CN103809439A - Hierarchical identification method applicable to control parameters of teleoperation system - Google Patents

Hierarchical identification method applicable to control parameters of teleoperation system Download PDF

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CN103809439A
CN103809439A CN201410012676.2A CN201410012676A CN103809439A CN 103809439 A CN103809439 A CN 103809439A CN 201410012676 A CN201410012676 A CN 201410012676A CN 103809439 A CN103809439 A CN 103809439A
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黄攀峰
鹿振宇
刘正雄
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Northwestern Polytechnical University
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Abstract

The invention relates to a hierarchical identification method applicable to the control parameters of a teleoperation system. The method comprises the steps of simplifying a teleoperation process in which input and output signals are sampled differently into a dual-rate sampling system, building an auxiliary model based on a minimal sampling period by using a re-sampling method, and estimating the middle state value of the re-sampling system; an output sampling period is greater than a re-sampling period, and the middle state value can not be directly corrected by the output estimated differential value of the system, so that the state estimation value in a Kalman forecasting process can be modified by adopting a state changing difference value, i.e. a differential method. According to the method, the parameters of the dual-rate teleoperation system can be identified under the two conditions of known and unknown state values, so that the feasibility and effectiveness of the method can be verified by a simulation result.

Description

A kind of be applicable to remote control system control parameter pass rank discrimination method
Technical field
The invention belongs to system control parameters identification field, be specifically related to a kind of be applicable to remote control system control parameter pass rank discrimination method.
Background technology
Two rate systems are general designations of the system different with output sampling frequency rate to input sample frequency.Two rate systems are not only widely used in Chemical Engineering Process Control field, also have great importance in spationautics application, for example, in the distant operating process in space, input control signal by main side is to controlling from the space manipulator of end, input control signal is position and the torque signals of main side hand controller, output feedback signal comprises the position at the distant shoulder joint place of operating machines, speed and torque signals etc., generally, main side control signal frequency ratio receives the frequency of feedback signal and wants high, this one side is relevant with the ability of the processing signals of spaceborne computer, also relevant with sample frequency and the information capacity of sensor on the other hand, can be by a pair of rate that the is reduced to system of this distant operating process according to input control signal and output feedback signal, thereby carry out identification by the control parameter to this system and draw the control output relation of distant operating process.
The discrimination method that is directed at present many rates system and two rate systems mainly contains: strong fraction transfer function model discrimination method, frequency-domain model discrimination method, wavelet model discrimination method, Stute space model identification method etc.Wherein, state-space method is an important method in two rate identifications, it is mainly can not be directly used in identification for two rate data in discrete state spatial model, constant single rate system model when two rate sampling systems being converted into by " lift technique ", and with reference to MOESP, the subspace state space system identification such as N4SID and CAV carries out identification to systematic parameter, although LPTV is converted into LTI system by lift technique, the direct application of conveniently recognized method, but also can cause the undesirable of the increase of number of parameters to be identified and calculated amount and identification precision, in addition, framework identified parameters cycle length of " lifting " once, can cause like this convergent cycle of identified parameters long, speed of convergence is slower.Therefore, needing a new method to solve utilizes lift technique to carry out to two rate systems the problem that parameter identification faces.
Summary of the invention
The technical matters solving
For fear of the deficiencies in the prior art part, the present invention propose a kind of be applicable to remote control system control parameter pass rank discrimination method.
Technical scheme
What be applicable to remote control system control parameter passs a rank discrimination method, it is characterized in that step is as follows:
Step 1: gather distant operation input control signal and output feedback signal, described input control signal is position and the torque signals of main side hand controller; Described output feedback signal comprises position, speed and the torque signals at the distant shoulder joint place of operating machines;
Distant operating process is reduced to a pair of rate system model, and its state-space model is:
x ( K + 1 ) = Ax ( K ) + Bu ( K ) + w ( K ) y ( K ) = Cx ( K ) + Du ( K ) + v ( K ) ;
Wherein, A, B, C, D are systematic parameter, and K represents the K time sampling of system, and x (K) is state value, and u (K) is input signal, and y (K) is output signal;
The control inputs sampling period that makes system is T 1with output sampling period be T 2, h is T 1and T 2highest common factor, T 1and T 2meet: T 1=ph, T 2=qh and p and q two numbers are relatively prime, and w (K) and v (K) represent respectively process noise and measurement noise, and the system model of system is: x ( kh + h ) = ax ( kh ) + bu ( kh ) + r ( kh ) y ( kh ) = cx ( kh ) + du ( kh ) + v ( kh ) , Wherein, a, b, c, d are submodel parameter, the k time sampling that k is submodel, and r (kh) and v (kh) are respectively submodel process noise and measure noise;
Parameters relationship between two models is: a = A 1 p , b = B / Σ i = 0 p - 1 A i p , c = C , d = D , r ( kh ) = w ( kh ) / Σ i = 0 p A i p ;
Step 2: make its expression formula of residual values o (kh) be:
o ( kh ) = ( y ( kh ) - c ^ ( kh ) x ( kh ) - d ^ ( kh ) u ( kh ) ) / Σ i = 0 q a ^ i
Its update cycle is identical with the cycle qh of output variable y (kh), varivance matrix and error covariance matrix expression are M (kh)=x (kh) x (kh-h), P (kh)=x (kh) x (kh), wherein x (kh)=x (kh)-x (kh), x (kh) is the estimated value of x (kh), order
Figure BDA0000455296290000031
Figure BDA0000455296290000032
utilization pushes through recurrence equation:
Figure BDA0000455296290000033
Wherein, a (kh),
Figure BDA0000455296290000034
d (kh) is respectively the estimated value of a (kh), b (kh), a (kh), d (kh), and the more new formula of Kalman filtering gain matrix L (kh), L1 (kh), P (kh) and M (kh) is:
L ( kh ) = [ a ( kh ) ( M ( kh ) c ^ T ( kh - h ) - P ( kh ) c ^ T ( kh ) ) + L 1 ( kh ) Ro ] [ 2 Ro + c ^ ( kh ) P ( kh ) c ^ T ( kh ) - 2 c ^ ( kh ) M ( kh ) c ^ T ( kh - h ) + c ^ ( kh - h ) P ( kh - h ) c ^ T ( kh - h ) ] - 1
L 1 ( kh ) = K 1 c ^ ( kh )
P ( kh + h ) = a ( kh ) P ( kh ) a T ( kh ) + Rr + L ( kh ) [ a ( kh ) ( P ( kh ) c ^ T ( kh ) - M ( kh ) c ^ T ( kh - h ) ) + L 1 ( kh ) Ro ] + L 1 ( kh ) ( L 1 ( kh ) + 2 I ) T Ro
M ( kh + h ) = a ( kh ) P ( kh ) + Rr + L ( kh ) ( P ( kh ) c ^ T ( kh ) - M ( kh ) c ^ T ( kh - h ) )
Wherein, cov (o (kh), o (kh) t)=Ro δ ij, cov (r (kh), r (kh) t)=Rr δ ij, wherein, cov () represents covariance computing, δ ijfor kronecker-δ function, K1 is constant, and the state value that further obtains submodel is estimated:
x ( kh + h ) = a ^ x ( kh ) + b ^ u ( kh ) + L ( kh ) [ y ( kh ) - y ( kh - h ) - ( c ^ ( kh ) - c ^ ( kh - h ) ) x ( kh ) - ( d ^ ( kh ) - d ^ ( kh - h ) ) u ( kh ) ] + L 1 ( kh ) o ( kh )
Obtain the input and output state moment state estimation value of original system according to the parameter corresponding relation of two rate remote control systems and submodel: x (KT 1)=x (Kph), x (KT 2)=x (Kqh);
Step 3: the state value doping according to submodel is passed rank parameter identification to two rate remote control systems, and expression is as follows:
Figure BDA00004552962900000310
Figure BDA00004552962900000311
Figure BDA00004552962900000312
Figure BDA00004552962900000313
Figure BDA00004552962900000314
Figure BDA0000455296290000041
Wherein, i, j represents respectively the sampling instant of input and output signal,
θ x(iph)=[A(iph),B(iph)] T
θ i(jqh)=[C(jqh),D(jqh)] T
Figure BDA0000455296290000042
X(iph+ph)=x(iph+ph),
A (iph), B (iph), C (jqh), D (jqh) represent respectively the estimated value of A (iph), B (iph), C (jqh), D (jqh);
Obtain again the parameter of next step submodel system according to the result of passing rank identification:
a = A 1 p , b ^ = B / Σ i = 0 p - 1 A i p , c ^ = C , d = D ;
Step 4: circulation step 2 and step 3 are passed rank parameter identification process until complete all two rate remote control systems.
In described step 2, Ro and Rr estimate by following formula:
Rr = 1 L Σ i = 1 L r ( kh + ih ) r T ( kh + ih )
Ro = 1 L Σ i = 1 L o ( kh + ih ) o T ( kh + ih )
Wherein, r ( kh + ih ) = x ( kh + ( i + 1 ) h ) - a ( kh + ih ) x ( kh + ih ) - b ^ ( kh + ih ) u ( kh + ih ) , L represents the data length of data r (kh) or o (kh).
Beneficial effect
The present invention proposes a kind of be applicable to remote control system control parameter pass rank discrimination method, the input/output signal different distant operating process of sampling is reduced to a pair of rate sampling system, utilize the method for resampling to set up a cycle submodel based on minimum sampling, and estimate the intermediateness value of resampling system with this, because the output sampling period is greater than the resampling cycle, the output estimation difference of system can not directly be revised intermediateness value, so having adopted state variation difference is herein that the method for difference is revised the state estimation value in Kalman Prediction process, the present invention can carry out identification to the two rate remote control system parameters in the known and unknown two kinds of situations of state value, simulation results show feasibility and the validity of the method.
The invention has the beneficial effects as follows: distant operating process is reduced to two rate sampling system model, promoting variable for traditional lift technique exists identified parameters more in the method for identification again, the problems such as the large and identification precision of calculated amount is undesirable, the present invention is estimation procedure state value effectively, and reduce calculated amount and computing time, than former method, calculation procedure is simple, is convenient to apply in engineering.There is good accuracy, robustness and validity through simulating, verifying this method.
Accompanying drawing explanation
What Fig. 1 was applicable to remote control system control parameter passs rank discrimination method
The process flow diagram of Fig. 2 submodel state-updating
Fig. 3 Parameter identification process
Fig. 4 Parameter identification result
embodiment
Now in conjunction with the embodiments, the invention will be further described for accompanying drawing:
As shown in Figure 1, it comprises following four steps to the process flow diagram of the embodiment of the present invention:
Step 1: distant operation input control signal and output feedback signal are gathered, input control signal is position and the torque signals of main side hand controller, output feedback signal comprises position, speed and the torque signals etc. at the distant shoulder joint place of operating machines, ignore the impact of system time delay and consider that the sample frequency of output feedback signal is lower than the frequency of input control signal, after input/output signal is processed, distant operating process is reduced to a pair of rate system model, its state-space model is:
x ( K + 1 ) = Ax ( K ) + Bu ( K ) + w ( K ) y ( K ) = Cx ( K ) + Du ( K ) + v ( K ) - - - ( 1 )
Wherein, A, B, C, D are systematic parameter, and K is for representing the K time sampling, and x (K) is state value, and u (K) is input signal, and y (K) is output signal, and the control inputs sampling period that makes system is T 1with output sampling period be T 2, h is T 1and T 2highest common factor, T 1and T 2expression formula be T 1=ph, T 2=qh and p and q two numbers are relatively prime, w (K) and v (K) represent respectively process noise and measure noise, and it is all zero-mean white noise sequence stably, meet: E (w (i))=0, E (v (i))=0cov (w (i), w (j) t)=Rw δ ij, cov (v (i), v (j) t)=Rv δ ij, cov () represents covariance computing, δ ijfor kronecker-δ function.Set up the submodel that has same structure with former pair of rate discrete system:
x ( kh + h ) = ax ( kh ) + bu ( kh ) + r ( kh ) y ( kh ) = cx ( kh ) + du ( kh ) + v ( kh ) - - - ( 2 )
Wherein, a, b, c, d are submodel parameter, the k time sampling that k is submodel, and r (kh) and v (kh) are respectively submodel process noise and measure noise, output sampling period T 1be greater than input refresh cycle T 2, meet p < q, by system (1) and system (2) coefficient of correspondence under the framework cycle equate, can obtain submodel coefficient:
a = A 1 p , b = B / &Sigma; i = 0 p - 1 A i p , c = C , d = D , r ( kh ) = w ( kh ) / &Sigma; i = 0 p A i p .
Step 2, submodel state estimation.Its process flow diagram is as shown in Figure 2:
First, calculate the residual values of submodel, the update cycle of residual values o (kh) is identical with the cycle qh of output variable y (kh), and its expression formula is:
o ( kh ) = ( y ( kh ) - c ^ ( kh ) x ( kh ) - d ^ ( kh ) u ( kh ) ) / &Sigma; i = 0 q a ^ i - - - ( 3 )
Its update cycle is identical with the cycle qh of output variable y (kh), varivance matrix and error covariance matrix expression are M (kh)=x (kh) x (kh-h), P (kh)=x (kh) x (kh), wherein x (kh)=x (kh)-x (kh), x (kh) is the estimated value of x (kh), order
Figure BDA0000455296290000065
Figure BDA0000455296290000066
utilization pushes through recurrence equation:
Figure BDA0000455296290000067
Wherein, a (kh),
Figure BDA0000455296290000068
d (kh) is respectively the estimated value of a (kh), b (kh), a (kh), d (kh), and the more new formula of Kalman filtering gain matrix L (kh), L1 (kh), P (kh) and M (kh) is:
L ( kh ) = [ a ( kh ) ( M ( kh ) c ^ T ( kh - h ) - P ( kh ) c ^ T ( kh ) ) + L 1 ( kh ) Ro ] [ 2 Ro + c ^ ( kh ) P ( kh ) c ^ T ( kh ) - 2 c ^ ( kh ) M ( kh ) c ^ T ( kh - h ) + c ^ ( kh - h ) P ( kh - h ) c ^ T ( kh - h ) ] - 1 - - - ( 5 )
L 1 ( kh ) = K 1 c ^ ( kh ) - - - ( 6 )
P ( kh + h ) = a ( kh ) P ( kh ) a T ( kh ) + Rr + L ( kh ) [ a ( kh ) ( P ( kh ) c ^ T ( kh ) - M ( kh ) c ^ T ( kh - h ) ) + L 1 ( kh ) Ro ] + L 1 ( kh ) ( L 1 ( kh ) + 2 I ) T Ro - - - ( 7 )
M ( kh + h ) = a ( kh ) P ( kh ) + Rr + L ( kh ) ( P ( kh ) c ^ T ( kh ) - M ( kh ) c ^ T ( kh - h ) ) - - - ( 8 )
Wherein, cov (o (kh), o (kh) t)=Ro δ ij, cov (r (kh), r (kh) t)=Rr δ ij, wherein δ i jfor kronecker-δ function, K1 is constant, and the state value that further obtains submodel is estimated:
x ( kh + h ) = a ^ x ( kh ) + b ^ u ( kh ) + L ( kh ) [ y ( kh ) - y ( kh - h ) - ( c ^ ( kh ) - c ^ ( kh - h ) ) x ( kh ) - ( d ^ ( kh ) - d ^ ( kh - h ) ) u ( kh ) ] + L 1 ( kh ) o ( kh ) - - - ( 9 )
The last parameter corresponding relation according to two rate systems and submodel obtains the input and output state moment state estimation value of former pair of rate system: x (KT 1)=x (Kph), x (KT 2)=x (Kqh).
Step 3: two rate remote control system parameters pass rank identification.Adopt the method for passing rank identification to carry out identification for two rate remote control system parameters, detailed process is as follows:
Figure BDA0000455296290000076
Figure BDA0000455296290000077
Figure BDA0000455296290000078
Figure BDA0000455296290000079
Figure BDA00004552962900000710
Figure BDA00004552962900000711
Wherein, i, j represents respectively the sampling instant of input and output signal,
θ x(iph)=[A(iph),B(iph)] T
θ i(jqh)=[C(jqh),D(jqh)] T
Figure BDA00004552962900000712
Figure BDA00004552962900000713
X(iph+ph)=x(iph+ph),
A (iph), B (iph), C (jqh), D (jqh) represent respectively the estimated value of A (iph), B (iph), C (jqh), D (jqh).And then obtain the parameter of next step submodel system according to the result of passing rank identification:
a = A 1 p , b ^ = B / &Sigma; i = 0 p - 1 A i p , c ^ = C , d = D
Step 4: the formula (3) in circulation step 2 and step 3 to formula (17) until complete two rate remote control system parameters pass rank identification process.
In step 2, Ro and Rr estimate by following formula:
Rr = 1 L &Sigma; i = 1 L r ( kh + ih ) r T ( kh + ih ) - - - ( 16 )
Ro = 1 L &Sigma; i = 1 L o ( kh + ih ) o T ( kh + ih ) - - - ( 17 )
Wherein, r ( kh + ih ) = x ( kh + ( i + 1 ) h ) - a ( kh + ih ) x ( kh + ih ) - b ^ ( kh + ih ) u ( kh + ih ) , L represents the data length of data r (kh) or o (kh).
For method of the present invention, carry out simulating, verifying, the state space equation of the two rate remote control systems of order is as follows:
x ( k + 1 ) = 0.9 x ( k ) + 1.2 u ( k ) + w ( k ) y ( k ) = 1.1 x ( k ) - 0.5 u ( k ) + v ( k ) - - - ( 18 )
Wherein, input sample cycle T 1=3h, the output sampling period is T 2=4h, h=1s, framework period p qh=12h, input signal is quasi stationary sequence E[u (k)]=1.5, system noise and measurement noise are respectively Rw=0.05 2, Rv=0.05 2, system (18) submodel data length to be identified is 10000.The parameter of system is carried out to identification, and as shown in Figure 3, Figure 4, simulation result shows for identification process and result, and the present invention can effectively carry out identification to systematic parameter at state value under known and unknown situation, and speed of convergence is very fast, and calculated amount is little, and identification result is accurate.

Claims (2)

1. what be applicable to remote control system control parameter passs a rank discrimination method, it is characterized in that step is as follows:
Step 1: gather distant operation input control signal and output feedback signal, described input control signal is position and the torque signals of main side hand controller; Described output feedback signal comprises position, speed and the torque signals at the distant shoulder joint place of operating machines;
Distant operating process is reduced to a pair of rate system model, and its state-space model is:
Figure FDA0000455296280000011
Wherein, A, B, C, D are systematic parameter, and K represents the K time sampling of system, and x (K) is state value, and u (K) is input signal, and y (K) is output signal;
The control inputs sampling period that makes system is T 1with output sampling period be T 2, h is T 1and T 2highest common factor, T 1and T 2meet: T 1=ph, T 2=qh and p and q two numbers are relatively prime, and w (K) and v (K) represent respectively process noise and measurement noise, and the system model of system is:
Figure FDA0000455296280000012
wherein, a, b, c, d are submodel parameter, the k time sampling that k is submodel, and r (kh) and v (kh) are respectively submodel process noise and measure noise;
Parameters relationship between two models is:
Figure FDA0000455296280000013
Step 2: make its expression formula of residual values o (kh) be:
Figure FDA0000455296280000014
Its update cycle is identical with the cycle qh of output variable y (kh), varivance matrix and error covariance matrix expression are M (kh)=x (kh) x (kh-h), P (kh)=x (kh) x (kh), wherein x (kh)=x (kh)-x (kh), x (kh) is the estimated value of x (kh), order
Figure FDA0000455296280000015
Figure FDA0000455296280000016
utilization pushes through recurrence equation:
Figure FDA0000455296280000017
Wherein, a (kh), d (kh) is respectively the estimated value of a (kh), b (kh), a (kh), d (kh), and the more new formula of Kalman filtering gain matrix L (kh), L1 (kh), P (kh) and M (kh) is:
Figure FDA0000455296280000021
Figure FDA0000455296280000022
Figure FDA0000455296280000023
Figure FDA0000455296280000024
Wherein, cov (o (kh), o (kh) t)=Ro δ ij, cov (r (kh), r (kh) t)=Rr δ ij, wherein, cov () represents covariance computing, δ ijfor kronecker-δ function, K1 is constant, and the state value that further obtains submodel is estimated:
Figure FDA0000455296280000025
Obtain the input and output state moment state estimation value of original system according to the parameter corresponding relation of two rate remote control systems and submodel: x (KT 1)=x (Kph), x (KT 2)=x (Kqh);
Step 3: the state value doping according to submodel is passed rank parameter identification to two rate remote control systems, and expression is as follows:
Figure FDA0000455296280000028
Figure FDA0000455296280000029
Figure FDA00004552962800000210
Figure FDA00004552962800000211
Wherein, i, j represents respectively the sampling instant of input and output signal,
θ x(iph)=[A(iph),B(iph)] T
θ i(jqh)=[C(jqh),D(jqh)] T
Figure FDA00004552962800000212
X(iph+ph)=x(iph+ph),
A (iph), B (iph), C (jqh), D (jqh) represent respectively the estimated value of A (iph), B (iph), C (jqh), D (jqh);
Obtain again the parameter of next step submodel system according to the result of passing rank identification:
Figure FDA0000455296280000032
Step 4: circulation step 2 and step 3 are passed rank parameter identification process until complete all two rate remote control systems.
2. what be applicable to according to claim 1 remote control system control parameter passs rank discrimination method, it is characterized in that:
In described step 2, Ro and Rr estimate by following formula:
Figure RE-FDA0000481469800000032
Figure RE-FDA0000481469800000033
Wherein,
Figure RE-FDA0000481469800000034
l represents the data length of data r (kh) or o (kh).
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CN110209482A (en) * 2019-05-28 2019-09-06 北京国电智深控制技术有限公司 A kind of dispatching method of periodic message and device, computer readable storage medium

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