) | Phase optimization-based strong anti-interference control method for output torque of harmonic reducer | |
| CN111673734B (en) | Vibration suppression control method for robot joint servo system | |
| CN114167725A (en) | Cooperative robot trajectory tracking control method and system | |
| Receanu | Modeling and simulation of the nonlinear computed torque control in simulink/MATLAB for an industrial robot | |
| JP2999330B2 (en) | Control method using sliding mode control system | |
| Chang et al. | Adaptive tracking control design of constrained robot systems | |
| CN111796509A (en) | Gyro self-stabilization control method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant |