CN113467247B - Design method of federal expanded state observer - Google Patents
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Abstract
The invention provides a federal extended state observer design method, which comprises the steps of constructing federal ESOs based on measured values and system state orders, constructing n sub-ESOs for n different observed values corresponding to each order of system state, adopting a main ESO to complete global fusion of local state estimation results of each sub-ESO, returning the global system state to each sub-ESO after the main ESO completes fusion, and carrying out secondary correction on local state estimation. According to the invention, the traditional extended state observation theory is used as a core to construct the sub ESO, meanwhile, the federal filtering framework is introduced, and the multi-source sensor data is introduced to correct the same system state while the observer gain is rapidly and conveniently determined based on the bandwidth setting method, so that the estimation precision of the ESO on the high-order system state and disturbance is improved.
Description
Technical Field
The invention belongs to the technical field of robot motion control, and particularly relates to a federal expanded state observer design method.
Background
Extended State Observers (ESO) are an effective means of estimating unknown term disturbances in a system that have low model dependence and are easy to program. The setting of ESO parameters can be calculated quickly using a 3w method based on observer bandwidth, which is widely verified in engineering applications. The traditional ESO design method is only suitable for observing single system state estimation, an observer can only correct a result by adopting a lowest-order system state, and the differential correction of an observation error only is used for correcting a high-order state estimation, so that larger errors are brought, the traditional bandwidth setting method cannot be suitable for the situation of a plurality of observables, a plurality of sensors are often used for measuring the same state in a plurality of actual robot control systems, and therefore, a method for designing the ESO by using a plurality of sensor data as measured values while the 3w bandwidth setting convenience is reserved is urgently needed.
Disclosure of Invention
First, the technical problem to be solved
The invention aims to provide a federal expanded state observer design method to solve the technical problem of how to improve the high-order system state and disturbance estimation precision of ESO on various sensor data.
(II) technical scheme
In order to solve the technical problems, the invention provides a federal expanded state observer design method, which comprises the following steps:
s1, constructing federal ESO based on measured values and system state orders
Constructing n sub-observers ESO-i for n different observation values with corresponding system states of each order, performing global fusion on local state estimation of each sub-observer by using a global state estimation feedback structure in a federal filtering frame by using a main observer M-ESO, obtaining optimal global state estimation by fusing local state estimation results of the sub-observers, and returning the global state to each sub-observer to perform secondary correction on the local state estimation;
s2, initializing states of each sub-observer and the main observer, and calculating state correction coefficients of each sub-observer based on a bandwidth setting method
Setting the bandwidths of the second-order sub-observer ESO-I and the third-order sub-observer ESO-II, and calculating the state correction coefficient of the corresponding sub-observer by adopting a bandwidth setting method according to the order of the sub-observer, wherein the state correction coefficient is shown in a formula (1):
wherein L is 1,I And L 2,I First-order and second-order state correction coefficients, w, of ESO-I, respectively 1 Is ESO-I bandwidth; l (L) 1,II 、L 2,II And L 3,II First, second and third order state correction coefficients, w, respectively, of ESO-II 2 Is ESO-II bandwidth;
s3, constructing a measurement error value by adopting a corresponding state measurement value, correcting the state estimation of the sub-observer, and correcting the state estimation of the ESO-I by using a second-order state corresponding measurement value of the original system, wherein the method is as shown in a formula (2):
wherein,,
for ESO-I error,/-, for>
For the corresponding measurement value of the second order state of the original system, +.>
And->
First and second order state estimates, b, of ESO-I, respectively I For ESO-I model gain, u I For ESO-I control input, +.>
And->
Differentiation of the first and second order state estimates of ESO-I, respectively;
the state estimation for ESO-II is corrected using the angle measurement as shown in equation (3):
wherein e θ For ESO-II error, θ is the corresponding measured value of the first-order state of the original system,
respectively estimating the first, second and third states of ESO-II, b II For ESO-II model gain, u II For the ESO-II control input,
differentiation of the first, second and third order state estimates of ESO-II, respectively;
s4, defining sub-observer information distribution factor beta i > 0, i=1, 2,..
Information distribution factor beta during global information fusion i Based on sensor measurement variance sigma i Determination of
S5, calculating sub-observer information allocation weights by using sensor measurement variances
Normalization processing is adopted when constructing information allocation weights, as shown in a formula (4):
wherein beta is i (k) Weight, beta, for ESO-I information allocation II (k) Assigning weights to the ESO-II information;
s6, calculating global state estimation based on information distribution weight of online calculation
The main observer global state estimation is a weighted result of the sub-observer local state estimation, as shown in formula (5):
wherein,,
and->
Global estimates of the first, second and third order states of the M-ESO, respectively;
s7, feeding back global state estimation of the main observer to the sub observer based on the federal filtering frame, and carrying out secondary correction on local state estimation of the sub observer
The local state estimate of ESO-I is secondarily modified as shown in equation (6):
wherein,,
and->
The correction value is estimated for the first-order and second-order states of ESO-I respectively;
the local state estimate for ESO-II is modified twice as shown in equation (7):
wherein,,
and->
Correction values are estimated for the first, second and third order states of ESO-II, respectively.
Further, in step S3, the first-order state corresponding measurement value of the original system is an angle measurement value, and the second-order state corresponding measurement value of the original system is an angular velocity measurement value.
Further, in step S4, the sensor measures the variance σ i Medium angular velocity measurement variance sigma I And attitude angle measurement variance sigma II Obtained by online statistics.
(III) technical effects
The invention provides a federal extended state observer design method, which comprises the steps of constructing federal ESOs based on measured values and system state orders, constructing n sub-ESOs for n different observed values corresponding to each order of system state, adopting a main ESO to complete global fusion of local state estimation results of each sub-ESO, returning the global system state to each sub-ESO after the main ESO completes fusion, and carrying out secondary correction on local state estimation. According to the invention, the traditional extended state observation theory is used as a core to construct the sub ESO, meanwhile, the federal filtering framework is introduced, and the multi-source sensor data is introduced to correct the same system state while the observer gain is rapidly and conveniently determined based on the bandwidth setting method, so that the estimation precision of the ESO on the high-order system state and disturbance is improved.
Drawings
FIG. 1 is a schematic diagram of a federal extended state observer according to the present invention.
Detailed Description
To make the objects, contents and advantages of the present invention more apparent, the following detailed description of the present invention will be given with reference to the accompanying drawings and examples.
Taking the application of robot gesture control as an example, the embodiment provides a federal expanded state observer design method, the method adopts angular velocity and gesture angle as measured values, a third-order control system is constructed, and the disturbance of the angle, the angular velocity and the angular acceleration is observed, and the method specifically comprises the following steps:
s1, constructing federal ESO based on measured values and system state orders
The main observer adopts a global state estimation feedback structure in the federal filtering framework to carry out global fusion on local state estimation of each sub-observer, and obtains the optimal global state estimation by fusing local state estimation results of the sub-observers, so that the estimation of the system state with the same order by using different sensor data is realized, and the global state is returned to each sub-observer to carry out secondary correction on the local state estimation.
For the case of n child observers, the federal ESO structure is shown in FIG. 1. In order to integrate the angular velocity measurement and the attitude fusion result and estimate the observer system state, and simultaneously preserve the convenience of the traditional bandwidth setting method, in the embodiment, the angular velocity is taken as a measured value to construct a second-order sub-observer ESO-I, the attitude angle is taken as a measured value to construct a third-order sub-observer ESO-II, and a third-order main observer M-ESO is constructed.
S2, initializing states of each sub-observer and the main observer, and calculating state correction coefficients of each sub-observer based on a bandwidth setting method
Setting the bandwidth of the sub-observer, and calculating a corresponding sub-observer state correction coefficient by adopting a bandwidth setting method according to the order of the sub-observer, wherein the correction coefficient is shown in a formula (1):
wherein L is 1,I And L 2,I First-order and second-order state correction coefficients, w, of ESO-I, respectively 1 Is ESO-I bandwidth; l (L) 1,II 、L 2,II And L 3,II First, second and third order state correction coefficients, w, respectively, of ESO-II 2 Is ESO-II bandwidth.
S3, constructing a measurement error value by adopting a corresponding state measurement value, correcting the state estimation of the sub-observer, and correcting the state estimation of the ESO-I by using an angular velocity measurement value, wherein the method is as shown in a formula (2):
wherein,,
for ESO-I error,/-, for>
For angular velocity measurement, +.>
And->
First and second order state estimates, b, of ESO-I, respectively I For ESO-I model gain, u I For ESO-I control input, +.>
And->
The differentiation of the first and second order state estimates of ESO-I, respectively.
The state estimation for ESO-II is corrected using the angle measurement as shown in equation (3):
wherein e θ For ESO-II error, θ is the angle measurement,
respectively estimating the first, second and third states of ESO-II, b II For ESO-II model gain, u II For ESO-II control input, +.>
The differentiation of the first, second and third order state estimates of ESO-II, respectively.
S4, defining sub-observer information distribution factor beta i > 0, i=1, 2,..
Information distribution factor beta during global information fusion i Based on sensor measurement variance sigma i Determination of
In the present embodiment, the angular velocity measurement variance σ I And attitude angle measurement variance sigma II Obtained by online statistics.
S5, calculating sub-observer information allocation weights by using sensor measurement variances
Since the measurement equation units of the sensors in the fusion are not consistent, normalization processing is adopted when constructing information distribution weights, as shown in a formula (4):
wherein beta is I (k) Weight, beta, for ESO-I information allocation II (k) The ESO-II information is assigned a weight.
S6, calculating global state estimation based on information distribution weight of online calculation
The main observer global state estimation is a weighted result of the sub-observer local state estimation, as shown in formula (5):
wherein,,
and->
Global estimates of the first, second and third order states of the M-ESO, respectively.
S7, feeding back global state estimation of the main observer to the sub observer based on the federal filtering frame, and carrying out secondary correction on local state estimation of the sub observer
The local state estimate of ESO-I is secondarily modified as shown in equation (6):
wherein,,
and->
Correction values are estimated for the first and second order states of ESO-I, respectively.
The local state estimate for ESO-II is modified twice as shown in equation (7):
wherein,,
and->
Correction values are estimated for the first, second and third order states of ESO-II, respectively.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.
Claims (3)
1. A method of federal expanded state observer design, the method comprising the steps of:
s1, constructing federal ESO based on measured values and system state orders
Constructing n sub-observers ESO-i for n different observation values with corresponding system states of each order, performing global fusion on local state estimation of each sub-observer by using a global state estimation feedback structure in a federal filtering frame by using a main observer M-ESO, obtaining optimal global state estimation by fusing local state estimation results of the sub-observers, and returning the global state to each sub-observer to perform secondary correction on the local state estimation;
s2, initializing states of each sub-observer and the main observer, and calculating state correction coefficients of each sub-observer based on a bandwidth setting method
Setting the bandwidths of the second-order sub-observer ESO-I and the third-order sub-observer ESO-II, and calculating the state correction coefficient of the corresponding sub-observer by adopting a bandwidth setting method according to the order of the sub-observer, wherein the state correction coefficient is shown in a formula (1):
wherein L is 1,I And L 2,I First-order and second-order state correction coefficients, w, of ESO-I, respectively 1 Is ESO-I bandwidth; l (L) 1,II 、L 2,II And L 3,II First, second and third order state correction coefficients, w, respectively, of ESO-II 2 Is ESO-II bandwidth;
s3, constructing a measurement error value by adopting the corresponding state measurement value, and correcting the state estimation of the sub observer
And (3) correcting the ESO-I by using the corresponding measured value of the second-order state of the original system, wherein the ESO-I is subjected to state estimation as shown in a formula (2):
wherein,,
for ESO-I error,/-, for>
For the corresponding measurement value of the second order state of the original system, +.>
And->
First and second order state estimates, b, of ESO-I, respectively I For ESO-I model gain, u I For ESO-I control input, +.>
And->
Differentiation of the first and second order state estimates of ESO-I, respectively;
the state estimation for ESO-II is corrected using the angle measurement as shown in equation (3):
wherein e θ For ESO-II error, θ is the corresponding measured value of the first-order state of the original system,
respectively estimating the first, second and third states of ESO-II, b II For ESO-II model gain, u II For the ESO-II control input,
differentiation of the first, second and third order state estimates of ESO-II, respectively;
s4, defining sub-observer information divisionLigand factor beta i > 0, i=1, 2,..
Information distribution factor beta during global information fusion i Based on sensor measurement variance sigma i Determination of
S5, calculating sub-observer information allocation weights by using sensor measurement variances
Normalization processing is adopted when constructing information allocation weights, as shown in a formula (4):
wherein beta is i (k) Weight, beta, for ESO-I information allocation II (k) Assigning weights to the ESO-II information;
s6, calculating global state estimation based on information distribution weight of online calculation
The main observer global state estimation is a weighted result of the sub-observer local state estimation, as shown in formula (5):
wherein,,
and->
Global estimates of the first, second and third order states of the M-ESO, respectively;
s7, feeding back global state estimation of the main observer to the sub observer based on the federal filtering frame, and carrying out secondary correction on local state estimation of the sub observer
The local state estimate of ESO-I is secondarily modified as shown in equation (6):
wherein,,
and->
The correction value is estimated for the first-order and second-order states of ESO-I respectively;
the local state estimate for ESO-II is modified twice as shown in equation (7):
wherein,,
and->
Correction values are estimated for the first, second and third order states of ESO-II, respectively.
2. The method of claim 1, wherein in step S3, the first-order state corresponding measurement value of the original system is an angle measurement value, and the second-order state corresponding measurement value of the original system is an angular velocity measurement value.
3. The federal expanded state observer design method according to claim 1, wherein in step S4, the sensor measures the variance σ i Medium angular velocity measurement variance sigma I And attitude angle measurement variance sigma II Obtained by online statistics.
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