CN112859598B - Recombination type empirical transformation type iterative learning control method - Google Patents
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Abstract
The invention discloses a recombinant empirical transformation type iterative learning control method. Aiming at the characteristic that the intrinsic structural essential characteristics of a controlled system are kept unchanged during the replacement of elements or the change of parameters of the controlled system, the controlled system is improved into a recombined iterative learning control system, the controlled system is converted and recombined into primary iterative control data of a new controlled system by inheriting and properly adjusting experiences obtained by the original iterative learning control according to the specific condition of the parameter change of the controlled system, the effective inheriting and application of the iterative learning control experiences in the operation process of the new controlled system are realized by a recombination mode, the primary iterative control data of the new controlled system with extremely small initial error are formed, the iteration times for achieving the target tracking accuracy are fewer, the times and time required by the new iterative learning are effectively reduced, and the time and the loss of raw materials are saved.
Description
Technical Field
The invention belongs to the field of advanced manufacturing, and particularly relates to a recombinant empirical transformation type iterative learning control method.
Background
The iterative learning control is a method for tracking and controlling a system working in a repetitive mode, and the basic principle is that for a certain repeatedly working specific controlled system, historical operating data of the system is used for continuously iteratively correcting control output, so that the control precision is continuously improved. The iterative learning control does not depend on a mathematical model, and can effectively track the expected track of the uncertainty nonlinear dynamic system in a given time period by a simple algorithm. Currently, iterative learning control has been applied in the fields of reciprocating robots, multi-batch chemical production processes, motor control for cyclic operation, and the like. In the basic application of such iterative learning control, the preconditions for its applicability are: the controlled system parameters and the desired trajectory and their initial state remain unchanged. On the premise that the condition cannot be strictly met, the problem of practical significance is solved by expanding the application range of iterative learning control, continuously utilizing control data obtained by earlier iterative learning and avoiding repeated relearning.
The document with the application number of 201810052525.8 discloses a method and a system for designing an industrial robot based on four-axis iterative learning control, wherein a gradual change curved surface of a processed part is divided into a group of homogeneous track groups, a method based on a track axis is provided, and the empirical data of the reference bottom-layer track iterative learning control is subjected to gain transformation and offset transformation along the track axis and is used for a control initial value of the next adjacent track iterative learning. However, the scheme only relates to the problem of how to effectively utilize experience data obtained by earlier iterative learning control under the condition that the tracking track of the iterative learning control is changed or uncertain, and does not relate to the inheritance and application problems of the iterative learning control experience under the condition that the parameters of the controlled system are changed.
If the control experience obtained by iterative learning of the old controlled system is directly used as the control initial value of the iterative learning of the new controlled system, the effect is better than that of the control initial value learned from the zero initial value, but the control experience is only simply inherited, and an experience pre-adjusting link according to specific differences between the new controlled system and the old controlled system is lacked, so that the setting of the iterative control initial value has a further optimization space.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to solve the technical problem of providing a recombinant empirical transformation type iterative learning control method.
The technical scheme for solving the technical problem is to provide a recombinant empirical transformation type iterative learning control method, which is characterized by comprising the following steps of:
u b,1 (k)＝u b,0 (k)+L*e b,0 (k) (6)
in formula (6), u b,1 (k) The control experience value of a certain time k of 1 st iterative learning of the new controlled system is shown; l represents a learning gain, which is a known quantity; e.g. of the type b,0 (k)＝y d (k)-y b,0 (k) Representing the expected output value y of the newly controlled system at a certain time k d (k) Actual output value y from initial iterative learning b,0 (k) An error therebetween.
Compared with the prior art, the invention has the beneficial effects that:
1. aiming at the characteristic that the intrinsic structural essential characteristics of a controlled system are kept unchanged during the replacement of elements or the change of parameters of the controlled system, the controlled system is improved into a recombined iterative learning control system, the controlled system is converted and recombined into the primary iterative control data of a new controlled system by inheriting and properly adjusting the experience obtained by the original iterative learning control according to the specific condition of the change of the parameters of the controlled system, the effective inheriting and application of the iterative learning control experience in the operation process of the new controlled system are realized by a recombination mode, the primary iterative control data of the new controlled system with extremely small initial error are formed, the iteration frequency for achieving the target tracking accuracy is less, the frequency and time required by the new iterative learning are effectively reduced, and the time and the loss of raw materials are saved.
2. The method is not only suitable for linear systems, but also has certain reference application value for pseudo-nonlinear systems with monotonicity but not satisfying the superposition theorem in input-output relation.
3. The feasibility and the effectiveness of the method are verified through simulation tests under the condition that the inertia time of the system is changed.
Drawings
FIG. 1 is a schematic diagram of unit step response curves of a new controlled system and an old controlled system according to the present invention;
FIG. 2 is a schematic diagram of a unit impulse response curve of a new controlled system and an old controlled system according to the present invention;
fig. 3 is a schematic diagram of an iterative learning process of an old controlled system in the case of an initial value of zero experience according to embodiment 1 of the present invention;
fig. 4 is a schematic diagram of a generation-by-generation error root change process of iterative learning of a new controlled system and an old controlled system in embodiment 1 of the present invention.
Detailed Description
Specific examples of the present invention are given below. The specific examples are only intended to illustrate the invention in further detail and do not limit the scope of protection of the claims of the present application.
The invention provides a recombinant empirical transformation type iterative learning control method (a method for short), which is characterized by comprising the following steps of:
wherein, the control experience sequence u of the ith iterative learning of the old controlled system a,i Control empirical value u at each time in (1) a,i (j) J is 0,1,2.. k is generated at each moment of each sampling period of the ith iterative learning of the old controlled systemRespective actual output value y a,i (j) J ═ 0,1,2.. k; then all the actual output values y are compared a,i (j) K, the expected locus y of the old controlled system is obtained by combining j 0,1,2 d ；
u a,i The control empirical value u of the old controlled system at each moment is iteratively learned for the ith time a,i (j) J is 0,1,2.. k; y is d From the desired output value y at each moment d (j) J is 0,1,2.. k;
according to the control experience value and the deviation change process of each cycle repeated working process, the iterative learning control of the old controlled system has the following relation:
u a,i+1 (k)＝u a,i (k)+L*e a,i (k) (1)
in the formula (1), u a,i+1 (k) The control experience value of the old controlled system at a certain time k in the (i + 1) th iterative learning is represented; u. u a,i (k) The control experience value of the old controlled system at a certain moment k is shown in the ith iterative learning; i represents the iteration times, k represents the discretization time, and k is a positive integer; l represents a learning gain; e.g. of the type a,i (k)＝y d (k)-y a,i (k) Represents the expected output value y of the old controlled system at a certain time k d (k) Learning the actual output value y of a certain moment k with the ith iteration a,i (k) The error between;
preferably, in step 1, the old controlled system iteratively learns the control empirical value u at a certain time k at the ith time a,i (k) And its corresponding output response y a,i (k) Can be expressed as:
in the formula (2), z is a complex variable defined on a complex plane and is called as a z transformation operator; p is 3 times of the inertia time constant Ta of the old controlled system; the corner mark k + p represents the sampling period; y is a,i,k+p (k) Representing the actual output value generated by k at a certain moment of k + p sampling periods of the ith iterative learning of the old controlled system; y is a,i,k+p (k)z -k-p After thatThe expansion term is considered to decay towards 0 and is ignored;
preferably, in step 2, with the new controlled system and the old controlled system as objects, applying driving signals with the same strength to the new controlled system and the old controlled system respectively in a unit step open loop test manner, and obtaining unit step response curves of the new controlled system and the old controlled system respectively (as shown in fig. 1); and calculating the inertia time constants of the new controlled system and the old controlled system respectively according to the maximum slope points of the two unit step response curves, and calculating the damping characteristics of the new controlled system and the old controlled system respectively according to the difference obtained by subtracting the final value from the maximum deviation amount of the two unit step response curves and dividing the difference by the percentage of the final value. It can be seen from fig. 1 that the inertia time constant and the damping characteristic in the unit step response curves of the new controlled system and the old controlled system are changed.
Said y a From the empirical value y of the unit impulse response of the old controlled system at each time a (j) J is 0,1,2.. k; y is b From the newly controlled systemEmpirical value y of unit impulse response of time b (j) J is 0,1,2.. k;
due to the influence of element replacement or parameter change of the controlled system, the unit impulse response curve obtained by the same unit impulse excitation changes, and as can be seen from fig. 2, due to the change of the inertia time constant and the damping characteristic caused by the element change or parameter change in the controlled system, the impulse response effect obtained by the same unit impulse excitation changes correspondingly.
Preferably, step 4 is specifically: according to the energy conservation and superposition principle of a linear system, the following relationship exists:
in formula (3), y a (0) An empirical value of a unit impulse response of an old controlled system at an initial moment is represented; y is b (0) An empirical value of a unit impulse response representing the initial time of a new controlled system; u. u a,i (0) The control experience value of the ith iterative learning initial moment of the old controlled system is represented; u. u b,0 (0) Representing a control experience value of a newly controlled system at an initial iterative learning initial moment; y is d (0) The expected output value of the new controlled system and the old controlled system at the initial moment is represented;
u is calculated by the formula (3) b,0 (0) (ii) a U is to be b,0 (0) In the second row relation formula of the transformation recombination formula, u is obtained by calculation b,0 (1) (ii) a By analogy, the control empirical value u of each moment of the initial iterative learning of the new controlled system is finally obtained through the transformation and recombination formula b,0 (j) J ═ 0,1,2.. k; then u is put b,0 (j) And j is 0,1,2.. k to obtain a control experience sequence u of the initial iterative learning of the new controlled system b,0 ；
The transformation recombination formula is shown as formula (4):
in the formula (4), y d (1) The expected output value of the new controlled system and the old controlled system at the moment 1 is represented; y is d (2) Representing expected output values of the new controlled system and the old controlled system at the time 2;
preferably, in step 4, the newly controlled system initially iteratively learns the control experience sequence u b,0 Control empirical value u at each time in (1) b,0 (j) J is 0,1,2.. k, and the actual output value y is generated at each moment of each cycle of the first iterative learning of the new controlled system b,0 (j) J ═ 0,1,2.. k; then all the actual output values y are compared b,0 (j) J is 0,1,2.. k, and an expected track of a newly controlled system is obtained; said u is b,0 Control empirical value u of each moment learned by first iteration of new controlled system b,0 (j) J is 0,1,2.. k;
the newly controlled system initially and iteratively learns the control empirical value u at a certain moment k b,0 (k) And its corresponding output response y b,0 (k) Can be expressed as:
in the formula (5), q is 3 times of the inertia time constant Tb of the new controlled system; the corner mark k + p represents the sampling period; y is b,0,k+q (k) Representing the actual output value generated by k at a certain moment of k + q sampling periods of the initial iterative learning of a new controlled system; y is b,0,k+q (k)z -k-q The latter expansion term is considered to attenuate towards 0 and is ignored;
u b,1 (k)＝u b,0 (k)+L*e b,0 (k) (6)
in the formula (6), u b,1 (k) The control experience value of a certain time k of 1 st iterative learning of the new controlled system is shown; l represents a learning gain, the value of which is obtained by equation (1); e.g. of the type b,0 (k)＝y d (k)-y b,0 (k) Represents the expected output value y of a new controlled system at a certain moment k d (k) Actual output value y from initial iterative learning b,0 (k) An error therebetween.
Example 1
In this embodiment, the old controlled system a applies proportional iterative learning control without empirical inheritance adjustment to obtain iterative learning control with a control experience being a zero-experience initial value, and the transfer function expression is
The new controlled system b is a new controlled system with inertia time constant changing because the old controlled system a replaces a certain part; the transfer function is expressed as
After transformation and recombination are carried out on a control experience sequence obtained by iterative learning of an old controlled system a by adopting the method of the invention, the control experience sequence is used as primary iterative control data of a new controlled system b; the expected track expression of the old controlled system and the new controlled system is y (t) 0.006t 2 (20-t),t∈[0,20]The results of the simulation test are as follows.
In fig. 3, the dashed line represents the output trajectory of the iterative learning of the old controlled system at the zero initial value of the experience, and the solid line represents the expected trajectory. As can be seen from fig. 3, the old controlled system needs to iterate a large number of times to reach the desired trajectory under the condition of zero initial empirical value.
In fig. 4, the dotted line is the generation-by-generation error root change process of the new controlled system b, and the solid line is the generation-by-generation error root change process of the old controlled system a. It can be seen from fig. 4 that the error root and the iteration number of the new controlled system b are obviously better than those of the old controlled system a.
As can be seen from the comparison effect of FIG. 3 and FIG. 4, the initial deviation of the iterative learning control method based on the recombinant empirical transformation and the iteration number required for achieving the same control precision are both superior to those of the zero-empirical initial value iterative learning control method, and the feasibility and the effectiveness of the method are verified.
The invention is applicable to the prior art where nothing is said.
Claims (8)
1. A recombinant empirical transformation type iterative learning control method is characterized by comprising the following steps:
step 1, giving a repeatedly working old controlled system a, knowing the control experience data of iterative learning of the old controlled system a in all the years, and including the control experience sequence u of the ith iterative learning of the old controlled system a,i ；
Step 2, taking the new controlled system b and the old controlled system a as objects, and respectively obtaining unit step response curves of the new controlled system and the old controlled system; the new controlled system is a controlled system obtained by the old controlled system due to element replacement or parameter change, so the expected trajectories of the new controlled system and the old controlled system are the same, and y is used d Represents;
step 3, respectively modeling the new controlled system and the old controlled system according to the inertia time constant and the damping characteristic of the unit step response curve of the new controlled system and the old controlled system, and performing simulation analysis of unit impulse response to respectively obtain a unit impulse response curve of the old controlled system and a unit impulse response curve of the new controlled system; and respectively discretizing the unit impulse response curve of the old controlled system and the unit impulse response curve of the new controlled system to obtain an experience sequence y of the unit impulse response of the old controlled system a And experience sequence y of unit impulse response of new controlled system b ；
Step 4, the control experience sequence u of the ith iterative learning of the old controlled system in the step 1 a,i Obtaining a control experience sequence u of the initial iterative learning of a new controlled system through transformation and recombination b,0 ；
According to the energy conservation and superposition principle of a linear system, the following relationship exists:
in the formula (3), y a (0) An empirical value representing a unit impulse response of an old controlled system at an initial time; y is b (0) An empirical value of a unit impulse response representing the initial time of a new controlled system; u. u a,i (0) The control experience value represents the initial moment of the ith iterative learning of the old controlled system; u. u b,0 (0) Representing a control experience value of a newly controlled system at an initial iterative learning initial moment; y is d (0) The expected output value of the new controlled system and the old controlled system at the initial moment is represented;
u is calculated by the formula (3) b,0 (0) (ii) a U is to be b,0 (0) In the second row relation formula of the transformation recombination formula, u is obtained by calculation b,0 (1) (ii) a By analogy, the control empirical value u of each moment of the initial iterative learning of the new controlled system is finally obtained through the transformation and recombination formula b,0 (j) J ═ 0,1,2.. k; then u is put b,0 (j) K, combining j to obtain a control experience sequence u of the initial iterative learning of the new controlled system b,0 ；
The transformation recombination formula is shown as formula (4):
in the formula (4), y d (1) The expected output value of the new controlled system and the old controlled system at the moment 1 is represented; y is d (2) Representing expected output values of the new controlled system and the old controlled system at the time 2;
step 5, the control experience sequence u of the initial iterative learning of the new controlled system obtained in the step 4 b,0 And as an input initial value of the new controlled system, performing iterative learning control on the new controlled system according to an equation (6):
u b,1 (k)＝u b,0 (k)+L*e b,0 (k) (6)
in the formula (6), u b,1 (k) Represents a new controlled systemIteratively learning a control experience value of k at a certain moment 1 time; l represents a learning gain, which is a known quantity; e.g. of the type b,0 (k)＝y d (k)-y b,0 (k) Representing the expected output value y of the newly controlled system at a certain time k d (k) Actual output value y from initial iterative learning b,0 (k) An error therebetween.
2. The iterative learning control method of the recombined empirical transformation according to claim 1, wherein in step 1, the iterative learning control of the old controlled system has the following relationship:
u a,i+1 (k)＝u a,i (k)+L*e a,i (k) (1)
in the formula (1), u a,i+1 (k) The control experience value of the old controlled system at a certain time k in the (i + 1) th iterative learning is represented; u. of a,i (k) The control experience value of the old controlled system at a certain moment k is shown in the ith iterative learning; i represents the number of iterations, and k represents the discretization time; l represents a learning gain; e.g. of a cylinder a,i (k)＝y d (k)-y a,i (k) Represents the expected output value y of the old controlled system at a certain time k d (k) Learning the actual output value y of a certain time k with the ith iteration a,i (k) The error between.
3. The iterative learning control method of claim 1, wherein in step 1, the control experience sequence u of the ith iterative learning of the old controlled system a,i Control empirical value u at each time in (1) a,i (j) J is 0,1,2.. k, and the actual output value y is generated at each moment of each sampling period of the ith iterative learning of the old controlled system a,i (j) J ═ 0,1,2.. k; then all the actual output values y are compared a,i (j) K, the expected locus y of the old controlled system is obtained by combining j 0,1,2 d 。
4. The iterative learning control method of claim 3, wherein in step 1, the old controlled system iteratively learns the control of a certain time k at the ith iterationEmpirical value u a,i (k) And its corresponding output response y a,i (k) The expression is as follows:
in the formula (2), z is a complex variable defined on a complex plane and is called as a z transformation operator; p is 3 times of the inertia time constant Ta of the old controlled system; the corner mark k + p represents the sampling period; y is a,i,k+p (k) Representing an actual output value generated at a certain moment k of k + p sampling periods of the ith iterative learning of the old controlled system; y is a,i,k+p (k)z -k-p The latter expansion term is considered to decay towards 0 and is ignored.
5. The iterative learning control method of claim 1, wherein in step 2, the new controlled system and the old controlled system are used as objects, and the unit step open loop test is performed to apply driving signals with the same strength to the new controlled system and the old controlled system respectively, so as to obtain unit step response curves of the new controlled system and the old controlled system respectively.
6. The iterative learning control method of claim 1, wherein in step 2, the inertia time constants of the new controlled system and the old controlled system are calculated from the maximum slope points of the two unit step response curves, and the damping characteristics of the new controlled system and the old controlled system are calculated from the difference between the maximum deviation of the two unit step response curves minus the final value and the percentage of the final value.
7. The iterative learning control method of claim 1, wherein in step 4, the newly controlled system initially iteratively learns the control experience sequence u b,0 Control empirical value u at each time in (1) b,0 (j) J is 0,1,2.. k respectively in each period of initial iterative learning of the new controlled systemGenerating respective actual output values y at respective times b,0 (j) J ═ 0,1,2.. k; then all the actual output values y are compared b,0 (j) And j is 0,1,2.. k, and the expected track of the newly controlled system is obtained through combination.
8. The iterative learning control method of claim 7, wherein in step 4, the newly controlled system initially iteratively learns the control empirical value u at a certain time k b,0 (k) And its corresponding output response y b,0 (k) The expression is as follows:
in the formula (5), q is 3 times of the inertia time constant Tb of the new controlled system; the corner mark k + p represents the sampling period; y is b,0,k+q (k) Representing the actual output value generated by k at a certain moment of k + q sampling periods of the initial iterative learning of a new controlled system; y is b,0,k+q (k)z -k-q The latter expansion term is considered to attenuate towards 0 and is ignored.
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